Category Archives: Book Reviews

Owen Gingerich (1930–2023)

When I first started delving into the history of astronomy there was a pantheon of the great historians, who ruled over the discipline far above us mere mortals–for example, I. Bernhard Cohen, Edward Rosen, Robert S. Westman, Richard S. Westfall, and others.

One of those giants, Owen Gingerich, died 28 May at the grand old age of 93. Gingerich was for many years a professor for both astronomy and the history of science at Harvard University.

His main area of research was the history of astronomy of the Early Modern Period, especially, but not exclusively, Copernicus and Kepler. Anybody, who reads this blog, will know that this in one of my key areas of interest, so over the years I have read many of Gingerich’s papers and books, several of the latter adorning my bookshelves. I learnt a great deal reading Gingerich. Just to give one example, I first learnt about the itinerant German mathematician, Paul Wittich (c. 1546–1586), who played a significant role in the evolution of the Tychonic geo-heliocentric model of the cosmos, as well as the distribution of prosthaphaeresis, a trigonometrical forerunner of logarithms, through a joint paper by Gingerich & Westman.[1]

Gingerich first ran across Wittich’s work on geo-heliocentric models in the marginalia of his copy of Copernicus’ De revolutionibus.

Paul Wittich’s geoheliocentric planetary model – as annotated in his copy of Copernicus’s De revolutionibus in February 1578 Source: Wikipedia Commons

Having been inspired by the marginalia in Erasmus Reinhold’s personal copy of De revolutionibus, Gingerich began a thirty-year-long survey of all the extant copies of the 1st and 2nd editions of De revolutionibus that he could find, recording provenance, marginalia, censorship etc. 

The results of this odyssey were published in his An Annotated Census of Copernicus’ De Revolutionibus (Nuremberg 1543 and Basel 1566) (Brill, 2002).

It is a monumental work of scholarship and an invaluable asset for all scholars of the history of Early Modern astronomy. It, of course, cost a fortune and was way outside of my book buying budget. However, one Sunday I walked past one of Erlangen’s university bookshops and espied a copy of the Census in their shop window on offer at a ridiculously low price. I returned to the shop when it was open and inquired why it was so cheap. The book seller explained that it had been ordered by a professor on approval and had been damaged and could not be returned. I didn’t hesitate and am as a result a proud owner of this unique volume. I have examined it many times over the years and still haven’t discovered the supposed damage. He also produced a much shorter, but equally useful, survey of the surviving copies of Peter Apian’s Astronomicum Caesareum.

Gingerich also wrote a highly entertaining collection of essays, documenting his adventures whilst researching his Copernicus CensusThe Book Nobody ReadChasing the Revolutions of Nicolaus Copernicus (Walker, 2004).

I do not have heroes, but Owen Gingerich was very much one of my go to sources for accurate and in-depth scholarship on the history of astronomy. Imagine my surprise, or better said shock, when he turned up to comment on my humble blog. He didn’t use the blog’s comments column but sent me an email. When I opened up my email account and saw that first email, I nearly fell off my chair. I opened it with trepidation, it was a very warm and friendly email pointing out an error in my most recent blog post. Although they remained few and far between, it was not the only email that I received from him and not always negative. He particularly praised my post on Johannes Petreius (c. 1497–1550), the publisher of De revolutionibus, saying that he had learned something new from it.

Yesterday the history of astronomy community lost one of its greats and the tributes are pouring in all over the Internet. Gingerich was, with justification, highly respected and, as everyone is reporting a generous and warm gentleman scholar. 

[1] Gingerich & Westman, The Wittich Connection, Transactions of the American Philosophical Society, Vol 78, Part 7, 1988


Filed under Book History, Book Reviews, History of Astronomy

Renaissance garbage ­– V

This is the fifth in a series of discussion of selected parts of Paul Strathern’s The Other RenaissanceFrom Copernicus to Shakespeare, (Atlantic Books, 2023). For more general details on both the author and his book see the first post in this series.

Today, I’m looking at Strathern’s chapter on Vesalius. It goes without saying that Strathern evokes the mythical religious taboo on dissection of the human body. 

The dissection of human bodies had been a religious taboo in the western world since well before the birth of Christ. This taboo extended through all Abrahamic religions – i.e. Judaism, Christianity and Islam – as well as most of the heterodox sects and cults which pervaded the Mediterranean region and the rest of Europe. 

Whilst there was a prohibition on the dissection of human cadavers from about 150 BCE in Ancient Rome that affected the work of Galen (129–c. 216 CE), who as Strathern reports carried out most of his anatomical work on animals, which of course led to anatomical errors; there was no taboo in the European Middle Ages or the Renaissance, when Leonardo, yes, he gets discussed too, and Vesalius carried out their anatomical studies. Human dissection had already begun in the fourteenth century with the work of Mondino de Luzzi (C. 1270–1326) and by 1400 regular anatomical dissections were an established part of the curriculum in most medical schools. Strathern then delivers up another of his errors on authority:

Despite such mistakes, Galen’s ‘authority’ on medical matters reigned supreme throughout the medieval era, alongside that of Aristotle. Not until the Renaissance would his errors come to light. 

Galen was just one of several medical authors whose texts were used on the medieval universities and despite challenges continued to be used throughout the Renaissance. In fact, there was during the Renaissance a strong neo-Galenic movement that challenged Vesalius. 

It’s almost unavoidable that Strathern, like everybody else, includes Leonardo, he writes:

A century prior to Vesalius, Leonardo da Vinci’s obsessive curiosity led him to carry out dissections of human cadavers, which he recorded in his notebooks. By now the prohibition of such activities had become somewhat more relaxed, though they remained frowned upon. 

As already noted, there was no prohibitions and Leonardo, like all the apprentices of Andrea del Verrochio (1435–1488), who insisted that his apprentices gain a thorough grounding in anatomy, would have attended dissections as an apprentice.

Leonardo carried out systematics anatomical investigations together with Marcantonio della Torre (1481–1511), lecturer on anatomy at the universities of Pavia and Padua, between 1510 and 1511. Vesalius’ principle anatomical work, his De fabrica, of which more later, in 1543. According to my arithmetic that is a span of thirty-one years and not a century. Maybe Strathern uses a different number system?

We get no account of Leonardo’s systematic work with Andrea del Verrochio this would spoil the image that Strathern creates of the chaotic nature of Leonardo’s work and notes. We do, however get a lengthy anecdote about his dissection of a man who claimed to be one hundred years old. Then Strathern drops the following gem:

But why this diversion? What possible relevance does such work by Leonardo have to the northern Renaissance? In fact, none. And that is the point. By recounting these pioneering anatomical experiments – unique in their breadth, depth and explication – we gain an insight into the immense difficulties involved in human dissection during this period. We can also witness the birth of a new, forbidden science coming into being. Or apparently so. For this infant body of learning would not survive its premature birth – stillborn before it could draw breath – largely through the procrastination of Leonardo himself. 

As already stated, we do not have “the birth of a new, forbidden science”, dissection of human cadavers was routine by the time that Leonardo was active. Also, if he poses the question, “What possible relevance does such work by Leonardo have to the northern Renaissance?” then he must also pose it for Vesalius, who although he came from the Netherlands did all his anatomical work in Padua and was very much an integral part of the Italian Renaissance. 

We then get a brief description of the fate of Leonardo’s papers and drawings which closes with the repeat of the arithmetical error:

Working a century later, Vesalius would remain unaware of Leonardo’s pioneering work, which remained lost to history. 

Leonardo lived from 1452 to 1519, Vesalius was born in 1514 and carried out his anatomical work in Padua beginning in 1537, publishing the De fabrica in 1543. No matter how I try I can’t make a century out of these dates! The century is merely a lead into a piece of pseudo historical pathos:

Such a lacuna leads one to speculate on how much more, of genuine worth, was lost during this period. Such discovery and progress had little place in the medieval era. The Renaissance would have to find its own way of accommodating and preserving the innovations it produced. All we know are the successes which eluded loss or destruction: Copernicus’s revolutionary work published by his friends and gifted to him on his deathbed; Paracelsus’s haphazard discoveries, and superstitious lapses, disseminated by means of Gutenberg’s invention, which was itself wrested from the hands of its creator. In this aspect, more than most, no history can be any more than an incomplete account. Fortunately for history, Vesalius would do his utmost to gainsay this fact, his work being both painstaking and thorough from the outset. And his motives throughout his long and arduous task would be single-mindedly focused on public recognition and public reward. 

In the history of science many new ideas, theories and discoveries have been lost, forgotten, or suffered a delayed reception. The reasons are numerous but, and it’s a very big but, they were not somehow actively repressed during the Middle Ages as Strathern would have us believe.  I have already pointed out in my review of the chapter on Copernicus, his work was not published by his friends in an act of deception as Strathern claims, but he sent his book to Petreius in Nürnberg to be published himself. Paracelsus’ work was mostly posthumously printed and published by his disciples, a case of late reception and in Gutenberg’s case, if you build up your business with large sums of borrowed cash and then get into a dispute with your financier, then you tend to lose your business. However, the invention of printing with moveable type was in no way effected by Gutenberg’s financial problems. Strathern’s examples don’t illustrate his argument at all. 

We now arrive at Vesalius and the usual brief biography. Strathern tries to paint his father as somehow inferior and suffering from an inferiority complex. Claiming that it was his mother who raised him and set him on his way entering him, like Mercator and Gemma Frisius before him, in a school of the Brotherhood of the Common life, in his case in Brussels. It was actually his father who entered him in the school. Like Mercator and Gemma Frisius, Vesalius now entered the University of Leuven, and Strathern displays his total ignorance of the medieval university system:

Surprisingly, Vesalius did not register at the school of medicine, but instead chose to study the arts and humanities, which included learning Latin and Greek, at which he thrived. (The books in his grandfather’s library would mostly have been written in Latin, and Vesalius almost certainly had extended his schoolboy Latin by reading these works.) After young Vesalius graduated with a good arts degree in 1532, he was accepted to study at the prestigious University of Paris, where he entered the school of medicine. Only now did he begin the formal study of this subject. 

On the medieval university the undergraduate course of study, in the lower faculty, was nominally the seven liberal arts. First when a student had graduated from the lower faculty, was he permitted to matriculate in one of the higher faculties to study, theology, law, or medicine. So, it was not a surprise that “Vesalius did not register at the school of medicine.”

We get some more misinformation from Strathern:

Despite its reputation, the University of Paris remained firmly committed to the teachings of Aristotle, and its school of medicine was still dominated by the 1,300-year-old ideas of Galen. Lectures in practical anatomy were a comparatively rare novelty, having only recently received limited Church dispensation [my emphasis].

Lectures in practical anatomy were a standard part of the medical curriculum in Paris, there being no Church restriction on them as I’ve already explained above. Strathern contradicts himself by explaining that anatomical lectures, with public dissections, were a standard part of the curriculum, although he correctly observes that the student were only allowed to observe but not to dissect themselves. He notes correctly that the one professor of anatomy, Jacobus Sylvius (1478–1555) was a strict adherent of Galen but that another, Johann Winter von Andernach (1505–1574) was more open minded and even allowed students to participate in dissections. Winter became Vesalius’ mentor and even employed Vesalius as an assistant in the preparation of his four volume Institutiones anatomicae (Paris, 1536) for the press, praising him in the preface; it would become a standard work, of which Vesalius published a second updated edition in 1539. It should, however, be pointed out that Winter was one of those who triggered to renaissance in Galenic anatomy when he produced and published a Latin translation of Galen’s newly discovered and most important De Anatomicis Administrationibus (On Anatomical Procedures) 9 vols. Paris in 1531, which Strathern doesn’t mention at all.

Strathern delivers up some waffle about what happened next when Vesalius was forced by war to leave Paris and return to the Netherlands, where he re-entered the University of Leuven to complete his medicine degree. Here he wrote his doctoral thesis and Strathern once again displays his ignorance:

At the same time, Vesalius began composing his graduation thesis. Interestingly, he chose for his subject the tenth-century Persian physician and alchemist known in the west as Rhazes. (In the Arabic world his full name was Abu Bakr Muhammad ibn Zakariya al-Razi.) The important fact about Rhazes was that he not only based his science upon the experiments he conducted himself, but he also wrote these out in detail, step by step. This meant that they could be precisely repeated by other scientists. Here, reliance upon the word of a universal and unchanging ‘authority’ was skilfully circumvented. 

This important lesson would soon begin to permeate the world of science in both the northern and the Italian Renaissance. The days when scientists – from mathematicians to alchemists – kept their discoveries secret in order to gain advantage over their rivals were coming to an end. Science was entering the public domain. Experimenters would publish their work in books, and their results could be verified (or shown to be faulty) by their peers. 

Vesalius’ doctoral thesis was actually Paraphrasis in nonum librum Rhazae medici Arabis clarissimi ad regem Almansorem, de affectuum singularum corporis partium curatione, a commentary on the ninth book of Rhazes.

Strathern tries to make it seem as if Vesalius’ thesis was in somehow exceptional in its choice of topic and in some way ground-breaking, whereas it was perfectly normal.  The book of Rhazes referred to here is his The Virtuous Life (al-Hawi), a nine-volume posthumous collection of his medical notebooks, which was translated into Latin in the late thirteenth century and was a standard textbook in the medical faculties of the European medieval universities, so there was nothing exception about Vesalius writing his doctoral thesis on part of it. Strathern continues:

Vesalius’s reputation as a talent of great promise seems to have spread far and wide, almost certainly aided by Andernach’s description of him in Institutiones Anatomicae. Immediately upon his graduation from Leuven, Vesalius received an invitation to become a professor of anatomy and surgery at the University of Padua, one of the finest centres of scientific research in Italy. 

This proving that Vesalius was very much part of the Italian Renaissance and not the Northern Renaissance! Now Strathern starts off on a path where he will begin to mix fact with fiction:

More importantly for Vesalius, Padua was just twenty miles from Venice, the commercial and cultural capital of the region, and it was here that he met the German-born artist Jan von Calcar, who had served his apprenticeship under Titian. Calcar’s particular talents were his ability to imitate the works of others and his supreme skill with woodcuts. 

In 1538 Vesalius collaborated with Calcar on the production of his first anatomical text, Tabulae Anatomicae Sex (Six Anatomical Charts.) Three of these charts were produced by Calcar, taken from a full-scale skeleton of the human body which Vesalius had put together. The other three made use of charts which Vesalius himself had drawn for lectures to his students. 

Although the story is well document, Strathern can’t get the facts right. The Tabulae Anatomicae Sex were originally six large, woodcut, wall posters that Vesalius had created for his lecture theatre. He discovered that students were copying them, so he decided to make a professional printed edition of them. Of the printed edition the first three were entirely his own work but for the second set of three he employed Jan van Calcar. Strathern notes correctly that here Vesalius corrects some of Galen’s anatomical errors but repeats some others.

Tabulae Anatomicae Sex the first three illustrations are by Vesalius the three skeletons by Calcar Source: Welcome Collection

Strathern now delivers up a classic historical myth in a footnote:

From now on, the more Vesalius continued with his investigations of the human body, the bolder he became. By this stage he had reached an agreement with the Paduan authorities, who allowed him to dissect the regular supply of cadavers of prisoners executed on the gallows. Vesalius’s retelling of how he carried out his researches paints a vivid, if lurid, picture. He described how he ‘would keep in my bedroom for several weeks bodies from graves or given me after public executions’. How did his neighbours put up with the appalling stench? To say nothing of their suspicions that he might be indulging in necromancy or demonology? The answer is that they may well have been unable to distinguish the stench from the general pervasive malodorousness.* 

* During this era the waterways of Padua, like the canals of Venice and its nearby lagoon, emitted powerful smells, especially in the summer. This was hardly helped by the customary lack of bathing and personal hygiene which pervaded all classes throughout Europe. [my emphasis] Indeed, such habits accounted for the constant use of sweet- smelling nosegays in genteel society. These consisted of flowers or herbs intended to mask the sense of smell. It is said that in Venice a certain type of nosegay evolved which went further, using citrus oil or extracts of resin intended to numb the olfactory sense altogether, rather than simply distracting it. 

The sentence that I have emphasised is, unfortunately, a widespread myth and total piffle! Europeans in the Renaissance bathed regularly and took great care of their personal hygiene. Nobody claiming to be an academic historian, as Strathern does, should be repeating this garbage in 2023! On the subject of demonology Strathern drops the following gem:

As for the suspicion that Vesalius might have been involved in occult practices – presumably he remained under the protection and good name of the university. This was still an era when a large majority of the population believed in demonology, witchcraft and the like – general superstition was rife. Here was one area where the power of the Church and its insistence on orthodoxy was beneficial: in its suppression of heretical practices and beliefs, it undoubtedly reduced the credulity [my emphasis] which led to the outbreaks of mass hysteria that were prevalent during this period. 

It was the Church with its insistence on the real existence of the Devil, demons, black magic, witches, and all the rest that was the main driving force fuelling the credulity.

It is now that Strathern begins mixing fact with fiction or maybe fantasy.

Vesalius now began assembling, together with Calcar, the large, precisely delineated drawings that would become the body of the master- piece which assured his lasting place in medical history. Apart from Leonardo’s, previous books containing anatomical illustrations had tended to be schematic, or cartoon-like, mostly drawn by their medical author – whose talent would often be amateurish at best. By contrast, Vesalius’s De Humani Corporis Fabrica (The Apparatus of the Human Body) would not only be comprehensive and encyclopedic in its knowledge, but its precise illustrations would also be works of art as much as science. Calcar’s large exact drawings, made under Vesalius’s painstaking direction, would in their own distinctly different style be a match for the as-yet-unseen drawings of Leonardo.* Meanwhile Vesalius’s text would set medicine free from the stranglehold of Galen. 

Vesalius Fabrica fronticepiece Source: Wikimedia Commons

That Calcar was the artist, who created the illustration in De fabrica is an unsubstantiated claim made by Giorgio Vasari (1511–1574) in his Le Vite de’ più eccellenti pittori, scultori, ed architettori (Lives of the Most Excellent Painters, Sculptors, and Architects), 1st edition 1550, 2nd expanded edition 1558, a book not exactly renowned for its historical accuracy. There is no mention in the De fabrica, who the artist actually was. In a footnote in her The Scientific Renaissance 1450–1630 (ppb. Dover, 1994) Marie Boas Hall writes about the illustrations:

These are attributed to Jan Stephen van Calcar (1499–c. 1550) by the sixteenth-century art historian, Vasari. Modern students have doubted this, because the figures are as superior to those of the Tabulae Sex as the text of the Fabrica is to that of the earlier work–though it is possible that the artist had learned as rapidly as the author. In place of Jan Stephen van Calcar, the only candidate is an unknown, also a member of Titian’s studio. It seems difficult to believe that so spirited a draughtsman as the artist who drew the pictures for the Fabrica should be otherwise unknown; though it is odd that Vesalius, who had given Jan Stephen credit for his work on the Tabulae Sex, did not mention the name of the artist of the Fabrica.

It has also been speculated that is unlikely that a single artist created all 273 illustrations in such a short period of time. So, Jan van Calcar as the author of the medical illustrations in De fabrica is anything but an established fact but this doesn’t stop Strathern writing the following in a footnote to the paragraph quoted above: 

* Such artistry did not come cheap. Indeed, Vesalius was unable to pay Calcar, and in lieu of a fee he signed over to the artist any future profits the Fabrica would make. 

Either Strathern is making things up or he is quoting a source, which he doesn’t name, that is making things up without checking on the accuracy of the claim made. It doesn’t stop here. Later in his lengthy description of the book itself he writes:

Alas, Vesalius’s perfectionism would result in an increasing number of quarrels with Calcar. Breaks in their collaboration now followed, and Vesalius began drawing a number of the anatomical illustrations in the Fabrica himself. 

A couple of paragraphs further on:

By now, it appears, Calcar had quit the project altogether. We must imagine him storming off in some indignation at Vesalius’s tenacious insistence upon the minutest detail. (This was woodcut, remember, not drawing; erasure was no simple matter with a gouged wooden surface.) 

Here also Strathern appears to not know the difference between the artist and the woodblock cutter. Calcar or whoever was the artist, would draw the images onto the surface of the woodblock, but the actual cutting would be done by a professional woodblock cutter and not the artist. 

I’m not going to do a blow-by-blow analysis of Strathern’s long account of De fabrica, as this review is already over long, but just mention a couple of salient points. To start with Strathern makes no mention of the fact that just as Copernicus modelled De revolutionibus on the Epytoma…in Almagestum Ptolomei of Peuerbach and Regiomontanus, so Vesalius modelled his De fabrica on Galen’s De Anatomicis Administrationibus (On Anatomical Procedures), which as I mentioned above was first translated into Latin and published by his mentor Johann Winter von Andernach.

At one point Strathern tells us, “As the work continues, the illustrations become less precise and their interpretation less exact.” The final chapter of De fabrica, Book VII, deals with the brain and Strathern writes, apparently contradicting himself, “Ensuing books of the Fabrica would prove similarly perceptive – especially Vesalius’s investigations of the human brain.” Do these images appear imprecise to you? 

Fabrica Book VII Source: Wikimedia Commons
Fabrica Book VII Source: Wikimedia Commons

Strathern also writes, And the illustration of the pregnant uterus containing a foetus is undeniably medieval in its crudity…” Vesalius has no illustration of the pregnant uterus containing a foetus;maybe he was confusing it with the illustration of the placenta with its attached foetus?

Fabric Book VII Source: Wikimedia Commons

Having completed his tour of De fabrica, Strathern now jumps the shark!

When he had completed the manuscript of Fabrica, he sent the text and illustrations north to Basel in Switzerland. This was the home of Johannes Oporinus, who sixteen years previously had worked as Paracelsus’s long-suffering assistant. Oporinus had now succeeded Paracelsus as a rather more orthodox professor of medicine in Basel. He also happened to come from a family renowned for their printing and engraving skills, and combined his medical knowledge with an expert understanding of the entire printing process. This was the only man in Europe whom Vesalius could trust with the production of his masterwork. 

Johannes Oporinus (1507–1568) had very little to do with Paracelsus, he was merely for a brief period in 1527 his famulus.  The son of a painter he studied law and Hebrew at Basel University, whilst working as a proofer in the print workshop of Johann Froben (c. 1460–1527). He also worked as a schoolteacher for Latin. From 1538 to 1542, he was professor for Greek at the University of Basel, resigning to devote himself fulltime to his own print workshop. 

Portrait of Johannes Oporinus by Hans Bock Source: Wikimedia Commons

Strathern closes his chapter on Vesalius with a long-winded account of further biography as Imperial physician to Charles V and later Philip II. Strathern of course cannot resist including the unsubstantiated anecdote that in Spain Vesalius started to carry out an autopsy on a corpse only to discover that the man wasn’t actually dead. There are numerous cases of this happening throughout history, and it even still occasionally occurs today, but whether it actually happened to Vesalius is, as I said, unsubstantiated.

In his chapter on Vesalius, as usual Strathern delivers up a collection of inaccuracies, myths, and in the case of the relationship between Vesalius and Calcar some pure fantasy. Once more I am forced to ask how did this book ever get published?

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Filed under Book Reviews, History of medicine, Renaissance Science

Counting the people

There is a widespread misconception amongst people, who are not particularly good at mathematics that mathematicians can do mathematics, by which I mean that a mathematicians can do the whole range of subdisciplines that are collected together under the term mathematics. Nothing could be further from the truth. It is claimed that there is a fundamental divide between mathematicians who think in diagrams, i.e., at the entry level geometry, and those who think in symbols, i.e., algebra and analysis. Not that I’m a mathematician but I certainly think in symbols, not diagrams. At a higher level, most mathematicians have a special discipline where they are at home and excel and other disciplines that that they have difficulties even comprehending. When I studied mathematics at university the introductory courses were allotted in rotation to the professors. My introductory analysis lectures were held by a really sweet guy, who was a world-renowned finite group theory specialist, where world renowned means that the fifty people in the world in his field all knew him. One day he came into the lecture hall and said, “today we should start with step functions, but I’ve never understood them, so we’ll do something else instead.” 

Although I studied mathematics at university up to about BSc level, worked in a research project into mathematical logic for a number of years, and have tutored school leaving/university entrance level (A-level, Abitur, Baccalauréat etc.) mathematics for the last twenty years, I do not consider myself a mathematician. Having said that, I definitely have my strengths and weaknesses in different mathematical disciplines. I could always do basic calculus without even think about it, in fact it was my love of calculus that led me into the history of mathematics, when I discovered that Newton and Leibniz had both invented/discovered (choose your preferred term) calculus independently of each other. I later discovered that this wasn’t true but that’s another story. An entry level discipline which I could never get my head around was probability theory and statistics and I used to groan inwardly when I had to teach them to one of my private pupils. 

When I studied mathematics at school before the second ice age, I did A-level maths, probability theory and statistics were not part of the curriculum. However, teaching Abitur in Germany over the last four years probability theory and statistics were very much part of the curriculum. Today, there is a widespread and very dynamic discussion in many lands about changing, extending, and improving the mathematics courses taught in schools at all levels, in order to combat a perceived mathematical illiteracy. See, for example, the Tory government’s call for maths to eighteen for school kids in the UK. One prominent argument in these discussions is for the reduction or removal of much of the tradition diet of algebra, geometry, and calculus and replacing it with a much-expanded emphasis on probability and statistics because these are the areas of mathematics that people need to understand and even use in everyday life. 

It is in fact true that we stumble across probability theory and statistics on a daily basis in the media, on the news, in advertising etc. often misused and mostly misunderstood by the people reading it. Probability turns up in the weather forecast, there’s a X% chance of rain, in sport betting, which has become a vast industry, in other forms of gambling, but also in areas of science and medicine. What is the probability of blah, blah blah… Here the quoted probabilities are derived from statistical analysis. Today, it is perfectly normal for all aspects of human existence to be analysed statistically. From trivial things like what percentage of the population is left-handed, to serious topics such as what is the probability of someone developing a particular type of cancer. We have statical analyses of opinion polls, election results, school exam results and …

We are so inundated with statistical information, oft presented as a probability, that we simple accept it without really thinking about it. However, where do these two areas of mathematics come from, when were they developed and why? Although there are earlier simple examples of the calculation of probabilities, both probability theory and statistics first emerged in the Early Modern Period. Not surprisingly, probability theory first emerged in the calculation of odds in gambling. The first major work on probability theory was written by one of my favourite Renaissance polymaths, Gerolamo Cardano (1501–1576), who was a passionate, and at time professional, gambler. His book, Liber de ludo aleae (Book on Games of Chance), written in the 1560s but first published in 1663, also includes advice on how to cheat. In their correspondence in 1654, Pierre Fermat (1607–1655) and Blaise Pascal (1623–1662) discussed various aspects of probability theory after being asked how the pot should be divided in an interrupted game. Christiaan Huygens (1629­–1695) came across this correspondence in Paris and wrote the most coherent and at that time, most advanced book on probability theory his De Ratiociniis in Ludo Aleae (On reasoning in games of chance). Originally written in Dutch, it was translated into Latin and published by Frans van Schooten Jr. in 1657. The mathematics of probability was firmly established in the early eighteenth century by Jacob Bernoulli (1655–1705) with his posthumously published Ars Conjectandi (The Art of Conjecturing) in 1713, which covers combinatorics and probability, and Abraham De Moivre (1667–1754) with his The doctrine of chances: or, a method for calculating the probabilities of events in play in 1718 with an expanded second edition in 1738, and a further expanded edition published posthumously in 1756. 

Statistics, however, developed from the start through a desire to count people, a development that had a long and complex prehistory before it began to become formalised on a very simple level in the second half of the seventeenth century. That formalisation took place in the work of John Graunt (1620–1674), Edmond Halley (1656–1741), John Arbuthnot (1667–1735), Gregory King (1648–1712), Charles Davenant (1656–1714), and William Petty (1623–1687), who gave the counting of people the early name of Political Arithmetick

Today, we use the term demography derived from the Ancient Greek demos meaning people, society and graphía meaning writing, drawing, description, and meaning the statistical study of populations. The American historian Ted McCormick, who teaches at Univesité Concordia in Montreal earlier wrote William Petty and the Ambitions of Political Arithmetic (OUP, 2009), using the manuscripts of Sir William Petty (1623-1687) to show how a mixture of alchemical and natural-philosophical ideas were brought bear governing colonial populations in Ireland and the Atlantic, as well as confessional and labouring populations in Britain (taken from his university webpage), which I haven’t read but I’ve now added to the infinite reading list. He has now followed up with Human EmpireMobility and Demographic Thought in the British Atlantic World1500–1800,[1] which details the gradual development of demography in Britain, Ireland and the American Colonies in the Early Modern Period.

Before I write more about McCormick’s book in any detail, a couple of important notes about it. Although this book relates the historical developments over a couple of centuries that led to the first low level uses of statistics by the scholars I named above, it is in no way whatsoever a history of mathematics text. In fact, actual numbers are strikingly absent from McCormick’s narrative. Rather it examines the social, political, environmental, cultural, philosophical, and economic circumstances that led authorities and individual to consider it necessary to enumerate elements of the population. Secondly, having said this, it should be fairly obvious from my general description that this is also in no way a popular book, but rather a deeply and intensively researched academic book. 

The word demography was first coined in the nineteenth century, but societies have been indulging in demographic thought at least since the emergence of the earliest civilisations. McCormick’s book might well be regarded as an extended case study into the structure and content of such thought in Britain and its colonies over four centuries. McCormick himself illustrates the ancient origins of the discipline, in his introduction, with references to the Bible. He also touched briefly on Aristotle’s thoughts on the topic, as these were of course relevant to those engaged in debates in the Early Modern and Modern periods. He writes the following:

Aristotle thus presented population not just as a measurable number of inhabitants but also, more saliently, as the living material of the city-state. Its size would be constrained by the territory that it occupied. It should be limited, too, by the counterpoised imperatives of magnitude and order in the context of polity conceived as an organic unit – a body politic – with a constitution. More significant than absolute size was the relative proportions of the body’s parts: The balance between citizens, slaves and foreigners, [my emphasis]and between soldiers, husbandmen and artisans (page, 29). 

Reading these lines and in particular the clause I have emphasised I was instantly reminded of current political and cultural debates that are currently raging in many countries about exactly that balance, (ignoring the slaves of course) or as many see the lack of what they see as the correct balance–too many foreigners, migrants, asylum seekers… take your pick. This was the first time that such parallels between the historical debates that McCormick outlines in great detail and the actual political debates of our times, but it was by no means the last time. Again and again, I found myself thinking this is all too familiar. My feelings were confirmed when in the closing pages of his book McCormick remarked:

To put it another way: what might the early modern history of demographic governance tell us about the persistence or reemergence of concerns about the mobility, mixture and mutability of populations in the nineteenth, twentieth and twenty-first centuries) Instances of such concerns are not only numerous but also fundamental to received interpretations of modern history (page 249)

The main text of the book covers four phases or periods of debate about perceived demographic topics. The first concerning the fifteenth century reminded me of my days as a field archaeologist. I spent several seasons, both Easter and summer, working on the major excavation of a deserted medieval village, or DMV, in the north of England. DMVs, shrunken medieval villages, SMVs and expanded medieval villages, otherwise known as towns, are the result of a major shift in population distribution during the High Middle Ages largely brought about by the enclosures. That is turning agricultural land, which peasants farmed to make a subsistence living, into pasture for sheep grazing, thereby forcing the ploughmen to abandon their villages and try to seek employment elsewhere. 

The socio-political debate that McCormick covers, about this depopulation, concerns the reformers, who wished to restore the honest ploughman to his rightful place in society. At this time the talk, however, is not of populations, but of the much more imprecise multitudes. In the second section of the book, we still have to do with multitudes but here, in the Elizabethan era, it is not a debate about a positive part of the body politic, the humble ploughman, but concerns about negative sections of that body, vagrants and the poor. Once again, the main participants in the public debate are reformers offering and discussing potential solutions what they see as the proliferation of undesirable elements in society. 

This second phase moves out of England into Ireland where the English had problems with various aspects of various parts of the island’s population.

In these sections and also in the ones to follow, McCormick outlines the perceived problems with selected parts of the population, the multitudes, and then presents the solutions proposed by the various reformers. He lets the participants in the various debates present their polemic themselves, in lengthy direct quotes all delivered up in the original English of the period, with its own vocabulary, orthography, and grammar. I must admit that I found it difficult reading some of these passages that appeared almost to be in a foreign language and not the English with which I grew up. However, it pays to persevere because it gives a much clearer picture of what the participants were aiming for than a simple modern English paraphrase. 

In the third section McCormick brings the political philosophers into play and the discussions on over population. Here we see the emergence of colonialism as a potential solution, as to what to do with surplus multitudes. Already practiced with little success in Ireland, we see the beginnings of the establishment of colonies in North America. The seventeenth century sees the move in the discussion from the multitudes of the earlier reformers to the perception of population and the slow move towards encapsulation through mathematics in the form of statistics driven by the writings of such as Francis Bacon and the Hartlib Circle, a precursor to the Royal Society. The latter offering up various projects for empire, colonialism, and population. 

Enter William Petty. Petty, an associate of the Hartlib Circle and a founding member of the Royal Society, no longer simply delivered polemics on population and population reform but in his survey of Ireland, on behalf of Cromwell, to organise the distribution of land to Cromwell’s soldiers, as payment for their services and also to dilute the troublesome Irish population, Petty was instrumental in putting a plan into action. McCormick covers Petty’s survey and its background in great detail. Out of his work in Ireland he developed his economic theories, marking him as a pioneer in economic science, and also his Political Arithmetick. It’s worth quoting McCormick here on Petty’s innovation:

“Political arithmetic” was coined sometime around 1670. It has appeared ever since as the invention of a new, scientific and, above all, quantitative age. Its inventor, Petty, has often seemed precocious in his focus on “number, weight and measure,” his imaginative exploitation of demographic and economic figures running well ahead of the empirical data at his disposal over a century before the census. While John Graunt’s “shop arithmetique” revealed a world of relationships hidden in the rows and columns of London’s weekly bills of mortality and in the patchy parish registers of baptisms, marriages and burials, Petty promised nothing less than a new “Instrument of Government” for the Stuart kingdoms and the growing colonial empire, predicted on the collection and analysis of vast amounts of information. Most of this was numerical. 

This introduction is followed by an in-depth analysis of what exactly Petty’s innovative creation was, what it meant and how it influenced future developments. 

The final section of McCormick’s main narrative follows how the rhetoric about population and demography evolved throughout the eighteenth century both in Britain and in its colonies in America. In Britain the reformist mode of thought is still dominant. In America the problem of increasing the colonial population to take over the land is predominant with Benjamin Franklin taking a lead in the debate. On the one side his acknowledgement that the land was occupied by Indians when the settlers first arrived but, on the other, that it would only be settled when the colonial population had grown enough shows a level of casual racism that I found deeply disturbing. There is also an extreme and dismissive level of racism shown by Franklin and others towards the negro slave population. 

McCormick closes his stimulating and fascinating narrative in the conclusion to his book with a discussion of Thomas Malthus’ 1798 Essay on the Principle of Population, a work that famous influenced by Charles Darwin and Alfred Russel Wallace in the formulation of their theories of evolution by natural selection. Darwin and Wallace do not put in an appearance here as McCormick is concerned with Malthus’ influence on the development of demography, which he presents as revolutionary:

From the perspective of the Henrician humanists, Elizabethan pamphleteers, Jacobian colonial promotors, Interregnum projectors, Restoration political arithmeticians and Enlightenment-era physicians, philanthropists and philosophers who have populated this book, T. R. Malthus’s 1798 Essay on the Principle of Populationappears scarcely less than the French Revolution, to mark the end of an age. 

Carrying on, McCormick runs revue over the polemics, reforms, schemes. and projects that he has described in the previous chapters and concludes:

Into this baroque edifice slammed the wrecking ball of Malthusian principle.

He then follows up with an analysis of that Malthusian wrecking ball. McCormick’s book closes with some very open and honest general thoughts on the limitations of his own research.

Fans of footnotes will love McCormick, the book has literally tons of them listing vast amounts of sources, that are included in a twenty-two-page bibliography, the whole closing out with an excellent index. This book does not have illustrations.

This is not an easy read. It is a book packed with intensive historical information and evidence with an equally intensive analysis. However, if you have any interest in the topics covered this is a must read.

Having started out with my personal relationship to probability theory and a very brief sketch of its early history, when the philosopher of science Ian Hacking died whilst I was writing this, I immediately got his excellent The Emergence of ProbabilityA Philosophical Study of Early Ideas about Probability, Induction and Statistical inference (CUP, 1975), a title that can be found in McCormick’s extensive bibliography, out of the university library. A book that I first consulted more than thirty years hence and is now my current bed time reading. 

[1] Ted McCormick, Human EmpireMobility and Demographic Thought in the British Atlantic World1500–1800, CUP, Cambridge, 2022


Filed under Book Reviews, History of Mathematics

Renaissance garbage ­– II

This is the second in a series of discussion of selected parts of Paul Strathern’s The Other RenaissanceFrom Copernicus to Shakespeare, (Atlantic Books, 2023). For more general details on both the author and his book see the first post in this series.

Today, I turn my attention to his chapter on the fifteenth century, German philosopher and theologian, Nicholas of Cusa, a large part of which is, as we shall see, actually devoted to another fifteenth century German scholar. Right in his opening paragraph to this chapter, Strathern lets a historical bomb of major dimensions explode, he writes:

As the world of art in northern Europe began its drastic transformation, shedding the stylistic formalism and religious subject- matter of medieval art, so the northern intellectual world underwent a similar revolution. The origins of the humanistic way of thought and its empirical attitude to learning were not the sole preserve of the Italian Renaissance. Indeed, the ‘father of humanism’ is generally recognized as a German, born in 1401 in the Electorate of Trier: Nicholas of Cusa [my emphasis].

Regular readers will already know that here at the Renaissance Mathematicus we react extremely allergically to the phrase ‘father of anything’, but to title Nicholas of Cusa ‘father of humanism’ is really breath takingly stupid, further to also claim that this is ‘generally recognised’ pushes the claim into the mindboggling. As I explained in the fourth part of my series on Renaissance science, Renaissance Humanism, which originated in Northern Italy, did so almost a century before Nicholas of Cusa was born, so if he was, as Strathern claims, the ‘father of humanism’ then his birth in 1401 must have been a reincarnation. 

Nicholas of Cusa, by Master of the Life of the Virgin Source: Wikimedia Commons

Strathern writes that Nicholas was “the son of ‘a prosperous boatman and ferryman’.” A boatman is, according to the dictionary, “a man who takes people or goods somewhere in a small boat, or who has small boats that you can rent for a period of time.” The Stanford Encyclopedia of Philosophy says his father was “a prosperous merchant who became one of the landed gentry in Trier” and German Wikipedia say he was “als Schiffer ein wohlhabender Kaufmann,” that is, “as shipper a wealthy merchant”. Once again according to the dictionary “a shipper is a company that arranges for goods to be taken somewhere by ship.” There appears to be a major disparity concerning the real profession of the father and Strathern’s version.  

Nicholas was a precocious student. In his early teens he entered the University of Heidelberg, the oldest in Germany, which had been established in the middle of the previous century. Here he studied law, before transferring to the University of Padua near Venice. He graduated in 1423, but instead of becoming a lawyer he took up minor holy orders. 

Early teens was a perfectly normal age to enter university in the fifteenth century, so not necessarily precocious. Strathern seems not to be aware that law was divided into civil law and canon law, that is church law, at medieval universities and Nicholas obtained a doctorate in canon law in Padua in 1423, so it was perfectly normal for him to take minor holy orders on graduating. 

From the outset, Nicholas was an imaginative polymath, his mind fecund with novel ideas on all manner of subjects. Under normal circumstances such ideas would have been controversial, and might even have put his life in mortal danger (almost 150 years later, the Italian philosopher Giordano Bruno would be burned at the stake for expressing similar ideas). However, it seems that the sheer brilliance of Nicholas of Cusa’s mind won him friends in high places. 

Here we have an oblique reference to Nicholas’ cosmological speculation, which did include, like Bruno, the idea that the stars were other suns and there might be other inhabited planets orbiting around them; speculations also shared by Nicole Oresme in the previous century. However, unlike Bruno, Nicholas did not travel around Europe pissing off everybody who was anybody, and also did not deny the divinity of Christ or the Virgin Birth, so his life was never in danger, because of his cosmological speculations. 

In 1450 Nicholas completed a work in the form of dialogues between a layman and a priest. This was entitled Idiota de Mente (literally translated as ‘An Idiot Speaks His Mind’). Surprisingly, it is the ‘idiot’ who puts forward Nicholas’s bold proposals, which contrast sharply with the orthodox Aristotelian views proposed by the priest. It should be borne in mind that during this period Aristotle was regarded as the highest authority on intellectual matters: his word was seen as little less than Holy Writ. 

In medieval Latin Idiota means layman so the title actually translates as A Layman Speaks his Mind. Strathern actually says this in a footnote, so I really don’t understand his next sentence. It is time for my favourite Edward Grant saying, medieval “Aristotelian philosophy is not Aristotle’s philosophy” and in fact it was constantly changing and evolving. Scholars were constantly discussing, criticising, and modifying Aristotle’s thoughts throughout the Middle Ages, so no, it was not Holy Writ.

Next up we have a rather thin presentation of Nicholas’ theological philosophy and his use therein of mathematics and measurement, which is not particular accurate, but I can’t be bothered to unravel it. However, Strathern makes the following claim: 

Despite the abstract flavour of Nicholas’s mathematical pronouncements, his motives were entirely practical. Delineating discrete parts of the world by measurement was what led to knowledge, which was essentially a practical matter. Such thoughts opened the way to an entirely different method of learning. 

He then states, “In order to understand the magnitude of Nicholas’s mode of thought it is necessary for the moment to take the wider view,” and proceeds to give a very thin and not very accurate account of the supposed decline of China. Re-enter Nicholas:

Ironically, it was the very opposite to the process which was taking place in Europe. And it was Nicholas of Cusa who was giving voice to this new direction. Mathematical measurement should be applied to the world. Architecture, commerce, shipbuilding, the very nature of tools and machines – all would undergo major developments during the Renaissance era as a result of this new attitude towards the practical world. 

I wrote a whole series of blog posts about those developments in practical knowledge in the Renaissance and the theological-philosophical ramblings of Nicholas of Cusa did not in any way play a significant role in them. 

As examples of Nicholas’ practical applications of mathematics and measurement he gives the following from his attempts to square the circle (of which more later):

However, in the course of his attempts by pure geometry to solve this problem he managed to calculate the value of π as 3.1423, a figure of greater accuracy than any before – including that calculated by Archimedes, who in fact only worked out its limits of between 223/71 and 22/7 (3.14084 and 3.14285). 

I love the “only” by Archimedes’ process of calculating Pi. It is one of the puzzles of the history of maths, as to why Archimedes stopped where he did and didn’t carry out the next iteration(s)of his calculation, which would, naturally, have given him value for Pi much more accurate than that of Nicholas. Some have suggested that there was a second, now missing, book where he completed his calculations.

In fact, Nicholas’ value is no more accurate than the value used by Ptolemaeus in the second century CE and less accurate than the value calculated by the Indian mathematician Āryabhaṭīya in the sixth century. Closer to Nicholas’s time in the fourteenth century the Indian mathematician Mādhava of Sangamagrāma calculated a value for Pi accurate to eleven decimal places and in 1425, the Persian mathematician Jamshīd al-Kāshī calculated Pi accurate to sixteen decimal places. 

Next up we have Nicholas as calendar reformer:

Nicholas also argued that there was a need to calculate a new calendar, as the seasons were gradually falling out of synchronization with the dates and the months (it would be almost 150 years before his suggestion was taken up by Pope Gregory XIII). 

The recognition of the need to reform the Julian calendar, to bring it back into line with the solar year, goes back at least to the Venerable Bede in the eighth century CE. Notable mathematicians, who made reform suggestions earlier that Nicholas, include Johannes de Sacrobosco (c. 1195–c. 1256), Roger Bacon (c. 12220–c. 1290) and Johannes de Muris (c. 1290–1344). When Gregory XII finally put that reform into practice, he was not taking up the suggestion of Nicholas of Cusa.

Strathern’s next claim completely blew my mind and sent me down a major rabbit hole:

Perhaps Nicholas’s most important invention was a new type of spectacle lens. Previously, lenses had been ground to a convex shape. This was an easier process, and it enabled the viewer to achieve long-sightedness. Nicholas tried the opposite method, grinding a lens into a concave shape, and found that it enabled the viewer to achieve near-sightedness. This brought about a revolution. Old men with failing sight could continue reading, learning, making suggestions, discoveries, inventions. It is little exaggeration to say that intellectual life almost doubled over the coming century as a result of Cusa’s innovation. 

Now, the history of optics, including the history of spectacles, has been a special area of interest of mine for at least thirty years and I have a rather large literature collection on the subject, as a result, but I have never ever come across the claim that Nicholas of Cusa invented the concave spectacle lens, indeed a major development in the history of optics. I was, as I said above, mind blown. I first of all googled Cusanus and spectacles and to my amazement came up with hundreds or even thousands of websites making exactly this claim that Nicholas of Cuse invented the concave spectacle lens in 1450/1. Mostly there was just one simple sentence with no explanation, no source, no history, nothing! Still not convinced I dug deeper and consulted Vincent Ilardi an expert on the history of spectacles and found the answer to this conundrum. 

More certain in this respect, on the other hand, is the often-cited quotation from Cardinal Nicholas of Cusa’s De beryllo (On the Beryl) as the first mention of concave lenses for the correction of myopia. In this treatise, written over a five-year period and completed in in 1485, Nicholas treated the beryl metaphorically but also as a practical magnifying device:

The beryl is a clear, bright, and transparent stone, to which is given a concave as well as a convex form, and by looking through it, one attains what was previously invisible. If the intellectual beryl, which possesses both the maximum and the minimum in the same way, is adapted to the intellectual eyes, the indivisible principle of all things is attained.

Shorn of its convolution, for which Nicholas had a special aptitude, this passage seems to indicate that the beryl used in its concave shape aided distant vision (“the maximum”) whereas the convex shaped one brought short distance images into focus (“the minimum”). And in another passage from his Compendium, completed in 1463, he again cited beryl as lenses to aid vision in a celebration of human creativeness and inventiveness to remedy the deficiencies of nature and master the environment at a level for superior than the capabilities of the animals. 


For man alone discovers how to supplement weakness of light with a burning candle, so that he can see, how to aid deficient vision with lenses [berylli], and how to correct errors concerning vision with the perspectival art.


The above quotations seem to indicate that Nicholas was familiar with spectacles fitted both with concave and convex lenses just a few years before we have unequivocal proof of the former’s availability in quantity.[1]

It is very clear that Nicholas is in no way claiming to have invented the concave spectacle lens, but is merely describing the fact that they exist. It would be an interesting exercise to try and discover who first misinterpreted this passage in this way. As an interesting side note, the use of beryl to make lenses, because of the poor quality of the available glass, led to the fact that spectacles are called Brillen in German. Of course, as Ilardi says, concave lenses aided distant vision and did not as Starter writes enable, old men with failing sight to continue reading, that task had already been covered by the convex spectacle lens. Personally, I think that a historian when confronted by this claim should weigh up the probability that a cardinal and high-ranking Church diplomat ground lenses in his spare time, possible but highly improbable.

A further revolution was instigated when Nicholas turned his attention to a study of the heavens. Despite the fact that the telescope had yet to be invented, his observations enabled him to reach some highly original conclusions. While several of the Ancient Greeks had speculated on such matters, drawing their own similar conclusions, Nicholas was perhaps the first to put these together into a truly universal structure. 

Nicholas’ thoughts on cosmology were based on speculation not observations and although interesting had almost no impact on the actual astronomy/cosmology debate in the Renaissance. He was also by no means “the first to put these together into a truly universal structure.”

However, none of this accounts for the sheer originality of his thinking. Besides the subjects already mentioned, Nicholas made original contributions in fields ranging from biology to medicine. By applying his belief in rigorous measurement to the field of medicine, he would introduce the practice of taking precise pulse rates to use as an indication of a patient’s health. Previously, physicians had been in the habit of taking a patient’s pulse and using their own estimation of its rate to infer the state of their health. Nicholas of Cusa introduced an exact method, weighing the quantity of water which had run from a water clock during one hundred pulse beats. 

As far as I can see, measuring the pulse using a water clock is the only original contributions in fields ranging from biology to medicine that he made. How original it was is debateable:

Pulse rate was first measured by ancient Greek physicians and scientists. The first person to measure the heartbeat was Herophilos of Alexandria, Egypt (c. 335–280 BC) who designed a water clock to time the pulse. (Wikipedia)

In the middle of a lot of stuff about Nicholas’ role as a Church diplomat we get:

Nicholas’s scientific work would go on to influence thinkers of the calibre of the German philosopher-mathematician Gottfried Leibniz, a leading philosopher of the Enlightenment who lived two centuries later. 

It is interesting to note that Nicholas of Cusa is regarded as one of the great Renaissance thinkers and although he was very widely read, his influence on others was actually minimal. Whether or not he influenced Leibniz is actually an open question.

For whatever reason, Strathern now turns to a completely different Renaissance thinker:

The work and thought of Nicholas of Cusa is indicative of the wide-ranging re-examination of the human condition which was beginning to take place, especially amongst thinkers of the northern Renaissance. Another leading German scientific thinker from this period, who would become a friend of Nicholas of Cusa, was Regiomontanus, who was born Johannes Müller in rural Bavaria, southern Germany, in 1436. 

Regiomontanus holding up an astrolabe , see below, Woodcut from the 1493 Nuremberg Chronicle vis Wikimedia Commons

We get a long spiel about scholars adopting Latin names during the Renaissance and the use of Latin in general during the medieval period, but nowhere does he mention that Johannes Müller never actually used the name Regiomontanus, which was first coined by Philip Melanchthon in 1535, that is almost seventy years after his death. 

“[Regiomontanus] would become a friend of Nicholas of Cusa”, really‽ I can find no references whatsoever to this ‘friendship’. There is no correspondence between the two of them, no record of their having ever met. Although, a meeting would have been possible as Regiomontanus lived and worked in Italy during the last three years of Nicholas’ life (1461–64), and even lived in Rome, where Nicholas was living, for some of this time. 

Regiomontanus’ view of Nicholas of Cusa can best be taken from his analysis of Nicholas’s attempts to square the circle.  Nicholas wrote four texts on the topic–De circuli quadratura , 1450, Quadratura circuli 1450, Dialogus de circuli quadratura  1457 and De caesarea circuli quadratura , 1457–all of which he sent to Georg von Peuerbach in Vienna. Regiomontanus wrote a series of notes analysing these texts during his time in Vienna and his conclusion was far from flattering, “Cusanus makes a laughable figure as a geometer; he has, through vanity, increased the claptrap in the world.” Regiomontanus’ very negative analysis of Nicholas of Cusa geometry was first published by Johannes Schöner as an appendix to Regiomontanus’ De triangulis omnimodis in 1533.

Nicholas of Cusa was a good friend of Regiomontanus’ teacher Georg von Peuerbach (1423–1461). Georg von Peuerbach travelled through Italy between graduating BA in 1448 and when he returned to Vienna to graduate MA in 1443.  In Italy he became acquainted with the astronomers Giovanni Bianchini (1410–after 1469), Paolo dal Pozzo Toscanelli (1397–1482), and Nicholas of Cusa. In fact, he lived with Nicholas in his apartment in Rome for a time. Later Georg von Peuerbach and Nicholas corresponded with each other. During his travels in Italy Regiomontanus met Toscanelli and Bianchini and also corresponded with both of them but for Nicholas we have no record of any personal contact whatsoever. As we have seen Regiomontanus heavily criticised Nicholas’ mathematics, but this only became public long after both of them were dead.

Strathern tells us:

Regiomontanus was sent to the University of Leipzig in 1437 [my emphasis], at the age of eleven. Five years later he was studying at the University of Vienna, where he took a master’s degree and began lecturing in optics and classical literature at the age of twenty-one. 

Note there is here no mention of Georg von Peuerbach, in fact, in the whole section about Regiomontanus Georg von Peuerbach gets no mention whatsoever. This is quite incredible! Writing about Regiomontanus without mentioning Georg von Peuerbach is like writing about Robin the Boy Wonder without mentioning Batman! Peuerbach was Regiomontanus’ principal and most influential teacher in Vienna and after Regiomontanus graduated MA, the worked closely together as a team, reforming, and modernising astronomy up till Peuerbach’s death in 1461. Their joint endeavours played a massive role in the history of European astronomy. 

But be warned gentle readers there is far worse to come. If we go and search for the good Georg von Peuerbach, reported missing here, we find the following horror in the chapter on Copernicus:

He had also read the work of the Austrian Georg von Peuerbach, who had lived during the earlier years of the century (1423–61). Peuerbach had been taught by Regiomontanus [my emphasis] and had collaborated with him, using instruments which he invented to measure the passage of the stars in the heavens. 

I don’t know whether to laugh or cry or simply to don rubber gloves, pick up the offending tome, and dump it in the garbage disposal.

You might also note that in 1437, Regiomontanus was one year old not eleven!

While Regiomontanus was teaching at the University of Vienna, the city was visited by the Greek scholar Bessarion, who would play a significant role in Regiomontanus’s subsequent career. As such, it is worth examining Bessarion’s unusual background. 

This is followed by a reasonable brief synopsis of Bessarion’s life prior to his visit to Vienna but no explanation of why he was there or what he did respective Peuerbach and Regiomontanus whilst he was there. This is important in order to understand future developments. Bessarion came to Vienna in 1460 as papal legate to negotiate with the Holy Roman Emperor Frederick III. He also sought out Georg von Peuerbach, who was acknowledged as one of the leading astronomer/mathematicians in Europe, for a special commission. Earlier Bessarion had commissioned another Greek scholar, Georg of Trebizond (1395–1472) to produce a new translation Ptolemy’s Mathēmatikē Syntaxis or as it is better known the Almagest from the original Greek into Latin, providing him with a Greek manuscriptGeorg of Trebizond made a mess of the translation and Bessarion asked Georg von Peuerbach to do a new translation. Georg von Peuerbach couldn’t read Greek, but he knew the Almagest inside out and offered instead to produce an improved, modernised Epitome of it instead. Bessarion accepted the offer and Georg von Peuerbach set to work. Bessarion then asked Georg von Peuerbach if he would become part of his familia (household) and accompany him back to Italy. Georg von Peuerbach agreed on the condition that Regiomontanus could accompany them; Bessarion accepted the condition. Unfortunately, Georg von Peuerbach, only having completed six of the thirteen books of the Almagest, died in 1461, so it was only Regiomontanus, who accompanied Bessarion back to Italy as a member of his familia. A more detailed version is here.

Back to Strathern:

Under Bessarion’s guidance, many works of Ancient Greece – of which western Europe was ignorant – were translated into Latin. And it was in this way that Regiomontanus learned sufficient Greek for him to be accepted as a member of Bessarion’s entourage while he travelled through Italy. 

Most of those works were actually already known in Europe, either through poor quality translations from the Greek or translation from Arabic. This was not how Regiomontanus learnt Greek. He was part of Bessarion’s familia and Bessarion taught him Greek during their travels. 

During these years, Regiomontanus would complete a new translation of the second-century Greek Almagest by Ptolemy. 

Regiomontanus didn’t complete a translation of Ptolemaeus’ Almagest, he completed Georg von Peuerbach’s Epitome of the Almagest (Epytoma in almagesti Ptolemei), fulfilling a death bed promise to Georg von Peuerbach to do so. To quote Michael H Shank

The Epitome is neither a translation (an oft repeated error) nor a commentary but a detailed sometimes updated, overview of the Almagest. Swerdlow once called it “the finest textbook of Ptolemaic astronomy ever written.

Epytoma in almagesti Ptolemei. frontispiece Source: Wikimedia Commons

Strathern continues:

This is the work in which Ptolemy describes the movements of the sun, the moon, the planets and the stars around the earth, which was deemed to be the centre of the universe. For many centuries, such geocentric teaching had been accepted by the early Christians as Holy Writ, and as such its authority lay beyond question. 

Strathern is perpetuating a popular myth. Geocentric cosmology and the Ptolemaic version of it were very often questioned and subjected to criticism throughout the medieval period, both by Islamic and European astronomers and philosophers, as I have documented in numerous blog posts. In fact, Copernicus’ heliocentric model appeared during an intense period of criticism of the accepted astronomy, which began around 1400. Strathern himself in this chapter details Nicholas of Cusa’s unorthodox cosmological speculations!

Strathern now delivers the standard speculation that Regiomontanus was moving towards a heliocentric view of the cosmos based on an over interpretation of a couple of quotes but then tells us:

Some suspect that Regiomontanus must surely have thought through the obvious implications of these remarks, i.e. that the earth moves around the sun. But there is no evidence for this. On the contrary, despite his suspicions as to the accuracy of Ptolemy’s universe, Regiomontanus seems to have continued to use geocentric astronomical mathematics, as well as accepting the authority of Aristotle’s pronouncement that ‘comets were dry exhalations of Earth that caught fire high in the atmosphere or similar exhalations of the planets and stars’. This reliance on ‘authority’ was certainly the case when he made observations of the comet which remained visible for two months during early 1472. He calculated this comet’s distance from the earth as 8,200 miles, and its coma (the diameter at its head) as 81 miles. According to the contemporary astronomer David A. J. Seargent: ‘These values, of course, fail by orders of magnitude, but he is to be commended for this attempt at determining the physical dimensions of the comet.’* 

In the footnote indicated by the *. Strathern writes:

* This comet is visible on earth at intervals ranging from seventy-four to seventy-nine years. Its first certain observation was recorded in a Chinese chronicle dating from 240 bc. When it was observed by the English astronomer Edmond Halley in 1705 it was named after him. The justification for this is that Halley was the first to realize that it was the same comet as had appeared at 74–79-year intervals since time immemorial. Even so, Regiomontanus deserves more than a little credit for his observation of the comet, for in the words of the twentieth-century American science writer Isaac Asimov: ‘This was the first time that comets were made the object of scientific study, instead of serving mainly to stir up superstitious terror.’ 

There is quite a lot to unpack in these two paragraphs, but we can start with the very simple fact that the Great Comet of 1472 was not Comet Halley! The most important point of Regiomontanus’ comet observations is that he tried to determine its distance from the Earth using parallax, this was an important development in the history of astronomy despite his highly inaccurate results. He wrote a book De Cometae, outlining how to determine the parallax of a moving object that was published in Nürnberg in 1531 and played an important role in the attempts to determine the nature of comets in the sixteenth century. 

Comet of 1472 Woodcut from the 1493 Nuremberg Chronicle via Wikimedia Commons

Regiomontanus was not the first to make comets “the object of scientific study” that honour goes to Paolo dal Pozzo Toscanelli, who began treating comets as celestial objects and trying to track their path through the heavens beginning with the comet of 1433, and continuing with the comets of 1449-50, Halley’s comet of 1456, the comet of May, 1457, of June-July-August, 1457, and that of 1472.  He did not publish his observations, but he almost certainly showed them to Georg von Peuerbach when they met. Georg von Peuerbach went back to Vienna in thee 1440s he applied Toscanelli’s methods of comet observation to Comet Halley in 1456 together with his then twenty-year-old student Regiomontanus, as did Toscanelli in Italy. 

Paolo dal Pozzo Toscanelli Source: Wikimedia Commons

Following on to the comet disaster Strathern writes: 

However, Regiomontanus would make two contributions of lasting importance. In his work on rules and methods applicable to arithmetic and algebra, Algorithmus Demonstratus, he reintroduced the symbolic algebraic notation used by the third-century Greek mathematician Diophantus of Alexandria. He also added certain improvements of his own. Basically, this is the algebra we use today, where unknown quantities are manipulated in symbolic form, such as ax by c. Here and are variable unknowns, and ab, and are constants. 

My first reaction was basically, “Yer wot!” I am, for my sins, supposed to be something of a Regiomontanus expert and I have never heard of a book titled Algorithmus Demonstratus and I know for a fact that Regiomontanus did not introduce or reintroduce symbolic algebra, so it was rabbit hole time again.

During his travels in Italy and Hungary, Regiomontanus collected a large number of mathematical, astrological, and astronomical manuscripts, a number of which he intended to print and publish when he settled down in Nürnberg; of which more later. Unfortunately, he died before he could print more than a handful and it turns out that the Algorithmus Demonstratus was one of those manuscripts, which was then edited by Johannes Schöner and published by Johannes Petreius in Nürnberg in 1535. Although it has been falsely attributed to both Regiomontanus, and to the thirteenth century mathematician Jordanus de Nemore, it is not actually known who the author was. Although it has some very primitive attempts to introduce letters for numbers It is in no way an (re)introduction of symbolic algebra as you can judge for yourself here.

As Frank J. Swetz, an expert for Early Modern arithmetic, writes on the MAA website:

On page 10 of the Algorithmus, we find crude attempts to employ symbolic notation. For example, the third paragraph down notes that digit a multiplied by digit b will result in articulum c. An example is given in the margin: 5 x 4 = 20; also articulum times articulum b gives [the product n, 50 x 40 = 2000].

Source: MAA see link above

It is obvious that Strathern literally doesn’t know what he’s talking about and has never even bothered to take a look at the book he is describing.

The garbage continues:

Regiomontanus also made considerable advances in trigonometry, although it has since been discovered that at least part of this was plagiarized from the twelfth-century Arab writer Jabir ibn Aflah. On top of this, Regiomontanus drew up books of trigonometric tables: these lists provided ready answers in the calculation of angles and lengths of sides of right-angle triangles. 

Strathern is here referencing Regiomontanus’ De triangulis omnimodis (On Triangles of All Kinds) edited by Johannes Schöner and printed and published posthumously by Johannes Petreius in Nürnberg in 1533. This is the book he should have featured and not the spurious  Algorithmus Demonstratus. The accusation that he had plagiarised Jābir ibn Aflah was already made in the sixteenth century by the Italian polymath Gerolamo Cardano (1501–1576), whose books were also printed and published by Petreius in Nürnberg. For its role in the history of trigonometry I quote Glen van Brummelen (In his own words, he is the “best trigonometry historian, and the worst trigonometry historian” (as he is the only one)):

[…] what separates the De triangulis from its predecessors is–as the title say–its universal coverage of all cases of triangles, plane or spherical, and its demonstrations from first principles of the most important theorems. It is remarkable in the way that Euclid’s Elements is: not because its results were new, but its structure codified the subject for the future. Although not published until 1533, the De triangulis was to be the foundation of trigonometrical work for centuries, and was a source of inspiration for Copernicus, Rheticus, and Brahe, among many others.[2]

Van Brummelen follows this with a section on possible sources, which Regiomontanus might have used:

There are several possible Arabic sources that Regiomontanus might have used for the De triangulis.


Rather, as the absence of the tangent function in the De triangulis suggests, Regiomontanus’s debt seems to lie mostly in the tradition of the Toledan Tables and Jābir ibn Aflah, whose writings were still being published after Regiomontanus’s death. Several Arabic antecedents have been suggested for particular theorems in De triangulis, but the smoking gun of transmission awaits discovery.[3]

Title page of De triangulis omnimodis  Source MAA

De triangulis does not include the tangent function because Regiomontanus had already dealt with that in his earlier Tabula directionem, which was written in 1467 but first published by Erhard Ratdolt in Augsburg in 1490. This book was a Renaissance bestseller and went through eleven edition the last appearing at the beginning of the seventeenth century. 

This is followed by another piece of misinformation from Strathern:

And it is in these tables that Regiomontanus popularized yet another notational advance. Instead of fractions, which could become increasingly complex, he started using decimal point notation, which was much easier to manipulate. A simple example: the sum of 1/8 + 1/5 is much easier to calculate when these numbers are written as 0.125 + 0.2. The answer in fractional form is 13/40, but in decimal form it is simply 0.325. Furthermore, the decimal answer is much more amenable to further addition, multiplication and so forth with other numbers in decimal form. 

Regiomontanus did not use decimal point notation, to quote Wikipedia, which paraphrases E. J Dijksterhuis, Simon StevinScience in the Netherlands around 1600, 1970 (Dutch original, 1943):

Simon Stevin in his book describing decimal representation of fractions (De Thiende), cites the trigonometric tables of Regiomontanus as suggestive of positional notation.  

Decimal positional notation had existed in Arabic mathematics since the tenth century and there is a complex history of its use over the centuries. Stevin is credited with having introduced it in European mathematics in1585, although, as stated, he credits Regiomontanus as a predecessor, Regiomontanus may be called an anticipator of the doctrine of decimal positional fractions.[4]   However, Stevin did not use a decimal point, this innovation is often falsely attributed to John Napier in his Mirifici logarithmorum canonis constructio written before 1614, but first published posthumously in 1620. However, Christoph Clavius had already used the decimal point in the goniometric tables of his astrolabium text in 1593.  

After leaving Rome, Regiomontanus travelled around Europe, continuing to compile his tables and frequently constructing ingenious objects for his hosts. In Hungary, for King Matthias I, he created a handheld astrolabe. Such devices were first made by the Ancient Greeks in around 200 BC. They contain many moving parts, which mirror the movements of the planets and the stars. Astrolabes can be put to a variety of uses, including astronomy, navigation, the calculation of tides, and the determining of horoscopes for astrologers. 

Strathern seems to be under the impression that Regiomontanus spent his four years as a member of Bessarion’s familia living in Rome, whereas in fact he spent most of his time travelling around Italy visiting libraries and archives to search out manuscripts which he copied both for himself and Bessarion. He left Italy in 1465 and for the next two years we don’t know where he was. In 1467 he was on the court of János Vitéz the Archbishop of Esztergom in Hungary, about 45 kilometres northwest of Budapest, working as his librarian. It was Vitéz, who commissioned him to write his Tabula directionem. In 1468 he moved to the court of the King, Matthias Corvinus (1443–1490), again as librarian, where he stayed until 1471, when he moved to Nürnberg. 

Strathern’s few sentences on the astrolabe are amongst to worst that I have ever read on the instrument. I shall forgive him the, “Such devices were first made by the Ancient Greeks in around 200 BC,” as variation on this myth can be found everywhere, including on Wikipedia, usually crediting the invention of the astrolabe to either Hipparchus or Apollonius. I shall take the opportunity to correct this myth.

We don’t actually know where or when the astrolabe first put in an appearance. The earliest mention of the stereographic projection of the celestial sphere that is at the heart of an astrolabe was the Planisphaerium of Ptolemy written in the second century CE. This text only survived as an Arabic translation. The earliest known description of the astrolabe and how to use it was attributed to Theon of Alexandria (c. 335–c. 405 CE), it hasn’t survived but is mentioned in the Suda, a tenth century Byzantine encyclopaedia of the ancient Mediterranean world, as well as Arabic sources. The extant treatises on the astrolabe of John Philoponus (c. 490–c. 570) and of Severus Sebokht (575–667) both draw on Theon’s work. The development of the instrument is attributed to Islamic astronomers; the oldest surviving astrolabe is a tenth century Arabic instrument.

An astrolabe usually only has two moving parts, the rete, a cut out star map with the ecliptic and, in the northern hemisphere, the tropic of cancer, that rotates on the front side over the stereographic projection of the celestial sphere. On the back of the astrolabe is an alidade, a sighting device. Some astrolabes also have a rotating rule on the front to make taking readings easier.

Arabic Astrolabe 1208 Above: Cut out Rete with eccentric ecliptic and stars as points of thorns. Below right: front of astrolabe with rete Left: rear of astrolabe with alidade Source: Wikimedia commons

Regiomontanus wrote a text on the construction and use of the astrolabe, whilst he was in Vienna. He is thought to have constructed several instruments of which the most famous is one he made for and dedicated to Bessarion in 1462. The instrument he made for Corvinus has not survived.

Regiomontanus astrolabe from 1462 dedicated to Bessarion

We move on:

In Nuremberg, Regiomontanus established a novel type of printing press, the first of its kind devoted entirely to the printing of scientific and mathematical works. 

I’m not sure how to interpret this sentence. Does Strathern mean that Regiomontanus’ printing press, meaning printing house, was novel, because “it was the first of its kind devoted entirely to the printing of scientific and mathematical works,” which is true. Or does he mean that Regiomontanus had created a novel mechanical printing press, which is not true.

He also oversaw the building of the earliest astronomical observatory, in Germany. 

This is simply not true, there was no observatory. Regiomontanus and his partner Bernhard Walter made their astronomical observations with portable instruments out in the street. 

Finally returning to Rome, he constructed a portable sundial for Pope Paul II. Later he also seems to have re-established contact with his friend and mentor, Cardinal Bessarion, who was in Rome in 1471 for the conclave to elect a new pope after the death of Paul II. 

Regiomontanus remained in Nürnberg from 1471 to 1475, when he was called to Rome to assist in a calendar reform. He died there in 1476 probably in an epidemic.

To call this capital of Strathern’s shoddy would be akin to praising it. It creates the impression that he gathered together a pile of out-of-date references and debunked myths, threw them up in the air and then sent the ones that landed on his desk to the publishers. 

[1] Vincent Ilardi, Renaissance Vision from Spectacles to Telescopes, American Philosophical Society, 2007, pp. 80-81

[2] Glen van Brummelen, The Mathematics of the Heavens and the EarthThe Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009 pp. 260-261

[3] Van Brummelen p. 261

[4] Dijksterhuis, Stevin. 


Filed under Book Reviews, Renaissance Science, Uncategorized

It’s elementary dear readers

The legendary soul singer, James Brown, was often referred to as “the Hardest Working Man in Show Business.” In analogy, one could refer to Philip Ball as “the Hardest Working Man in Science Communication.” He churns out books at a higher rate than most other science writers articles, as well as a constant stream of articles for a range of journals. On top of the flood of print on paper he also writes, produces, and presents an excellent radio broadcast for BBC Radio 4, called Science Stories; it’s well worth a listen if you don’t already. I have a running gag on Twitter that the work is actually done by a team of gnomes chained to their desks in the cellars of Ball mansions. As we follow each other on Twitter I finally managed to con him into sending me one of his books to be reviewed here at the Renaissance Mathematicus.[1]

The book in question is The ElementsA Visual History of Their Discovery[2], it’s actually from 2021, as the publishers kept on ignoring Phil’s request that they should send me a review copy, but I kept reminding Phil and he kept prodding the publishers and persistence won out in the end. 

The visual history is to be taken literally, it is a large format book chock full of incredible colour and sepia illustration with accompanying text. It is what is also sometimes, somewhat deprecatingly, referred to as a coffee table book, but despite the format and the visual emphasis this is a high value, easy access volume of absolutely first class, popular history of science. 

The money quote in Ball’s introduction is:

All this implies that charting the history of the discovery of the chemical elements is more than an account of the development of chemistry as a science. It also offers us a view of how we have come to understand the natural world, including our own constitution. Furthermore, it shows how this knowledge has accompanied the evolution of our technologies and crafts – and ‘accompany’ is the right word to use, because this narrative challenges the common but inaccurate view that science always moves from discovery to application. Often it the reverse: practical concerns (such as mining or manufacture) generate questions and challenges that lead to fresh discoveries.

The book wonderfully illustrates all that is stated and implied in these few sentences. 

Before I look at the book in more detail, one last general comment. The book consists of a large number of short, compact, stand-alone essays. Each one of these covers a single topic in at most a few pages. A lot of them are only two or three pages long and I think the longest only run to five pages. It should be noted that a large percentage of those pages are also taken up by the lavish illustrations. However, Ball is an absolute master of the short essay form. He manages, in each case, to include all of the relevant, cultural, historical, and scientific information necessary for a clear understanding of the topic at hand in a style that is easy to read and comprehend, even for the previously, completely uninformed reader. Believe me, as the author of a blog, I know how difficult that is. 

As one might expect, given the subject, the book opens with a multi-coloured double page spread, periodic table. Each article on an element or group of elements has a small schematic periodic table at the top of a sidebar that shows their position in the periodic table. This sidebar also, to quote the author:

…show their atomic number, atomic symbol, atomic weight, periodic group name and number, and in some cases their phase at standard temperature and pressure (solid, liquid or gas)

Although the book opens with the periodic table, we don’t jump straight in with the modern chemical elements, it is constructed chronologically, and the first chapter starts with a general essay on the four classical elements, earth, water, fire, air. This is followed by one on the various ancient Greek philosophical matter theories before we plunge into individual essays on those four elements. This is followed by an excellent introduction to the Chinese five element system. We now go in search of the atom and having found it investigate the aether, the fifth element or quintessence, which closes out the first chapter. 

Chapter Two introduces us to the metal of antiquity. After an introductory essay, we have the precious metals, gold, silver, and copper, followed by an essay on tin and lead and the chapter closes with a comparatively long one on iron, in many senses one of the most important materials discovered and exploited by humanity. 

Chapter Three takes us into the world of the alchemist with the same schema, first an introduction then essays on sulphur, phosphorus, and antimony. Up next is a discourse on a substance that never existed but proved incredibly productive in the history of chemistry, phlogiston. The chapter closes with the question, “What exactly is an element?” answered with a presentation of the thoughts of Robert Boyle, a practicing alchemist, who is considered to have given the first halfway modern answer to the question. 

Chapter Four delivers up the new metals, nine in total, leading us into Chapter Five and chemistry’s golden age. We have the gasses, hydrogen, oxygen, and nitrogen, followed by carbon. Once again, we have a substance that never existed but formed the basis for much experimentation, caloric. Just as phlogiston was considered to be substance given off by burning, so calorific was thought to be the elemental form of heat. The elements now come thick and fast, the halogens, chromium and cadmium, the sixteen rare earth elements. The chapter closes with John Dalton and the beginnings of the modern atomic theory.

Silver mining in Kutná Hora, Bohemia (now the Czech Republic). From an illuminated choirbook, 1490, Sotheby’s London.

Electricity enters the scene in Chapter Six and with it the elements discovered using it by chemists such as Humphry Davy: potassium, sodium, calcium, magnesium, barium, strontium, boron, aluminium, silicon, and zirconium. The book opens with the periodic table known. I think, to all of us from the classroom wall, now we get introduced to the man, who is credited with having discovered it, Dmitri Mendeleev, although Ball also credits those who laid the trail to its discovery before Mendeleev. 

I’ve already described the sidebars on the element essays, on the introductory essays the sidebars have a continuous chronic of the histories of science and technology interspersed with general historical events. In Chapter Seven, The Radiant Age, this chronic starts with the first transatlantic telegraph communication in 1858 and ends with the Russian Revolution in 1917. We have entered the realm of modern physics, electromagnetism, radiation, James Clerk Maxwell, Wilhelm Röntgen, Henri Becquerel, Marie and Pierre Curie, and many more. Following the introductory essay, we have caesium and rubidium with an introduction to spectroscopy, thallium and indium, helium, the inert gases, and to close radium and polonium.

The final chapter takes us into the nuclear age the chronic running from Albert Einstein in 1905 to the dissolution of the USSR in 1991. We fill a gap with technetium and extend the table with neptunium and plutonium, the accelerator elements–americium, curium, berkelium, californium–with claims and counter claims as to who created them first and thus won the right to name them. The bomb-test deliver up einsteinium and fermium. We have eight early trans-fermium elements, from atomic number 101 to 108, and the proofs of their existence gets harder. We enter the realm of less than a teaspoon full, and does it really exist with elements 109 to 118. 

The book closes with a ‘sources for quotes’, or as they are known hanging endnotes to which there are no references in the text, as it is not an academic book, not so bad. There is then a very brief but very good list for further reading, followed by a very extensive picture credits list. It ends with a usable index.

All in all, Philip Ball is to be congratulated on an excellent, accessible, entertaining, and educational tome and I wish I could say that it is as near perfect as a commercial history of science book can be, but I can’t. The book has a serious blemish, a lacuna that I simply can’t ignore. I will introduce it with a couple of quotes from the book:

Paracelsus broadened this ‘unified theory of metals’ to include all substances, by adding a third principle, salt. He argued that mercury was the principle that made things fluid, salt gave them ‘body’ and made them solid. While sulphur was the principle of flammability: it made things burn. (page, 56) 

The ‘alchemist’s trinity’ of sulphur, mercury and salt. An allegorical image from Zoroaster’s Clauvis Artis, Ms-2-27, Vol. 3, 1858, Attilio Hortis Civic Library, Trieste

First the German alchemist Johann Joachim Becher modified the Paracelsian scheme in claiming that there were three types of ‘earth’: a fluid sort (like mercury), a solid sort (like salt), and a fatty and combustible sort (like sulphur). (page, 66)

In ancient times, philosophers and craftspeople recognised seven different metals: gold, silver, mercury, copper, iron, tin and lead. This was a neat scheme, because each of the metals could be assigned a heavenly body: the Sun, Moon, and the five known planets Mercury, Venus, Mars, Jupiter and Saturn. Why do that, though? Because many natural philosophers believed that nature was governed by ‘correspondences’ like this between different classes of things. (page, 78)

Remember Chapter Two, The Antique Metals? We had gold, silver, and copper, followed by tin and lead, and then came iron, where was mercury? When I first realised that there was no entry for mercury, I couldn’t believe it and searched the book from beginning to end thinking I must have somehow overlooked it, but no, there is no entry for mercury. Still not believing my eyes I contacted Phil Ball and discretely inquired whether it was really so that he had forgotten, left out, mercury. His reply was an expletive, that I won’t repeat here. This has got to be the biggest copyediting error that I’ve ever encountered in a book. Phil says he will correct it in the paperback edition. At least he didn’t blame the gnomes.

Despite the absence of mercury, I whole heartedly recommend this wonderful book to just about everybody. In particular I think every home with children should own a copy, not stowed away on a bookshelf but laying around, on a coffee table for example, where inquiring minds could from time-to-time dip in and out of its beautifully illustrated and informative pages. It is a book that lends itself perfectly to dipping. 

One small improvement that I would recommend, apart from an essay on mercury, is that each copy should come with a CD with Tom Lehrer’s The Elements.

[1] Actually, he was quite happy to do so, even the threat of a mauling by the HISTSCI_HULK didn’t stop him from doing so.

[2] Philip Ball, The ElementsA Visual History of Their Discovery, Thames and Hudson, London, 2021


Filed under Book Reviews, History of Chemistry

Renaissance garbage ­– I

In case you hadn’t noticed there is a four-weekly cycle of blog posts here at the Renaissance Mathematicus. Week one is a new series post, week two a fairly random #histSTM post, week three the next new series post, and week four a book review. Sometimes I throw in a random HISTSCI_HULK post just because. Today should be the next series post but I posted the last episode of my Renaissance Science series two weeks ago. You might be pleased or dismayed to learn that I have a new series lined up, at least in my head, but I want to take a little breathing space before I start in on it. To bridge the gap, I shall be posting a series of posts, which are sort of related to the Renaissance Science series, on a book by Paul Strathern, The Other RenaissanceFrom Copernicus to Shakespeare, (Atlantic Books, 2023). The Other Renaissance is, of course, what is normally referred to as the Northern Renaissance.

I must admit that I had never heard of Paul Strathern, but a friend, who shall remain nameless, received a review copy of this book, and thought it was so bad that he decided not to review it at all. My historical garbage antenna went up and I made further inquiries, whereupon said friend was kind enough to send me a pdf of said book. And yes folks, it is truly a stinker. I don’t intend to review the whole thing, but I thought I would post a series of HISTSCI_HULK typical put downs of selected elements of the text.

However, before we get down to the nitty-gritty a few words about our author. According to his Wikipedia page, Paul Strathern (born 1940!!) is a Scots Irish writer and academic, and an incredibly prolific writer he is too. To date, he has published five novels, fifteen “academic” books, nineteen titles in his Philosophers in 90 Minutesseries, eleven titles in his Great Writers in 90 Minutes series, twelve titles in his The Big Idea: Scientists Who Changed the World series, and finally three travel guides. I wonder what he does in his spare time? Also, if his The Big Idea: Scientists Who Changed the World are as bad as his The Other RenaissanceFrom Copernicus to Shakespeare, then I’m glad that the HISTSCI_HULK hasn’t read any of them.

As I will be only commenting on selected bits of the book here is the full contents list:

Map viii–ix Timeline of Significant Events during the Northern Renaissance x-xi 

Prologue: Lifting the Lid 1 

1 Gutenberg 13 

2 Jan van Eyck 21 

3 Nicholas of Cusa 33 

4 Francis I and the French Renaissance 47 

5 A New Literature: Rabelais 63 

6 Martin Luther and the Protestant Reformation 73 

7 The Rise of England 89 

8 The Rise and Rise of the Fuggers 105 

9 Copernicus 125 

10 Erasmus 141 

11 Dürer 157

12 Straddling Two Ages: Paracelsus and Bruegel the Elder 175 

13 Versions of the True: Mercator and Viète 193 

14 Vesalius 211 

15 Catherine de’ Medici 229 

16 Montaigne 249 

17 Elizabethan England 265 

18 Brahe and Kepler 281 

19 Europe Expands 301 

Conclusion: A Last Legacy 317 

And the timeline: (The formatting is a bit weird, result of my cut and paste)


1415 Jan Hus, founder of the Hussites, burned at the stake
1432 Van Eyck completes the Ghent Altarpiece
1460s Regiomontanus oversees the building of the first observatory in Europe (Rubbish!)
1464 Death of Nicholas of Cusa
1474 Technique of painting in oils spreads from the Netherlands to Italy
1494 Signing of the Treaty of Tordesillas: Pope Alexander VI draws a line down the Atlantic Ocean, dividing the globe between Spain and Portugal
1497 John Cabot sails from Bristol and reaches North America 

1509 Erasmus writes In Praise of Folly
1512 Torrigiano is commissioned by Henry VIII to create a Renaissance tomb for Henry VII

1514  Dürer produces Melencolia I 

1515  Francis I ascends to the throne of France

1517 Martin Luther nails his Ninety-Five Theses to the door of Wittenberg Castle Church
1519 The death of Leonardo da Vinci in France
1519 Charles V is crowned Holy Roman Emperor
1525 Death of Jacob Fugger the Rich
1529 The Colloquy of Marburg fails to unite Protestants 

1533 Henry VIII breaks with Rome 

1536 John Calvin arrives in Geneva; Calvinist missionaries soon begin to spread over northern Europe 

1536 French explorer Jacques Cartier brings Chief Donnacona from the New World to see Francis I 

1541 Death of Paracelsus
1543 Copernicus is shown the first published edition of his De Revolutionibus Orbium Coelestium, describing the solar system, while on his deathbed
1543 Vesalius publishes De Fabrica, describing human anatomy
1547 The completion of the Château de Chambord in the Loire Valley 

1547 The death of Francis I of France
1553 The death of Rabelais
1553 English explorer Richard Chancellor visits the court of Ivan the Terrible
1558 The death of Holy Roman Emperor Charles V
1569 Mercator publishes his Atlas, containing his cylindrical projection map of the world
1572 The St Bartholomew’s Day massacre of Huguenots in France 

1588  The Spanish Armada fails to invade Elizabethan England 

1589  The death of Catherine de’ Medici, mother of French kings and ruler of France 

1596 Johannes Kepler publishes his laws describing the elliptical orbit of plants (Love this typo!)

1600  The founding of the East India Company in London 

1601  Tycho Brahe dies in Prague 

1608 Invention of the perspicillium in Holland, which inspires Galileo to create the telescope (Rubbish!)
1616 The death of Shakespeare
1642 Cardinal Richelieu dies in France
1648 The Peace of Westphalia ends the Thirty Years’ War 

I decided to start this week with Strathern’s chapter on Albrecht Dürer, as I have a local connection to the man. 

After a conventional biographical introduction from birth to marriage, Strathern tells us:

Dürer did not travel on his own. He is thought to have been accompanied by an ebullient rugged-faced companion named Willibald Pirckheimer, [my emphasis] whose appearance belied his acute intelligence and thirst for learning. Pirckheimer came from a distinguished family in Nuremberg, was a year older than Dürer, and was filled with patrician self-confidence. He was studying law at Padua, and during the course of their friendship Pirckheimer would fill the huge gaps in Dürer’s education, introducing him to the humanist ideas he had picked up at university and amongst his father’s intellectual circle in Nuremberg. 

When I read that Dürer, on his first journey to Italy, was accompanied by Willibald Pirckheimer, I did a double take. Having read quite a lot about Dürer and Pirckheimer and I’ve never come across any such claim. So back to the literature. My first stop was German Wikipedia, where to my surprise I read the following:

In der Folgezeit bis 1500 schuf er eine Serie von kleinen Landschaftsaquarellen mit Nürnberger Motiven bzw. mit Motiven von Stationen seiner ersten Italienreise, die er in der ersten Hälfte des Oktobers 1494, bereits drei Monate nach seiner Hochzeit, antrat. Diese Reise verstärkte sein Interesse an der Kunst des Quattrocento. Im Mai 1495 kehrte er zurück nach Nürnberg.

Von der jüngeren Forschung wird angezweifelt, dass Dürer im Rahmen dieser Reise jemals die Grenzen des deutschen Sprachgebiets überschritt, und die Indizien, die gegen einen Aufenthalt in Venedig sprechen, häufen sich: Dürer selbst erwähnte in seiner Familienchronik 1494/95 keine Reise nach Venedig. Die italienischen Züge in seinen Werken ab 1497 interpretieren manche als direkten Einfluss des paduanischen Malers Andrea Mantegna, der 1494/95 zwar nicht in Padua war, dessen Werke Dürer aber dort gesehen haben könnte. Beweisbar ist nur, dass Dürer in Innsbruck, Trient und Arco beim Gardasee war. Von Orten südlich von Arco gibt es bei Dürers Aquarellen keine Spur, also auch nicht von Venedig. Auch die Route spricht gegen die Venedig-Theorie: Für Dürer hätte es näher gelegen, den für Nürnberger (Kaufleute) üblichen Weg nach Venedig zu nehmen, der über Cortina und Treviso verlief und „Via Norimbergi“ genannt wurde. Die Bilder aus seiner späteren, nachweisbar venezianischen Zeit ab 1505 haben deutlich stärker venezianische Charakteristika.

For those who don’t read German, it basically says that recent research doubts that Dürer ever left the German language area in 1494 and thus was never in Italy on this journey. This was new to me as I have always read about and accepted that Dürer made two journeys to Italy, the first in 1494. Happily, in 2021, the National Gallery in London put on a major expedition Dürer’s JourneysTravels of a Renaissance Artist for which there is an amazing book[1], which thanks to my very generous stepmother I own a copy. Turning to this wonderful tome I discovered that it is really so that historians now believe that Dürer did not reach Italy in 1494. Apparently, the whole story of the first Italian journey is based on two very short ambiguous quotes and the rest has been built up over the years based on reading the tealeaves in Dürer’s work. 

I actually began to question these two paragraphs of Strathern because of his claim that Pirckheimer had accompanied Dürer on this journey. No journey so no Pirckheimer but there is more. Strathern correctly states that Pirckheimer was studying in law in Padua, which he did for seven years from 1488, first returning to Nürnberg on 1495. This was when Willibald and Albrecht first met!

Later Strathern turns to the “second” Italian journey, the one that really did take place and dishing up a myth that has been long debunked, he tells us:

Between 1507 and 1509 Dürer paid a second visit to Italy, passing beyond Venice to Padua and maybe even Mantua. He certainly visited Bologna, for it was here that he met Luca Pacioli, the friar mathematician and friend of Leonardo da Vinci. It was Pacioli who had taught Leonardo mathematics, and it seems that Dürer too studied with him. Dürer’s meticulous and exact art inclined him to mathematics, and it would play an increasing role in both his painting and his other intellectual interests. Pacioli is known to have taught Dürer linear perspective, which was by now widely developed amongst Italian Renaissance artists. But Pacioli probably taught Dürer much more than this useful mathematical–artistic device, for Dürer would continue to study mathematics over the coming years. 

It is simply not known from whom Dürer learnt the basics of, the then still comparatively new, linear perspective. The question has a certain historical importance, as he is credited with having introduced linear perspective into Northern European art. I have no idea who first introduced the theory that he learnt it from Luca Pacioli during his time in Bologna but that is absolutely no evidence to support it. The theory was finally totally debunked, when somebody pointed out that when Dürer was in Bologna, Pacioli was in Milano! Maybe Pacioli taught him telepathically? As for the implication that Pacioli also taught Dürer mathematics, we know from fairly solid evidence that Dürer didn’t need to go to Italy for his maths lessons, he got them at home in Nürnberg from Johannes Werner. (1468–1522)

Source: Wikimedia Commons

Next up we get a strange twist in the Dürer timeline from Strathern:

By the time Dürer returned home from his second visit to Italy, he was known by reputation throughout Europe. In 1512, the Holy Roman Emperor Maximilian I became one of his patrons. Despite this, Dürer found that he was making insufficient income from his paintings, and even abandoned this art form for several years in favour of making woodcuts and engravings – which could be reproduced and thus sold many times over. He may not have been the best painter in Europe, but his engravings were unsurpassed. 

Dürer served his apprenticeship in the studio of Michael Wolgemut between 1486 and 1490. Wolgemut specialised in producing woodblock prints as book illustrations. For example, his studio produced the illustrations for the famous  Liber Chronicarum, better known as the Nuremberg Chronicle in English and Die Schedel’sche Weltchronik in German. There are even speculations by art historians as to whether the young apprentice was responsible for some of those illustrations. From the very beginning when he set up his own workshop in 1495, Dürer specialised in woodblock printing. He also developed his skill in engraving, almost certainly learnt in his original apprenticeship under his father, a goldsmith. To illustrate a couple of quotes from Wikipedia:

Arguably his best works in the first years of the workshop were his woodcut prints, mostly religious, but including secular scenes such as The Men’s Bath House (ca. 1496). These were larger and more finely cut than the great majority of German woodcuts hitherto, and far more complex and balanced in composition.

His series of sixteen designs for the Apocalypse] is dated 1498, as is his engraving of St Michael Fighting the Dragon. He made the first seven scenes of the Great Passion in the same year, and a little later, a series of eleven on the Holy Family and saints. The Seven Sorrows Polyptych, commissioned by Frederick III of Saxony in 1496, was executed by Dürer and his assistants c. 1500. In 1502, Dürer’s father died. Around 1503–1505 Dürer produced the first 17 of a set illustrating the Life of the Virgin which he did not finish for some years. Neither these nor the Great Passion were published as sets until several years later, but prints were sold individually in considerable numbers.

In 1496 he executed the Prodigal Son, which the Italian Renaissance art historian Giorgio Vasari singled out for praise some decades later, noting its Germanic quality. He was soon producing some spectacular and original images, notably Nemesis (1502), The Sea Monster (1498), and Saint Eustace (c. 1501), with a highly detailed landscape background and animals.

Prints are highly portable and these works made Dürer famous throughout the main artistic centres of Europe within a very few years.

As you can see this is not post 1512 but we have just reached 1505 and Dürer is a highly prolific and famous producer of fine art prints. In fact, rather than being a painter, who turned to fine art printing for financial reasons, as Strathern would have us believe, Dürer was a highly successful fine art printer, who painted on the side.

We get the standard discussions of The Rhinoceros, Dürer’s most famous print, and Melencolia I, his most enigmatic and most interpreted print. I have only one question about Strathern’s waffle here, he writes about Melencolia I:

Though mathematics, especially geometry (Plato’s favourite), underlies much of the scene. 

There is no other reference to Plato anywhere in his convoluted discussion of Melencolia I, so why shove him in here? Earlier he makes the equally strange comment:

Set into the wall above the angel’s head is a four-by-four magic square, indisputable evidence of Dürer’s continuing mathematical interest. 

There was nothing to say that Dürer had ever stopped being interested in mathematics.

Having dealt with The Rhinoceros and before Melencolia I, Strathern enlightens us with the following paragraph:

As we have seen, the year 1500 marked one and a half millennia since the birth of Christ, and there was a widespread belief around this time that it heralded the Second Coming of Christ, which is mentioned in the Bible: ‘This same Jesus, which is taken up from you into heaven, shall so come in like manner as ye have seen him go into heaven.’ Such an event would precede the Last Judgement, after which our souls would be despatched to Purgatory, Hell or Heaven.

Various dates were considered by various people to signify the second coming but I personally have never come across a reference to 1500 as one of them.

Strathern also turns his spotlight on the Ehrenpforte Maximilians I, known in English as The Triumphal Arch or the Arch of Maximillian I, he writes:

Dürer created a number of works for his most important patron, Maximilian I. Amongst these is a large, highly complex woodcut of a triumphal arch, which measures almost ten feet by ten feet. Dürer spent over two years – on and off – busying himself with this work, which includes 195 separate woodcuts printed on 36 sheets of paper. The intention was that it should be hung in princely palaces and city halls throughout the Holy Roman Empire. Indeed, Maximilian I made a habit of giving away copies of this work with this intention. 

The work itself is a suitably grandiose hotchpotch of styles – resembling, if anything, an example of Indian architecture rather than any classical triumphal arch (such as Marble Arch in London, or the Washington Square Arch in New York). It stands more as a monument to Dürer’s indefatigable technical expertise than any aesthetic achievement. Such a work made him rich, allowing him independence – even if it contributed nothing to his artistic attainment and was otherwise a complete waste of his time. [my emphasis]

Ehrenpforte Maximilians I, Source: Wikimedia Commons

As is, unfortunately, all to common Strathern attributes this work to Dürer alone but it was the work of a group of people, quoting, yet again, Wikipedia:

The design program and explanations were devised by Johannes Stabius, the architectural design by the master builder and court-painter Jörg Kölderer and the woodcutting itself by Hieronymous Andreae, with Dürer as designer-in-chief. […] the flanking round towers are attributed to Albrecht Altdorfer.

The closing clause from Strathern, that I have emphasised, displays, in my opinion, his ignorance of the professional life of an artist and in particular that of his subject Albrecht Dürer. Dürer ran a highly professional, commercial fine art print studio, with which he not only earned the money on which he and his family lived but also the money with which he paid his employees. The Ehrenpforte was anything but a complete waste of time, as the commission raised the status of his studio and did in fact contribute to his artistic attainment, as it displayed his mastership in woodblock printing to the world. 

Here we have the name of the mathematician, Johannes Stabius 1450–1522), who was the Imperial Court historian, was the director of the project, as he would employ Dürer on two further commissions, neither of which Strathern considers worth mentioning, despite his continued references to Dürer’s interest in mathematics.

Johannes Stabius portrait by Albrecht Dürer Source: Wikimedia Commons

The first was the Stabius-Dürer World Map

Stabius-Dürer World Map published in 1515, a perspective representation of the earth as a globe. Source: Wikimedia Commons

and the second, and historically much more important the Stabius-Dürer-Heinfogel planispheres of the southern and northern hemispheres, the first European, printed celestial maps, which I wrote about here.

The Dürer Star Maps in a hand coloured edition Source: Ian Ridpath Star Tales

 We get accounts of Dürer’s journey to the Netherlands to get his Imperial pension renewed following the death of Maximillian, including an account of his portrait of Erasmus and Strathern’s rather bizarre interpretation of its Greek inscription. 

Almost at the end of his chapter, Strathern turns to Dürer the mathematician:

With Dürer’s eyesight fading, he devoted less of his energies to his art. Instead he concentrated on writing treatises on such subjects as ‘human proportions’ and ‘fortifications’. However, his most important work was his Four Books on Measurement. These contain the wealth of mathematical knowledge he accumulated during his life – including the geometrical construction of shadows in prints (projective geometry), as well as several ideas by the Tuscan artist Piero della Francesca which had not yet been published. (These Dürer had almost certainly learned from Luca Pacioli.) Very little of this vast compendium of work is original, but it was written in the vernacular German rather than in Latin. This established Dürer as the first figure of the northern Renaissance to outline in German Euclidean geometry and demonstrate the construction of the five Platonic solids, other Archimedean semi-regular truncated solids, and a number of constructed figures which are thought to have been of his own invention. His treatises were the first printed north of the Alps to view art in a scientific fashion, exposing the mathematical bones upon which much artistic flesh is based. 

I’m sure Dürer would be delighted to know that his Four Books on Measurement was his most important work, whereas his ‘human proportions’ was just a treatise on “such subjects”! 

About the time of his “second” journey to Italy, Dürer became obsessed with the idea that the secret of beauty lies in the mathematical theory of proportions. He began working on his Vier Bücher von menschlicher Proportion (Four Books on Human Proportion) in 1512 and the four books, written at different time over the years, deal with various aspects of exactly that, human proportion. An appendix to the book explains Dürer’s theories on ideal beauty.

Title page of Vier Bücher von menschlicher Proportion Source: Wikimedia Commons

The book was written for apprentice artists and in the middle of the 1520s, Dürer realised that the geometry of the book was too advanced for the intended readers, so he sat down and wrote his Four Books on Measurement (Underweysung der Messung mit dem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler), (which I wrote about here) an introductory textbook on geometry for apprentice artists. It is the book on human proportions that is his most important work, the Four Books on Measurement merely developed the mathematical tools needed to understand it. 

Underweysung der Messung mit dem Zirkel und Richtscheyt Title Page

I have no idea which not yet published ideas from Piero della Francesca Dürer’s book supposedly contains. It goes without saying that Dürer didn’t learn anything from Luca Pacioli, whom he never met and with whom, as far as we know, he didn’t correspond. However, he might have accessed della Francesca work via Pacioli, who had plagiarised it in his Divina proportione, published in 1509, which was possibly owned by one of the Nürnberg mathematicians, Werner or Stabius, but that’s just speculation. 

Far from being a vast compendium of work, Underweysung der Messung is 27cm X 18cm and probably less than 200 pages long, it’s not paginated so I had to guess. Dürer’s Underweysung der Messung is actually the very first mathematics book printed in German and like most textbooks it is of course derivative. However, it does contain one important geometrical innovation. Dürer introduced the geometry net, which is the two-dimensional figure that arises when you open a three-dimensional figure along edges.

Underweysung der Messung geometrical net

In one sense Underweysung der Messung did become more important than Vier Bücher von menschlicher Proportion both were into Latin and Underweysung der Messung was translated into several different European languages. Vier Bücher von menschlicher Proportion appealed to a very limited readership but Underweysung der Messung became a very widely read geometry textbook throughout Europe for most of the next hundred years. 

Strathern has obviously not bothered to do serious research for his book but has just thrown it together from the first sources that crossed his path without bothering to check whether they were factually correct or not. As we will see in later chapters this sloppy approach is not confined to Dürer but is characteristic of the whole book. 

[1] Susan Foister and Peter van den Brink eds., Dürer’s JourneysTravels of a Renaissance Artist, National Gallery, London, distributed by Yale University Press, 2021. 


Filed under Book Reviews, Renaissance Science, Uncategorized

A masterclass in wide-ranging narrative history

 Long ago in another life, when I first became interested in, involved in, began learning, the history of science, the classic texts one was supposed to have read where all big books. Big theme books, big in scope and big in message. They covered deep periods of time and extensive areas of the evolution of a branch of science. All the big names had at least one big book and often more than one. Over time the big book went out of fashion, too general, too concentrated on big names and big events. They became replaced with close, detailed studies of one aspect of one corner of one discipline. 

Over the years, the Welsh historian of science, Iwan Rhys Morus has written a series of detailed studies of various aspects of nineteenth-century British science, in particular detailing the history of electricity. 2005 saw When Physics Became King (University of Chicago Press), 2011, Shocking Bodies: Life, Death & Electricity in Victorian England (The history Press), 2017, Michael Faraday and the Electrical Century (Icon Books), also 2017, Willian Robert Grove: Victorian Gentleman of Science (University of Wales press, and most recently, 2019, Nikola Tesla and the Electric Future (Icon Books) (reviewed here), with a raft of papers to similar topics both in journals and collected volumes in between. Now he has written and published as big book and what a book it is, How the Victorians Took Us to the MoonThe Story of the 19th-Centuiry Innovators Who Forged Our Future[1], covering as it does a very wide range of science and technology throughout the nineteenth century, it is an absolute master class in how to write wide-ranging, big theme, narrative history. 

Morus weaves internal history of science and technology together with the political, social, and cultural histories of science and technology into a single multidimensional, narrative strand that in not quite three hundred pages gives a densely packed, comprehensive overview of the development of the two disciplines in the nineteenth-century United Kingdom. A narrative that pulls the reader into that century and lets them breathe in the excitement and expectation that sparkles and crackles in the air generated by the future visionaries of Victorian Britain. 

The book is structured chronologically on two different but interrelated levels.  Each of the chapters, which are perhaps better described as sections, deals with a different aspect of the developments in the nineteenth century but taken together they describe an arc beginning in the late eighteenth and early nineteenth centuries science wars between the old guard Baconian naturalists gathered around Sir Joseph Banks, a gentleman’s club that dominated the Royal Society, Britain’s leading scientific institution, on the one side and the younger generation of Cambridge University mathematical scientists led by Charles Babbage and John Herschel, who believed that science should be carried out by those with expertise and not those with social privilege. Travelling topic by topic through the century the arc closes with the advent of powered, heavier than air flight at the end of the nineteenth century, beginning of the twentieth century. However, within each topic there is a second chronological arc tracing the development of that topic from its early gleam in the eyes of its initial innovators through to its final fruition as a successful trendsetting, future defining technology. 

The book opens with a science fiction vignette, describing the launch of the first British moon-landing mission in 1909 and closes with its successful return. Here Morus displays a quality of narrative writing that he maintains throughout the main text of the book, making it a pleasure to read, as well as both an entertaining and highly informative discourse. 

Following the opening chapter with its description of the war between the Banksian gentlemen of science and the Cambridge mathematical men of science, Morus takes to another arena of conflict between the much-heralded engineers such as the Stephensons and Brunels, who shaped the infrastructure of the Victorian future with their railways, ships, bridges and tunnels, and the craftsmen who actually constructed those railway lines, tunnels, and bridges. Morus delivers here a fine demolition of the big names, big events style of historiography. 

The third chapter illustrates the efforts to tame the new technology of electricity by fitting it with a solid quantified scientific corset. Defining the standards for the units of electrical potential, force and resistance and the laboratories and their researchers that grew out of those endeavours. Chapter four takes us into the wonderful world of the Victorian scientific and technological exhibitions in which innovators and inventors competed in their endeavours to persuade the general public and those in power to back their latest concepts designed to shape the future. Here we have everything from shop style exhibition spaces on the high street to the legendary spectacle that was the 1851 Great Exhibition of the Works of Industry of All Nations held in the specially constructed Crystal Palace.  

Chapter five is an object lesson in how quickly times change. It leads off with the euphoria that followed the introduction of the railways and how steam power was going to shape and revolutionise the future. A euphoria that was quickly pushed out of the way and replaced with exaltations for a future powered by the newest trend in energy, electricity. Both this and the previous chapter, on exhibitions, bring one of the book’s central themes to the fore, how the Victorians shaped their visions of the future based on emerging technology. 

Chapter six deals with one of the great technological leaps of the nineteenth century, long distance communication. Electrical signals, first through wires, the telegraph and then the telephone and finally through the air with the wireless telegraph. Here another central theme of the book is emphasised the role played by the British Empire, in nineteenth-century Britain, in the production of new technologies, and in the marketing and exploitation. The Empire provided much of the raw materials needed to produce new technologies and a world-wide market where the inventors and innovators could maximise their profits. Technologies such as the telegraph and wireless telegraphy were, of course, useful tools to control and govern the Empire.

Another useful tool for those in control and governance that came into general use in the nineteenth century were the mechanical and later electro-mechanical calculators. Chapter seven, which deals with those development, features one of my personal favourite Victorians, Charles Babbage, who had major vision for his computing machines, vision that would only be truly realised in our own computer age. However, the slightly simpler calculating machines provided the politicians with a tool to develop the realm of social statistics and plan for the future. 

As, stated earlier, the closing chapter deals with the history of manned flight. It was only in 1783 that the world saw the advent of unmanned and manned flights with both hot air and hydrogen balloons. The nineteenth century saw attempts to first power and steer balloons, rather than just letting them drift on the whims of the wind and then latter the development of the heavier than air aeroplane, including early plans to build steam powered flying machines. 

The book closes with an epilogue that opens with the account of the return of the successful British moon landing expedition that opened the book. Morus then poses the question, whether the Victorians really could have staged a Moon landing? The answer is of course no, but is it? As Morus tells us:

In that sense, at least, the Victorians really did take us to the Moon. When Apollo 11 took off from the Kennedy Space Center on 16 July 1969 – just 60 years after the scene imagined after the scene imagined at the beginning of this book – and when the Eagle landed on the lunar surface on 20 July, it really was the culmination of a technological fantasy that began with the Victorians. What this book has tried to describe is the emergence during the course of the nineteenth century of new ways of thinking of thinking about and organising science that were directed at the future in a wholly new and unprecedented way, and some of the consequences of that reorientation. It is, by and large, the way we think about and organise science now, and the book is also an invitation to think what it means that we still do things the Victorian.

Page 287

This paragraph summarises Morus’ book far better than I ever could in fact the entire epilogue is a better review of the book than the one that I’ve written. Maybe I should just have scanned and posted it instead.

The book is well illustrated with the now ubiquitous grayscale picture, which Victorian media delivers lots of. There are extensive end notes listing the sources used but, as has become quite common in recent years, there is no separate bibliography. The book closes with an excellent index. 

The title of this blog post reveals quite clearly what I think about this book but I’m now going to double down on it. Morus is a truly excellent writer and he has obviously invested much effort and thought in producing this jewel of a book. I have grown old and now read very slowly but I have had my nose stuck in a book since I was three years old and have over the decades read literally hundred of tomes. From time to time in my perusal of the world’s literature I have stumbled across a book that has left the deepest of impression on me. Such volumes are rare and with Iwan Morus’ latest publication I have added a new one to that brief list. If you study nineteenth century British history this book should be obligatory. As a case study for historians of science and/or technology it should probably also be obligatory. If you just like reading accessible, good quality, well written history books then you will love this one, so just acquire a copy and enjoy. 

[1] Iwan Rhys Morus, How the Victorians Took Us to the MoonThe Story of the 19th-Centuiry Innovators Who Forged Our Future, Icon Books, London, 2022

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

Finding things in books

I suppose it’s almost inevitable that if one begins to take a deeper interest in the history of science, then at some point one’s attention turns to the history of the book. After all, whether in the form of wedges impressed in clay tablets, symbols carved in stone or wood[1], or various forms of writing on leaves, papyrus, parchment, vellum or paper, books are the medium with which creators of knowledge transmit that knowledge to other. Science based only on oral transmission would develop very slowly and not very far. 

My interest began with the cliché that the invention of the printed book was a major factor in the expansion of scientific activity in the Early Modern Period, in Europe that is called the scientific revolution. In this case it’s a cliché that is true. I acquired and read Elizabeth Eisenstein’s excellent, classic The printing press as an agent of change (ppb. CUP, 1980), which is a comprehensive introduction to the early world of the printed book. This was followed by the equally classic The Coming of the BookThe Impact of Printing 1450­–1800 by Lucien Febvre and Henri-Jean Martin (Verso, 1976), originally published in French as L’Apparition du livre (Editions Albin Michel, 1958), now somewhat dated by still highly informative. 

My interest in book history began to deepen when I began to examine the question, why was Copernicus’ De Revolutionibus published in Nürnberg, leading to the study of all aspects of Renaissance scientific book publishing. 

Over the years I have acquired a shelf full of books on the history of the book that includes, Addrian Johns’ The Nature of the BookPrint and Knowledge in the Making (University of Chicago Press, 1998), with it’s rejection of some of Eisenstein’s key theories. I followed the ensuing debate between the two in various papers. Also on that shelf, amongst others, are Erik Kwakkel’s excellent Books Before Print (ARC Humanities Press, 2018) on medieval manuscripts, Keith Houston’s delightful, and beautifully presented The BookA Cover-to-cover Exploration of the Most Powerful Object of Our Times (W. W. Norton & Company, 2016), Andrew Pettegree’s The Book in the Renaissance (Yale University Press, 2010).

A slightly more detailed look at these and a couple of other volumes can be found here in an earlier post here, with a link to a full review of Houston’s The Book.

Not included in that earlier post is Tom Moles’ The Secret Life of Books (Elliot & Thompson, 2019), which looks at the functions that books fulfil outside of being reading material, and which I sort of reviewed here. As a footnote to the second footnote on that blog post, I did buy Henry Petroski’s The Book on the Bookshelf (Vintage Books, 1999).

One book on book history that I’m very pleased to have acquired, relatively cheaply, was a second-hand copy of is Margaret Bingham Stillwell’s The Awaking Interest in Science During the First Century of Printing 1450–1550An annotated Checklist of First Editions viewed from the Angle of their Subject Content – Astronomy • Mathematics • Medicine • Natural Science • Physics • Technology, which is a 430 page mine of information and proved very useful in writing my Renaissance Science series of blog posts. 

A fairly recent acquisition is Book Parts edited by Dennis Duncan & Adam Smyth (OUP, 2019), which is what the title says it is, a collection of essays on the individual parts that make up a book – Introductions, Dust Jackets, Frontispieces, Title Pages and eighteen more. It contains a fascinating ten-page essay by Dennis Duncan on the history of indexes. So, it was fairly obvious that when he brought out a whole book on the subject Dennis Duncan IndexA History of theA Bookish Adventure from Medieval Manuscripts to the Digital Age (W. W. Norton, 2022) that I would acquire a copy. The hardback appeared in February, but economic straights caused me to wait until the paperback appeared in Penguin in October, but I can happily report that it was worth the wait.

Readers of my book reviews may have noticed that I always include a brief comment on the index of the book I’m reviewing. In my opinion, for an academic volume a good index is of prime importance. You have borrowed a massive tome out of the library and are only interested in one of the topics that it contains, you turn immediately to the index to find the relevant passages, to save you having to read the whole thing. A good index is a boon and an important research tool, a bad or non-existent index is a nightmare. I have a paperback of one very important history of science biography in which almost none of the pages listed in the index under a given heading match up with the pagination of the text. It frustrates me every time I turn to it. I suspect that the paperback has a different pagination to the hardback, and nobody thought to redo or adjust the index. Recently l borrowed Marshall Claggett, Archimedes in the Middle Ages, Volume Three: The Fate of the Medieval Archimedes 1300 to 1565, Part III The Medieval Archimedes in the Renaissance, 1450–1566 (The American Philosophical Society, 1978) from the library, only to discover when I got it home that it is 1246 pages long and has no table of contents and no index! For my purposes next to useless!

Indexes and tables of contents are important tools in academic books, which enable the reader to find things without having to read the entire texts. We tend to take them for granted and probably implicitly assumes that they are always there, will always be there, and always have been. The last, of course, is nonsense. The first books were not born with a neat table of contents at the front and a comprehensive index at the back, so where and when did they first appear, how do they differ from each other and how did they evolve into their current forms? These are the questions that Duncan’s volume answers and does so both excellently and highly entertainingly.

It is seldom the case that I read an academic book with a smile on my face, whilst doing so, or break out into laughter at irregular intervals in the text. I did with Duncan’s charming tome. He has a wry sense of humour and a love of bad jokes and is not reluctant to use them. These traits are already obvious in the book’s title, whereby Index, A history of the is a classic index entry, which also, rest assured, appears in the book’s index.  

Duncan doesn’t start with the index but with alphabets, it’s a trivial fact that without an ordered alphabet, one can’t have an ordered index, but not something that one usually thinks about, so ingrained is our ability to rattle off the alphabet at the drop of a hat, that we give no thought to where and when this ordering comes from. 

Having acquired part of the skeleton with which to compile an index we now move onto its birth in the writings of medieval monks or rather its twin parallel births! We also have the birth on the concordance and what differentiates an index from a concordance. 

I said before that we had acquired part of the skeleton with which to compile an index, why only part? What’s missing? What is missing is pagination, without the page number an index entry is a lost term in search of a page. Having launched the alphabetical, paginated index on the world stage, our author know takes it on a romp and at time a wild ride through its evolution down to the present, its changing status its pros and cons, and its uses and abuses. Along the way we meet the table of contents and sort out the similarities and differences between it, the index, and the concordance. A stimulating and fascinating journey, which I can only recommend that you embark on. The price of a ticket is Duncan’s wonderful book. The paperback is one of the best €10.77[2]s I have every spent on a book.

Embellished with the now ubiquitous grayscale illustrations, Duncan’s book is, naturally, equipped with a first-class apparatus, an intriguing table of contents, extensive endnotes, and of course probably the best index that a book ever had. 

You don’t have to be a book historian, or even interested in book history to enjoy this book. It is a truly delightful read for all those who love reading and who have an open and inquiring mind.

[1] I find it a fascinating etymological fact that the English word book comes from the German Buch, which derives from Buche the German for beech tree as German books were originally written on sheets of beech wood.

[2] Prices will of course vary, depending on where you buy a copy


Filed under Book History, Book Reviews

God made all things by measure, number and weight[1]

God made all things by measure, number and weight[1]

The first history of science, history of mathematics book I ever read was Lancelot Hogben’s Man Must Measure: The Wonderful World of Mathematics, when I was about six years old.

It almost certainly belonged to my older brother, who was six years older than I. This didn’t matter, everybody in our house had books and everybody could and did read everybody’s books. We were a household of readers. I got my first library card at three; there were weekly family excursions to the village library. But I digress.

It is seldom, when people discuss the history of mathematics for them to think about how or where it all begins. It begins with questions like how much? How many? How big? How small? How long? How short? How far? How near? All of these questions imply counting, comparison, and measurement. The need to quantify, to measure lies at the beginning of all systems of mathematics. The histories of mathematics, science, and technology all have a strong stream of mensuration, i.e., the act or process of measuring, running through them. Basically, without measurement they wouldn’t exist. 

Throughout history measuring and measurement have also played a significant role in politics, often leading to political disputes. In modern history there have been at least three well known cases. The original introduction of the metric system during the French revolution, the battle of the systems, metric contra imperialism, during the nineteenth century, and most recently the bizarre wish of the supporters of Brexit to reintroduce the imperial system into the UK in their desire to distance themselves as far as possible from the evil EU. 

It was with some anticipation that I greeted the news that James Vincent had written and published Beyond MeasureThe Hidden History of Measurement.[2] Vincent’s book is not actually a history of measurement on a nuts and bolts level i.e., systems of measurement, units of measurement and so on, but what I would call a social history of the uses of measurement. This is not a negative judgement; some parts of the book are excellent exactly because it is about the use and abuse of methods of measurement rather than the systems of measurement themselves.

Although roughly chronological, the book is not a systematic treatment of the use of measurement from the first group of hunter gatherers, who tried to work out an equitable method of dividing the spoils down to the recent redefinition of the kilogram in the metric system. The latter being apparently the episode that stimulated Vincent into writing his book. Such a volume would have to be encyclopaedic in scope, but is rather an episodic examination of various passages in the history of mensuration. 

The first episode or chapter takes a rather sweeping look at what the author sees as the origins of measurement in the early civilisations of Egypt and Babylon. Whilst OK in and of itself, what about other cultures, civilisations, such as China or India just to mention the most obvious. This emphasises something that was already clear from the introduction this is the usual predominantly Eurocentric take on history. 

The second chapter moves into the realm of politics and the role that measurement has always played in social order, with examples from all over the historical landscape. Measurement as a tool of political control. This demonstrates one of the strengths of Vincent’s socio-political approach. Particularly, his detailed analysis of how farmers, millers, and tax collectors all used different tricks to their advantage when measuring grain and the regulation that as a result were introduced is fascinating.

Vincent is, however, a journalist and not a historian and is working from secondary sources and in the introduction, we get the first of a series of really bad takes on the history of science that show Vincent relying on myths and clichés rather than doing proper research. He delivers up the following mess:

Consider, for example, the unlikely patron saint of patient measurement that is the sixteenth-century Danish nobleman Tycho Brahe. By most accounts Brahe was an eccentric, possessed of a huge fortune (his uncle Jørgen Brahe was one of the wealthiest men in the country), a metal nose (he lost the original in a duel), and a pet elk (which allegedly died after drinking too much beer and falling down the stairs of one of his castles). After witnessing the appearance of a new star in the night sky in 1572, one of the handful of supernovae ever seen in our galaxy, Brahe devoted himself to astronomy.

Tycho’s astronomical work was financed with his apanage from the Danish Crown, as a member of the aristocratical oligarchy that ruled Denmark. His uncle Jørgen, Vice-Admiral of the Danish navy, was not wealthier than Tycho’s father or his independently wealthy mother. Tycho had been actively interested in astronomy since 1560 and a serious astronomer since 1563, not first after observing the 1572 supernova.

After describing Tycho’s observational activities, Vincent writes:

It was the data collected here that would allow Brahe’s apprentice, the visionary German astronomer Johannes Kepler, to derive the first mathematical laws of planetary motion which correctly described the elliptical orbits of the planets…

I don’t know why people can’t get Kepler’s status in Prague right. He was not Tycho’s apprentice. He was thirty years old, a university graduate, who had studied under Michael Mästlin one of the leading astronomers in Europe. He was the author of a complex book on mathematical astronomy, which is why Tycho wanted to employ him. He was Tycho’s colleague, who succeeded him in his office as Imperial Mathematicus. 

It might seem that I’m nit picking but if Vincent can’t get simple history of science facts right that he could look up on Wikipedia, then why should the reader place any faith in the rest of what he writes?

The third chapter launches its way into the so-called scientific revolution under the title, The Proper Subject of Measurement. Here Vincent selectively presents the Middle Ages in the worst possible anti-science light, although he does give a nod to the Oxford Calculatores but of course criticises them for being purely theoretical and not experimental. In Vincent’s version they have no predecessors, Philoponus or the Arabic scholars, and no successors, the Paris physicists. He then moves into the Renaissance in a section titled Measuring art, music, and time. First, we get a brief section on the introduction of linear perspective. Here Vincent, first, quoting Alberti, tells us:

I set this up between the eye and the object to be represented, so that the visual pyramid passes through the loose weave of the veil.

The ‘visual pyramid’ described by Alberti refers to medieval theories of optics. Prior to the thirteenth century, Western thinkers believed that vision worked via ‘extramission,’ with the eye emitting rays that interacted with the world like a ‘visual finger reaching out to palpated things’ (a mechanism captured by the Shakespearean imperative to ‘see feelingly’). Thanks largely to the work of the eleventh-century Arabic scholar Ibn al-Haytham, known in the West as Alhacen, this was succeeded by an ‘intromisionist’ explanation, which reverses the causality so that it is the eye that receives impressions from reality. It’s believed that these theories informed the work of artists like Alberti, encouraging the geometrical techniques of the perspective grids and creating a new incentive to divide the world into spatially abstract units.

Here, once again, we have Vincent perpetuating myths because he hasn’t done his homework. The visual pyramid is, of course, from Euclid and like the work of the other Greek promoters of geometrical optics was indeed based on an extramission theory of vision. As I have pointed out on numerous occasions the Greeks actually had both extramission and intromission theories of vision, as well as mixed models. Al-Haytham’s great achievement was not the introduction of an intromission theory, but was in showing that an intromission theory was compatible with the geometrical optics, inclusive visual pyramid, of Euclid et al. The geometrical optics of Alberti and other perspective theorists is pure Euclidian and does not reference al-Haytham. In fact, Alberti explicitly states that it is irrelevant whether the user of his system of linear perspective believes in an extramission or an intromission theory of vision. 

Linear perspective is followed by a two page romp through the medieval invention of musical notation before turning to the invention of the mechanical clock. Here, Vincent makes the standard error of over emphasising the influence of the mechanical clock in the early centuries after its invention and introduction. 

Without mentioning Thomas Kuhn, we now get a Kuhnian explanation of the so-called astronomical revolution, which is wonderfully or should that be horrifyingly anachronistic:

This model [the Aristotelian geocentric one] sustained its authority for centuries, but close observation of the night skies using increasingly accurate telescopes [my emphasis] revealed discrepancies. These were changes that belied its immutable status and movements that didn’t fit the predictions of a simple geocentric universe. A lot of work was done to make the older models account for such eccentricities, but as they accrued mathematical like sticky notes, [apparently sticky notes are the 21st century version of Kuhnian ‘circles upon circles’] doubts about their veracity became unavoidable. 

Where to begin with what can only be described as a clusterfuck. The attempts to reform the Aristotelian-Ptolemaic geocentric model began at the latest with the first Viennese School of Mathematics in the middle of the fifteenth century, about one hundred and fifty years before the invention of the telescope. Those reform attempts began not because of any planetary problems with the model but because the data that it delivered was inaccurate. Major contributions to the development of a heliocentric model such as the work of Copernicus and Tycho Brahe, as well as Kepler’s first two laws of planetary motion also all predate the invention of the telescope. Kepler’s third law is also derived from pre-telescope data. The implication that the geocentric model collapsed under the weight of ad hoc explanation (the sticky notes) was Kuhn’s explanation for his infamous paradigm change and is quite simply wrong. I wrote 52 blog posts explaining what really happened, I’m not going to repeat myself here.

We now get the usual Galileo hagiography for example Vincent tells us: 

It was Galileo who truly mathematised motion following the early attempts of the Oxford Calculators, using practical experiments to demonstrate flaws in Aristotelian wisdom.

Vincent ignores the fact that Aristotle’s concepts of motion had been thrown overboard long before and completely ignores the work of sixteenth century mathematicians, such as Tartaglia and Benedetti. 

He then writes:

In one famous experiment he dropped cannonballs and musket balls from the Leaning Tower of Pisa (an exercise that likely never took place in the way Galileo claims [my emphasis]) and showed that, contra to Aristotle, objects accelerate at a uniform rate, not proportionally to their mass.

Galileo never claimed to have dropped anything from the Leaning Tower, somebody else said that he had and if it ‘never took place’, why fucking mention it?

Now the telescope:

From 1609, Galileo’s work moved to a new plane itself. Using home-made telescopes he’d constructed solely by reading descriptions of the device…

The myth, created by himself, that Galileo had never seen a telescope before he constructed one has been effectively debunked by Mario Biagioli. This is followed by the usually one man circus claims about the telescopic discoveries, completely ignoring the other early telescope observers. Copernicus and Kepler now each get a couple of lines before we head off to Isaac Newton. Vincent tells us that Newton devised the three laws of motion and the universal law of gravitation. He didn’t he took them from others and combined them to create his synthesis.

The fourth chapter of the book is concerned with the invention of the thermometer and the problems of creating accurate temperature scales. This chapter is OK, however, Vincent is a journalist and not a historian and relies on secondary sources written by historians. There is nothing wrong with this, it’s how I write my blog posts. In this chapter his source is the excellent work of Hasok Chang, which I’ve read myself and if any reader in really interested in this topic, I recommend that they read Chang rather than Chang filtered by Vincent. Once again, we have some very sloppy pieces of history of science, Vincent writes: 

Writing in 1693, the English astronomer Edmond Halley, discoverer of the eponymous comet…”

Just for the record, Halley was much more than just an astronomer, he could for example have been featured along with Graunt in chapter seven, see below. It is wrong to credit Halley with the discovery of Comet Halley. The discoverer is the first person to observe a comet and record that observation. Comet Halley had been observed and recorded many times throughout history and Halley’s achievement was to recognise that those observations were all of one and the same comet.

 A few pages further on Vincent writes: 

Unlike caloric, phlogiston had mass, but Lavoisier disproved this theory, in part by showing how some substances gain weight when burned. (This would eventually lead to the discovery of oxygen as the key element in combustion.) [my emphasis]

I can hear both Carl Scheele and Joseph Priestley turning in their graves. Both of them discovered oxygen, independently of each other; Scheele discovered it first bur Priestly published first, and both were very much aware of its role in combustion and all of this well before Lavoisier became involved. 

Chapter five is dedicated to the introduction of the metric system in France correctly giving more attention to the political aspects than the numerical ones. Once again, an excellent chapter.

Chapter six which deals primarily with land surveying had a grandiose title, A Grid Laid Across the World, but is in fact largely limited to the US. Having said that it is a very good and informative chapter, which explains how it came about that the majority of US towns and properties are laid out of a unified rectangular grid system. Most importantly it explains how the land grant systems with its mathematical surveying was utilised to deprive the indigenous population of their traditional territories. The chapter closes with a brief more general look at how mathematical surveying and mapping played a significant role in imperialist expansion, with a very trenchant quote from map historian, Matthew Edney, “The empire exists because it can be mapped; the meaning of empire is inscribed into each map.”

Unfortunately, this chapter also contains some more sloppy history of science, Vincent tells us:

In such a world, measurement of the land was of the utmost importance. As a result, sixteenth-century England gave rise to one of the most widely used measuring tools in the world: the surveyor’s chain, or Gunter’s chain, named after its inventor the seventeenth-century English priest and mathematician Edmund Gunter. 

Sixteenth or seventeenth century? Which copy editor missed that one? It’s actually a bit of a problem because Gunter’s life starts in the one century and ends in the other, 1581–1626. However, we can safely say that he produced his chain in the seventeenth century. Vincent makes the classic error of attributing the invention of the surveyors’ chain to Gunter, to quote myself from my blog post on Renaissance surveying:

In English the surveyor’s chain is usually referred to as Gunter’s chain after the English practical mathematician Edmund Gunter (1581–1626) and he is also often referred to erroneously as the inventor of the surveyor’s chain but there are references to the use of the surveyor’s chain in 1579, before Gunter was born. 

Even worse he writes:

Political theorist Hannah Arendt described the work of surveying and mapping that began with the colonisation of America as one of three great events that ‘stand at the threshold of the modern age and determine its character’ (the other two being the Reformation of the Catholic Church and the cosmological revolution begun by Galileo) [my emphasis]

I don’t know whether to attribute this arrant nonsense to Arendt or to Vincent. Whether he is quoting her or made this up himself he should know better, it’s complete bullshit. Whatever Galileo contributed to the ‘cosmological revolution,’ and it’s much, much less than is often claimed, he did not in anyway begin it. Never heard of Copernicus, Tycho, Kepler, Mr Vincent? Oh yes, you talk about them in chapter three!

Chapter seven turns to population statistics starting with the Royal Society and John Graunt’s Natural and Political Observations Made Upon the Bills of Mortality. Having dealt quite extensively with Graunt, with a nod to William Petty, but completely ignoring the work of Caspar Neumann and Edmond Halley, Vincent now gives a brief account of the origins of the new statistics. Strangely attributing this entirely to the astronomers, completely ignoring the work on probability in games of chance by Cardano, Fermat, Pascal, and Christian Huygens. He briefly mentions the work of Abraham de Moivre but ignores the equally important, if not more important work of Jacob Bernoulli. He now gives an extensive analysis of Quetelet’s application of statistics to the social sciences. Quetelet, being an astronomer, is Vincent’s reason d’être for claiming that it was astronomers, who initial developed statistics and not the gamblers. Quetelet’s the man who gave us the ubiquitous body mass index. The chapter then closes with a good section on the abuses of statistics in the social sciences, first in Galton’s eugenics and secondly in the misuse of IQ tests by Henry Goddard. All in all, one of the good essays in the book

Continuing the somewhat erratic course from theme to theme, the eighth chapter addresses what Vincent calls The Battle of the Standards: Metric vs Imperial and metrology’s culture war. A very thin chapter, more of a sketch that an in-depth analysis, which gives as much space to the post Brexit anti-metric loonies, as to the major debates of the nineteenth century. This is mainly so that Vincent can tell the tale of his excursion with said loonies to deface street signs as an act of rebellion. 

In the ninth chapter, Vincent turns his attention to replacement of arbitrary definitions of units of measurement with definitions based on constants of nature, with an emphasis on the recent new definition of the kilogram. At various point in the book, Vincent steps out from his role of playing historian and presents himself in the first person as an investigative journalist, a device that I personally found irritating. In this chapter this is most pronounced. He opens with, “On a damp but cheerful Friday in November 2018, I travelled to the outskirts of Paris to witness the overthrow of a king.” He carries on in the same overblown style finally revealing that he, as a journalist was attending the conference officially launching the redefining of the kilogram, going on to explain in equally overblown terms how the kilogram was originally defined. The purple prose continues with the introduction of another attendee, his acquaintance, the German physicist, Stephan Schlamminger:

Schlamminger is something of a genius loci of metrology: an animating spirit full of cheer and knowledge, as comfortable in the weights and measures as a fire in a heath. He is also a key player in the American team that helped create the kilogram’s new definition. I’d spoken to him before, but always delighted in his enthusiasm and generosity. ‘James, James, James,’ he says in a rapid-fire German accent as he beckoned me to join his group. ‘Welcome to the party.’

We then get a long, overblown speech by Schlamminger about the history of the definitions in the metric system ending with an explanation, as to why the kilogram must be redefined.

This is followed by a long discourse over Charles Sanders Peirce and his attempts to define the metre using the speed of light, which failed. Vincent claims that Peirce was the first to attempt to attempt to define units of measurement using constants of nature, a claim that I find dubious, but it might be right. This leads on to Michelson and Morley defining the metre using the wavelength of sodium light, a definition that in modified form is still used today. The chapter closes with a long, very technical, and rather opaque explanation of the new definition of the kilogram based on Planck’s constant, h

The final chapter of Vincent’s book is a sociological or anthropological mixed basket of wares under the title The Managed Life: Measurements place in modern society in our understanding of ourselves, which is far too short to in anyway fulfil its grandiose title.

The book closes with an epilogue that left me simply baffled. He tells a personal story about how he came to listen to Beethoven’s Ninth Symphony only when he had a personal success in his life and through this came to ruin his enjoyment of the piece. Despite his explanation I fail to see what the fuck this has to do with measurement.

The book has a rather small, random collection of colour prints, related to various bits of the text, in the middle. There are extensive endnotes relating bits of the text to there bibliographical sources, but no separate bibliography, and an extensive index.

I came away feeling that there is a good book contained in Vincent’s tome, struggling to get out. However, there is somehow too much in the way for it to emerge. Some of the individual essays are excellent and I particularly liked his strong emphasis on some of the negative results of applying systems of measurement. People reading this review might think that I, as a historian of science, have placed too much emphasis on his truly shoddy treatment of that discipline; ‘the cosmological revolution begun by Galileo,’ I ask you? However, as I have already stated if we can’t trust his research in this area, how much can we trust the rest of his work?

[1] Wisdom of Solomon 11:20

[2] James Vincent, Beyond MeasureThe Hidden History of Measurement, Faber & Faber, London, 2022


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

You Are History

Do you have children, grandchildren, nephews & nieces, grandnephews & grandnieces, the children of friends, age group 7–12, that you would like to give a book as a Christmas present. An entertaining but also educational book, a well written and beautifully illustrated book, a fascinating and intriguing book? Then look no further, I have the very thing for you. It’s Greg Jenner’s You Are History, illustrated by Jenny Taylor. 

That’s historian Greg Jenner star of radio and TV, he’s part of the crew that magic Horrible Histories onto your TV screens, and mega podcast star with his You’re Dead to Me. The book follows a child through its day, from being woken up by the alarm clock in the early morning to finally going to bed at night. At each station throughout the day the history of the everyday objects encountered is presented and explained is entertaining witty texts illustrated by wonderful pictures. Alarm clock, Toothpaste, letterbox, pencil case, chocolate, bicycle, cutlery, pyjamas, and, and, and, and, and … in total 137 objects that we encounter almost daily. This book is a winner. Greg is a serious historian, despite his love of bad jokes, and a little bird has told me that he has had everything fact checked by experts, so the child, who reads this delightful tome, is getting some solid history served up to them, as well as being entertained.

The book is available from 3 November, so get your orders in now and delight that child in your life on Christmas Day, or any other day for that matter.  

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