Category Archives: 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

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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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The Jesuits and science in the seventeenth century

One myth in the history of science that refuses to go away is that the Catholic Church was fundamental opposed to the modern science that emerged during the seventeenth century. They even according to one prevalent theory declared war on it. This myth is of course fuelled by the equally persistent false accounts of the conflicts between the Church and both Giordano Bruno and Galileo Galilei. English scholars, not necessarily historian of science, armed with their knowledge of the reputation of the Jesuits in Early Modern Protestant England, where they were denounced as spawn of the Devil, also polemicise against them, as particularly anti-progress including science. 

Long term readers of this blog will know that over the years I have posted numerous essays that try to correct this false perception both for the Catholic Church in general and for the Jesuits in particular. In fact, my very first substantive history of science post was an attempt to restore the reputation of Christoph Clavius, who introduced the mathematical sciences into the Jesuit’s educational programme, making them amongst the best educated mathematician of the period. 

Long ago I read The New Science and Jesuit Science: Seventeenth Century Perspectives, edited by Mordechai Feingold, (Springer, 2003), an excellent book, in which the first essay is by Michael John Gorman, and now I have been reading Gorman’s The Scientific Counter-RevolutionThe Jesuits and the Invention of Modern Science[1], of which the paperback was published this year, and which contains the essay mentioned above. This book is a must read for anybody interested in the Jesuit contribution to seventeenth century science.

I have included a scan of the back cover of the book, because the two ringing endorsements from Paula Findlen and Simon Schaffer, together with the publisher’s blurb should be enough to convince anybody interested in the topic that this is a must read, without further comment from me. However, I will, of course, make some comments.

This book is based on Gorman’s doctoral dissertation from 1999. It is not a continuous flowing narrative but, rather, a set of seven essays connected by a common theme, version of six of which have already been published in other contexts. Despite the previous publications, the book is more than worth reading, because the essays, as a whole, create a rounded picture of the Jesuits evolving role in mathematics and natural philosophy in the seventeenth century. 

The opening chapter, Establishing Mathematical AuthorityThe Politics of Christoph Clavius, the only one not previously published, deals with Clavius’ introduction of mathematics into the Jesuits’ educational curriculum with a strong emphasis on his motivation for doing so and the political arguments he used to justify this move. 

The second chapter, Mathematics and ModestyThe Problemata of Christoph Grienberger, illustrates the Jesuits personal requirement of humility and rejection of vanity in their work. This is illustrated with a description of the life and work of Christoph Grienberger, Clavius’ successor as professor for mathematics at the Collegio Romano, who almost completely disappeared behind his work. Perhaps the most extreme example of the abrogation of personality. 

The Jesuits provide a difficult subject for the historian of the scientific revolution because they are not the enemies of science that some try to paint them nor are they, despite their own substantial contributions, unrestricted supporters of the new developments in science. There is a tension between the Clavian application of modern mathematics and experimentation to the sciences and the fundamental Jesuit obligation to adhere to the Aristotelian science of Thomist philosophy. Gorman’s book expertly brings this paradox out into the open displaying and analysing it from all sides.

The third chapter of the book, Discipline, Authority and Jesuit CensorshipFrom the Galileo Trial to the Ordinatio Pro Studiis Superioribus, is an in-depth analysis of this paradox. Gorman actually argues, convincingly, that the Jesuits’ requirement that all scientific texts be submitted to the Oder’s authorities for censorship is an early form of peer review.

The fourth chapter, The Jesuits and the Vacuum Debate, was the one that I found most fascinating and from which I learnt the most. The invention of the Torricellian Tube, or barometer, unleashed a heated debate in the seventeenth century as to whether the empty space at the top of the tube was or was not a vacuum. Aristotle had argued that a vacuum could not exist, so the Jesuits were forced to take the side of denial, as we now know the wrong side. As is often the case in the history of science, their opposition actually stimulated the advancement of the science, as the supporters of the vacuum theory were required to counter their arguments. Interestingly the Jesuit opposition was not just philosophical. One of the principal supporters of the vacuum theory was another, non-Jesuit, Catholic scholar, and the Jesuits feared that if he won the debate that this would lead to a diminishing of their dominance in Catholic education. The whole chapter is an excellent example of the complexity of scientific evolution and its history.

There now follow two chapters on Athanasius Kircher, perhaps the most well-known scientific, Jesuit scholar of the century. The first, The Angel and the CompassAthanasius Kircher’s Geographical Project, deals with Kircher’s failed project to create a new, reformed  geography of the entire world by creating a world spanning network of researchers providing input to a central authority, himself. Although Kircher’s project, inspired by similar smaller collective research projects of Peiresc and Mersenne, in the end failed, Gorman sees the attempt as an important step in the evolving practice of scientific research. He also sees the Jesuits process of the central accumulation of scientific data in the Collegio Romano via world-wide correspondence, as an important model for others working in science.

The second chapter on Kircher, Between the Domonic and the MiraculousAthanasius Kircher and the Baroque Culture of Machines, takes a detailed look at Musaeum Kircherianum and its role as a public magnet to promote the Jesuit Order under the European civil and scientific aristocracies. He details the explanations of natural magic given by Kircher and above all his disciple Kasper Schott to explain the function of Kircher’s automatons, machines that initially appear to contradict the laws of nature but whose secret can be explained by those same laws.

Gorman’s final chapter, From ‘The Eyes Of All’ to ‘Usefull Quarries in Philosophy and Good Literature’: The Changing Reputation of the Jesuit Mathematicus, re-examines the trajectory of his book from Clavius to Kircher and how the emphasis and public presentation of the mathematicians of the Collegio Romano had changed over the century, not necessarily for the better. 

Gorman is an excellent writer and his prose is clear and a pleasure to red. The book is illustrated with a series of greyscale illustration. There are informative endnotes, no footnotes, at the end of each essay but unfortunately no general bibliography. There is a good index. 

At the end of the introduction, we can read:

A visit to the publisher’s website reveals the following

The site you are trying to reach has now been archived. Please contact onlineresources@bloomsbury.com for access.

Apart from this irritation, the book is, as already stated, excellent and definitely a must read for anybody interested in the Jesuits’ contribution to the evolution of science in the seventeenth century.


[1] Michael John Gorman, The Scientific Counter-RevolutionThe Jesuits and the Invention of Modern Science, Bloomsbury Academic, London, New York, Oxford, New Delhi, Sydney, 2020, ppb. 2022

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History of science is global history

The simple statement that the history of science is global history is for me and, I assume, for every reasonably well-informed historian of science a rather trivial truism. So, I feel that James Poskett and the publishers Viking are presenting something of a strawman with the sensational claims for Poskett’s new book, HorizonsA Global History of Science[1]; claims that are made prominently by a series of pop science celebrities on the cover of the book. 

“Hugely Important,” Jim al-Khalili, really? 

“Revolutionary and revelatory,” Alice Roberts what’s so revolutionary about it?  

“This treasure trove of a book puts the case persuasively and compellingly that modern science did not develop solely in Europe,” Jim al-Khalili, I don’t know any sane historian of science, who would claim it did.

“Horizons is a remarkable book that challenges almost everything we know about science in the West. [Poskett brings to light an extraordinary array of material to change our thinking on virtually every great scientific breakthrough in the last 500 years… An explosive book that truly broadens our global scientific horizons, past and present.”] Jerry Brotton (The bit in square brackets is on the publisher’s website not on the book cover) I find this particularly fascinating as Brotton’s own The RenaissanceA Very Short Introduction (OUP, 2006) very much emphasises what is purportedly the main thesis of Horizons that science, in Brotton’s case the Renaissance, is not a purely Western or European phenomenon.

On June 22, Canadian historian Ted McCormick tweeted the following:

It’s not unusual for popular history to present as radical what has been scholarly consensus for a generation. If this bridges the gap between scholarship and public perception, then it is understandable. But what happens when the authors who do this are scholars who know better?

This is exactly what we have with Poskett’s book, he attempts to present in a popular format the actually stand amongst historian of science on the development of science over the last approximately five hundred years. I know Viking are only trying to drum up sales for the book, but I personally find it wrong that they use misleading hyperbole to do so. 

Having complained about the publisher’s pitch, let’s take a look at what Poskett is actually trying to sell to his readers and how he goes about doing so. Central to his message is that claims that science is a European invention/discovery[2] are false and that it is actually a global phenomenon. To back up his stand that such claims exist he reproduces a series of rather dated quotes making that claim. I would contend that very, very few historians of science actually believe that claim nowadays. He also proposes, what he sees as a new approach to the history of science of the last five hundred years, in that he divides the period into four epochs or eras, in which he sees science external factors during each era as the defining or driving force behind the scientific development in that era. Each is split into two central themes: Part One: Scientific Revolution, c. 1450–1700 1. New Worlds 2. Heaven and Earth, Part Two: Empire and Enlightenment, c. 1650–1800 3. Newton’s Slaves 4. Economy of Nature, Part Three:  Capitalism and Conflict, c. 1790–­1914 5. Struggle for Existence 6. Industrial Experiments, Part Four: Ideology and Aftermath, c. 1914–200 7. Faster Than Light 8. Genetic States.

I must sadly report that Part One, the area in which I claim a modicum of knowledge, is as appears recently oft to be the case strewn with factual errors and misleading statements and would have benefited from some basic fact checking.

New Worlds starts with a description of the palace of Emperor Moctezuma II and presents right away the first misleading claim. Poskett write:

Each morning he would take a walk around the royal botanical garden. Roses and vanilla flowers lined the paths, whilst hundreds of Aztec gardeners tended to rows of medicinal plants. Built in 1467, this Aztec botanical garden predated European examples by almost a century.[3]

Here Poskett is taking the university botanical gardens as his measure, the first of which was establish in Pisa in 1544, that is 77 years after Moctezuma’s Garden. However, there were herbal gardens, on which the university botanical gardens were modelled, in the European monasteries dating back to at least the ninth century. Matthaeus Silvaticus (c.1280–c. 1342) created a botanical garden at Salerno in 1334. Pope Nicholas V established a botanical garden in the Vatican in 1544. 

This is not as trivial as it might a first appear, as Poskett uses the discovery of South America to make a much bigger claim. First, he sets up a cardboard cut out image of the medieval university in the fifteenth century, he writes:

Surprisingly as it may sound today, the idea of making observations or preforming experiments was largely unknown to medieval thinkers. Instead, students at medieval universities in Europe spent their time reading, reciting, and discussing the works of Greek and Roman authors. This was a tradition known as scholasticism. Commonly read texts included Aristotle’s Physics, written in the fourth century BCE, and Pliny the Elder’s Natural History, written in the first century CE. The same approach was common to medicine. Studying medicine at medieval university in Europe involved almost no contact with actual human bodies. There was certainly no dissections or experiments on the working of particular organs. Instead, medieval medical students read and recited the works of the ancient Greek physician Galen. Why, then, sometime between 1500 and 1700, did European scholars turn away from investigating the natural world for themselves?[4]

His answer:

The answer has a lot to do with colonization of the New World alongside the accompanying appropriation of Aztec and Aztec and Inca knowledge, something that traditional histories of science fail to account for.[5]

Addressing European, medieval, medical education first, the practical turn to dissection began in the fourteenth century and by 1400 public dissections were part of the curriculum of nearly all European universities. The introduction of a practical materia medica education on a practical basis began towards the end of the fifteenth century. Both of these practical changes to an empirical approach to teaching medicine at the medieval university well before any possible influence from the New World. In general, the turn to empiricism in the European Renaissance took place before any such influence, which is not to say that that process was not accelerated by the discovery of a whole New World not covered by the authors of antiquity. However, it was not triggered by it, as Poskett would have us believe. 

Poskett’s next example to bolster his thesis is quite frankly bizarre. He tells the story of José de Acosta (c. 1539–1600), the Jesuit missionary who travelled and worked in South America and published his account of what he experienced, Natural and Moral History of the Indies in 1590. Poskett tells us: 

The young priest was anxious about the journey, not least because of what ancient authorities said about the equator. According to Aristotle, the world was divided into three climatic zones. The north and south poles were characterized by extreme cold and known as the ‘frigid zone’. Around the equator was the ‘torrid zone’, a region of burning dry heat. Finally, between the two extremes, at around the same latitudes as Europe, was the ‘temperate zone’. Crucially, Aristotle argued that life, particularly human life, could only be sustained in the ‘temperate zone’. Everywhere else was either too hot nor too cold.

Poskett pp. 17-18

Poskett goes on to quote Acosta:

I must confess I laughed and jeered at Aristotle’s meteorological theories and his philosophy, seeing that in the very place where, according to his rules, everything must be burning and on fire, I and all my companions were cold.

Poskett p. 18

Instead of commenting on Acosta’s ignorance or naivety, Aristotle’s myth of the ‘torrid zone’ had been busted decades earlier, at the very latest when Bartolomeu Dias (c. 1450–1500) had rounded the southern tip of Africa fifty-two years before Acosta was born and eight-two year before he travelled to Peru, Poskett sees this as some sort of great anti-Aristotelian revelation. He writes:

This was certainly a blow to classical authority. If Aristotle had been mistaken about the climate zones, what else might he have been wrong about?

Poskett p.18

This is all part of Poskett’s fake narrative that the breakdown of the scholastic system was first provoked by the contact with the new world. We have Poskett making this claim directly:

It was this commercial attitude towards the New World that really transformed the study of natural history. Merchants and doctors tended to place much greater emphasis on collecting and experimentation over classical authority.[6]

This transformation had begun in Europe well before any scholar set foot in the New World and was well established before any reports on the natural history of the New World had become known in Europe. The discovery of the New World accelerated the process but it in no way initiated it as Poskett would have his readers believe. Poskett once again paints a totally misleading picture a few pages on:

This new approach to natural history was also reflected in the increasing use of images. Whereas ancient texts on natural history tended not to be illustrated, the new natural histories of the sixteenth and seventeenth centuries were full of drawings and engravings, many of which were hand-coloured. This was partly a reaction to the novelty of what had been discovered. How else would those in Europe know what a vanilla plant or a hummingbird looked like?

Poskett pp.29-30

Firstly, both ancient and medieval natural history texts were illustrated, I refer Mr Proskett, for example, to the lavishly illustrated Vienna Dioscorides from 512 CE. Secondly, the introduction of heavily illustrated, printed herbals began in the sixteenth century before any illustrated natural history books or manuscripts from the New World had arrived in Europe. For example, Otto Brunfels’ Herbarium vivae eicones three volumes 1530-1536 or the second edition of Hieronymus Bock’s Neu Kreütterbuch in 1546 and finally the truly lavishly illustrated De Historia Stirpium Commentarii by Leonhard Fuchs published in 1542. The later inclusion of illustrations plants and animals from the New World in such books was the continuation of an already established tradition. 

Poskett moves on from natural history to cartography and produced what I can only call a train wreck. He tells us:

The basic problem, which was now more pressing [following the discovery of the New World], stemmed from the fact that the world is round, but a map is flat. What then was the best way to represent a three-dimensional space on a two-dimensional plane? Ptolemy had used what is known as a ‘conic’ projection, in which the world is divided into arcs radiating out from the north pole, rather like a fan. This worked well for depicting one hemisphere, but not both. It also made it difficult for navigators to follow compass bearings, as the lines spread outwards the further one got from the north pole. In the sixteenth century, European cartographers started experimenting with new projections. In 1569, the Flemish cartographer Gerardus Mercator produced an influential map he titled ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’. Mercator effectively stretched the earth at the poles and shrunk it in the middle. This allowed him to produce a map of the world in which the lines of latitude are always at right angles to one another. This was particularly useful for sailors, as it allowed them to follow compass bearings as straight lines.

Poskett p. 39

Where to begin? First off, the discovery of the New World is almost contemporaneous with the development of the printed terrestrial globe, Waldseemüller 1507 and more significantly Johannes Schöner 1515. So, it became fairly common in the sixteenth century to represent the three-dimensional world three-dimensionally as a globe. In fact, Mercator, the only Early Modern cartographer mentioned here, was in his time the premium globe maker in Europe. Secondly, in the fifteenth and sixteenth centuries mariners did not even attempt to use a Ptolemaic projection on the marine charts, instead they used portulan charts–which first emerged in the Mediterranean in the fourteenth century–to navigate in the Atlantic, and which used an equiangular or plane chart projection that ignores the curvature of the earth. Thirdly between the re-emergence of Ptolemy’s Geographia in 1406 and Mercator’s world map of 1569, Johannes Werner published Johannes Stabius’ cordiform projection in 1514, which can be used to depict two hemispheres and in fact Mercator used a pair of cordiform maps to do just that in his world map from 1538. In 1508, Francesco Rosselli published his oval projection, which can be used to display two hemispheres and was used by Abraham Ortelius for his world map from 1564. Fourthly, stereographic projection, known at least since the second century CE and used in astrolabes, can be used in pairs to depict two hemispheres, as was demonstrated by Mercator’s son Rumold in his version of his father’s world map in 1587. Fifthly, the Mercator projection if based on the equator, as it normally is, does not shrink the earth in the middle. Lastly, far from being influential, Mercator’s ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’, even in the improved version of Edward Wright from 1599 had very little influence on practical navigation in the first century after it first was published. 

After this abuse of the history of cartography Poskett introduces something, which is actually very interesting. He describes how the Spanish crown went about creating a map of their newly won territories in the New World. The authorities sent out questionnaires to each province asking the local governors or mayors to describe their province. Poskett notes quite correctly that a lot of the information gathered by this method came from the indigenous population. However, he once again displays his ignorance of the history of European cartography. He writes:

A questionnaire might seem like an obvious way to collect geographical information, but in the sixteenth century this idea was entirely novel. It represented a new way of doing geography, one that – like science more generally in this period – relied less and less on ancient Greek and Roman authority.

Poskett p. 41

It would appear that Poskett has never heard of Sebastian Münster and his Cosmographia, published in 1544, probably the biggest selling book of the sixteenth century. An atlas of the entire world it was compiled by Münster from the contributions from over one hundred scholars from all over Europe, who provided maps and texts on various topics for inclusion in what was effectively an encyclopaedia. Münster, who was not a political authority did not send out a questionnaire but appealed for contributions both in publications and with personal letters. Whilst not exactly the same, the methodology is very similar to that used later in 1577 by the Spanish authorities. 

In his conclusion to the section on the New World Poskett repeats his misleading summation of the development of science in the sixteenth century:

Prior to the sixteenth century, European scholars relied almost exclusively on ancient Greek and Roman authorities. For natural history they read Pliny for geography they read Ptolemy. However, following the colonization of the Americas, a new generation of thinkers started to place a greater emphasis on experience as the main source of scientific knowledge. They conducted experiments, collected specimens, and organised geographical surveys. This might seem an obvious way to do science to us today, but at the time it was a revelation. This new emphasis on experience was in part a response to the fact that the Americas were completely unknown to the ancients.

Poskett p. 44

Poskett’s claim simply ignores the fact that the turn to empirical science had already begun in the latter part of the fifteenth century and by the time Europeans began to investigate the Americas was well established, those investigators carrying the new methods with them rather than developing them in situ. 

Following on from the New World, Poskett takes us into the age of Renaissance astronomy serving up a well worn and well know story of non-European contributions to the Early Modern history of the discipline which has been well represented in basic texts for decades. Nothing ‘revolutionary and revelatory’ here, to quote Alice Roberts. However, despite the fact that everything he in presenting in this section is well documented he still manages to include some errors. To start with he attributes all of the mechanics of Ptolemy’s geocentric astronomy–deferent, eccentric, epicycle, equant–to Ptolemy, whereas in fact they were largely developed by other astronomers–Hipparchus, Apollonius–and merely taken over by Ptolemy.  

Next up we get the so-called twelfth century “scientific Renaissance” dealt with in one paragraph. Poskett tells us the Gerard of Cremona translated Ptolemy from Arabic into Latin in 1175, completely ignoring the fact that it was translated from Greek into Latin in Sicily at around the same time. This is a lead into the Humanist Renaissance, which Poskett presents with the totally outdated thesis that it was the result of the fall of Constantinople, which he rather confusingly calls Istanbul, in 1453, evoking images of Christians fleeing across the Adriatic with armfuls of books; the Humanist Renaissance had been in full swing for about a century by that point. 

Following the introduction of Georg of Trebizond and his translation of the Almagest from Greek, not the first as already noted above as Poskett seems to imply, up next is a very mangled account of the connections between Bessarion, Regiomontanus, and Peuerbach and Bessarion’s request that Peuerbach produce a new translation of the Almagest from the Greek because of the deficiencies in Trebizond’s translation. Poskett completely misses the fact that Peuerbach couldn’t read Greek and the Epitome, the Peuerbach-Regiomontanus Almagest, started as a compendium of his extensive knowledge of the existing Latin translations. Poskett then sends Regiomontanus off the Italy for ten years collecting manuscripts to improve his translation. In fact, Regiomontanus only spent four years in Italy in the service of Bessarion collecting manuscripts for Bessarion’s library, whilst also making copies for himself, and learning Greek to finish the Epitome.

Poskett correctly points out that the Epitome was an improved, modernised version of the Almagest drawing on Greek, Latin and Arabic sources. Poskett now claims that Regiomontanus introduced an innovation borrowed from the Islamic astronomer, Ali Qushji, that deferent and epicycles could be replaced by the eccentric. Poskett supports this argument by the fact that Regiomontanus uses Ali Qushji diagram to illustrate this possibility. The argument is not original to Poskett but is taken from the work of historian of astronomy, F. Jamil Ragip. Like Ragip, Poskett now argues thus:

In short, Ali Qushji argued that the motion of all the planets could be modelled simply by imagining that the centre of their orbits was at a point other than the Earth. Neither he nor Regiomontanus went as far as to suggest this point might in fact be the Sun. By dispensing with Ptolemy’s notion of the epicycle, Ali Qushji opened the door for a much more radical version of the structure of the cosmos.[7]

This is Ragip theory of what motivated Copernicus to adopt a heliocentric model of the cosmos. The question of Copernicus’s motivation remains open and there are numerous theories. This theory, as presented, however, has several problems. That the planetary models can be presented either with the deferent-epicycle model or the eccentric model goes back to Apollonius and is actually included in the Almagest by Ptolemy as Apollonius’ theorem (Almagest, Book XII, first two paragraphs), so this is neither an innovation from Ali Qushji nor from Regiomontanus. In Copernicus’ work the Sun is not actually at the centre of the planetary orbits but slightly offset, as has been pointed out his system is not actually heliocentric but more accurately heliostatic. Lastly, Copernicus in his heliostatic system continues to use the deferent-epicycle model to describe planetary orbits.

Poskett is presenting Ragip’s disputed theory to bolster his presentation of Copernicus’ dependency on Arabic sources, somewhat unnecessary as no historian of astronomy would dispute that dependency. Poskett continues along this line, when introducing Copernicus and De revolutionibus. After a highly inaccurate half paragraph biography of Copernicus–for example he has the good Nicolaus appointed canon of Frombork Cathedral after he had finished his studies in Italy, whereas he was actually appointed before he began his studies, he introduces us to De revolutionibus. He emphasis the wide range of international sources on which the book is based, and then presents Ragip’s high speculative hypothesis, for which there is very little supporting evidence, as fact:

Copernicus suggested that all these problems could be solved if we imagined the Sun was at the centre of the universe. In making this move he was directly inspired by the Epitome of the Almagest. Regiomontanus, drawing on Ali Qushji, had shown it was possible to imagine that the centre of all the orbits of the planets was somewhere other than the Earth. Copernicus took the final step, arguing that that this point was in fact the Sun.[8]

We simply do not know what inspired Copernicus to adopt a heliocentric model and to present a speculative hypothesis, one of a number, as the factual answer to this problem in a popular book is in my opinion irresponsible and not something a historian should be doing. 

Poskett now follows on with the next misleading statement. Having, a couple of pages earlier, introduced the Persian astronomer Nasir al-Din al-Tusi and the so-called Tusi couple, a mathematical device that allows linear motion to be reproduced geometrically with circles, Poskett now turns to Copernicus’ use of the Tusi couple. He writes:

The diagram in On the Revolution of the Heavenly Spheres shows the Tusi couple in action. Copernicus used this idea to solve exactly the same problem as al-Tusi. He wanted a way to generate an oscillating circular movement without sacrificing a commitment to uniform circular motion. He used the Tusi couple to model planetary motion around the Sun rather than the Earth. This mathematical tool, invented in thirteenth-century Persia, found its way into the most important work in the history of European astronomy. Without it, Copernicus would not have been able to place the Sun at the centre of the universe.[9] [my emphasis]

As my alter-ego the HISTSCI_HULK would say the emphasised sentence is pure and utter bullshit!

The bizarre claims continue, Poskett writes:

The publication of On the Revolution of the Heavenly Spheres in 1543 has long been considered the starting point for the scientific revolution. However, what is less often recognised is that Nicolaus Copernicus was in fact building on a much longer Islamic tradition.[10]

When I first read the second sentence here, I had a truly WTF! moment. There was a time in the past when it was claimed that the Islamic astronomers merely conserved ancient Greek astronomy, adding nothing new to it before passing it on to the Europeans in the High Middle Ages. However, this myth was exploded long ago. All the general histories of astronomy, the histories of Early Modern and Renaissance astronomy, and the histories of Copernicus, his De revolutionibus and its reception that I have on my bookshelf emphasise quite clearly and in detail the influence that Islamic astronomy had on the development of astronomy in Europe in the Middle Ages, the Renaissance, and the Early Modern period. Either Poskett is ignorant of the true facts, which I don’t believe, or he is presenting a false picture to support his own incorrect thesis.

Having botched European Renaissance astronomy, Poskett turns his attention to the Ottoman Empire and the Istanbul observatory of Taqi al-Din with a couple of pages that are OK, but he does indulge in a bit of hype when talking about al-Din’s use of a clock in an observatory, whilst quietly ignoring Jost Bürgi’s far more advanced clocks used in the observatories of Wilhelm IV of Hessen-Kassel and Tycho Brahe contemporaneously. 

This is followed by a brief section on astronomy in North Africa in the same period, which is basically an extension of Islamic astronomy with a bit of local colouration. Travelling around the globe we land in China and, of course, the Jesuits. Nothing really to complain about here but Poskett does allow himself another clangour on the subject of calendar reform. Having correctly discussed the Chinese obsession with calendar reform and the Jesuit missionaries’ involvement in it in the seventeenth century Poskett add an aside about the Gregorian Calendar reform in Europe. He writes:

The problem was not unique to China. In 1582, Pope Gregory XIII had asked the Jesuits to help reform the Christian Calendar back in Europe. As both leading astronomers and Catholic servants, the Jesuits proved an ideal group to undertake such a task. Christoph Clavius, Ricci’s tutor at the Roman College [Ricci had featured prominently in the section on the Jesuits in China], led the reforms. He integrated the latest mathematical methods alongside data taken from Copernicus’s astronomical tables. The result was the Gregorian calendar, still in use today throughout many parts of the world.[11]

I have no idea what source Poskett used for this brief account, but he has managed to get almost everything wrong that one can get wrong. The process of calendar reform didn’t start in 1582, that’s the year in which the finished calendar reform was announced in the papal bull Inter gravissimas. The whole process had begun many years before when the Vatican issued two appeals for suggestion on how to reform the Julian calendar which was now ten days out of sync with the solar year. Eventually, the suggestion of the physician Luigi Lilio was adopted for consideration and a committee was set up to do just that. We don’t actually know how long the committee deliberated but it was at least ten years. We also don’t know, who sat in that committee over those years; we only know the nine members who signed the final report. Clavius was not the leader of the reform, in fact he was the least important member of the committee, the leader being naturally a cardinal. You can read all of the details in this earlier blog post. At the time there were not a lot of Jesuit astronomers, that development came later and data from Copernicus’ astronomical tables were not used for the reform. Just for those who don’t want to read my blog post, Clavius only became associated with the reform after the fact, when he was commissioned by the pope to defend it against its numerous detractors.  I do feel that a bit of fact checking might prevent Poskett and Viking from filling the world with false information about what is after all a major historical event. 

The section Heaven and Earth closes with an account of Jai Singh’s observatories in India in the eighteenth century, the spectacular instruments of the Jantar Mantar observatory in Jaipur still stand today. 

Readers of this review need not worry that I’m going to go on at such length about the other three quarters of Poskett’s book. I’m not for two reasons. Firstly, he appears to be on territory where he knows his way around better than in the Early Modern period, which was dealt with in the first quarter Secondly, my knowledge of the periods and sciences he now deals with are severely limited so I might not necessarily have seen any errors. 

There are however a couple more train wrecks before we reach the end and the biggest one of all comes at the beginning of the second quarter in the section titled Newton’s Slaves. I’ll start with a series of partial quote, then analyse them:

(a) Where did Newton get this idea [theory of gravity] from? Contrary to popular belief, Newton did not make his great discovery after an apple fell on his head. Instead in a key passage in the Principia, Newton cited the experiments of a French astronomer named Jean Richer. In 1672, Richer had travelled to the French colony of Cayenne in South America. The voyage was sponsored by King Louis XIV through the Royal Academy of Science in Paris.

[…]

(b) Once in Cayenne, Richer made a series of astronomical observations, focusing on the movements of the planets and cataloguing stars close to the equator.

[…]

(c) Whilst in Cayenne, Richer also undertook a number of experiments with a pendulum clock.

[…]

(d) In particular, a pendulum with a length of just one metre makes a complete swing, left to right, every second. This became known as a ‘seconds pendulum’…

[…]

(e) In Cayenne, Richer noticed that his carefully calibrated pendulum was running slow, taking longer than a second to complete each swing.

[…]

(f) [On a second voyage] Richer found that, on both Gorée and Guadeloupe, he needed to shorten the pendulum by about four millimetres to keep it running on time.

[…]

(g) What could explain this variation?

[…]

(h) Newton, however, quickly realised the implications the implications of what Richer had observed. Writing in the Principia, Newton argued that the force of gravity varied across the surface of the planet. 

[…]

(i) This was a radical suggestion, one which seemed to go against common sense. But Newton did the calculations and showed how his equations for the gravitational force matched exactly Richer’s results from Cayenne and Gorée. Gravity really was weaker nearer the equator.

[…]

(j) All this implied a second, even more controversial, conclusion. If gravity was variable, then the Earth could not be a perfect sphere. Instead, Newton argued, the Earth must be a ‘spheroid’, flattened at the poles rather like a pumpkin. 

[…]

(k) Today, it is easy to see the Principia as a scientific masterpiece, the validity of which nobody could deny. But at the time, Newton’s ideas were incredibly controversial.

[…]

(l) Many preferred the mechanical philosophy of the French mathematician René Descartes. Writing in his Principles of Philosophy (1644), Descartes denied the possibility of any kind of invisible force like gravity, instead arguing that force was only transferred through direct contact. Descartes also suggested that, according to his own theory of matter, the Earth should be stretched the other way, elongated like an egg rather than squashed like a pumpkin.

[…]

(m) These differences were not simply a case of national rivalry or scientific ignorance. When Newton published the Principia in 1687, his theories were in fact incomplete. Two major problems remained to be solved. First, there were the aforementioned conflicting reports of the shape of the Earth. And if Newton was wrong about the shape of the Earth, then he was wrong about gravity.[12]

To begin at the beginning: (a) The suggestion or implication that Newton got the idea of the theory of gravity from Richer’s second pendulum experiments is quite simply grotesque. The concept of a force holding the solar system together and propelling the planets in their orbits evolved throughout the seventeenth century beginning with Kepler. The inverse square law of gravity was first hypothesised by Ismaël Boulliau, although he didn’t believe it existed. Newton made his first attempt to show that the force causing an object to fall to the Earth, an apple for example, and the force that held the Moon in its orbit and prevented it shooting off at a tangent as the law of inertia required, before Richer even went to Cayenne.

(c)–(g) It is probable that Richer didn’t make the discovery of the difference in length between a second pendulum in Northern Europe and the equatorial region, this had already ben observed earlier. What he did was to carry out systematic experiments to determine the size of the difference.

(l) Descartes did not suggest, according to his own theory of matter, that the Earth was an elongated spheroid. In fact, using Descartes theories Huygens arrived at the same shape for the Earth as Newton. This suggestion was first made by Jean-Dominique Cassini and his son Jacques long after Descartes death. Their reasoning was based on the difference in the length of one degree of latitude as measured by Willebrord Snel in The Netherlands in 1615 and by Jean Picard in France in 1670. 

This is all a prelude for the main train wreck, which I will now elucidate. In the middle of the eighteenth century, to solve the dispute on the shape of the Earth, Huygens & Newton vs the Cassinis, the French Academy of Science organised two expeditions, one to Lapland and one to Peru in order to determine as accurately as possible the length of one degree of latitude at each location. Re-enter Poskett, who almost completely ignoring the Lapland expedition, now gives his account of the French expedition to Peru. He tells us:

The basic technique for conducting a survey [triangulation] of this kind had been pioneered in France in the seventeenth century. To begin the team needed to construct what was known as a ‘baseline’. This was a perfectly straight trench, only a few inches deep, but at least a couple of miles long.[13]

Triangulation was not first pioneered in France in the seventeenth century. First described in print in the sixteenth century by Gemma Frisius, it was pioneered in the sixteenth century by Mercator when he surveyed the Duchy of Lorraine, and also used by Tycho Brahe to map his island of Hven. To determine the length of one degree of latitude it was pioneered, as already stated, by Willebrord Snell. However, although wrong this is not what most disturbed me about this quote. One of my major interests is the history of triangulation and its use in surveying the Earth and determining its shape and I have never come across any reference to digging a trench to lay out a baseline. Clearing the undergrowth and levelling the surface, yes, but a trench? Uncertain, I consulted the book that Poskett references for this section of his book, Larrie D Ferreiro’s Measure of the EarthThe Enlightenment Expedition that Reshaped the World (Basic Books, 2011), which I have on my bookshelf. Mr Ferreiro make no mention of a baseline trench. Still uncertain and not wishing to do Poskett wrong I consulter Professor Matthew Edney, a leading expert on the history of surveying by triangulation, his answer:

This is the first I’ve heard of digging a trench for a baseline. It makes little sense. The key is to have a flat surface (flat within the tolerance dictated by the quality of the instruments being used, which wasn’t great before 1770). Natural forces (erosion) and human forces (road building) can construct a sufficiently level surface; digging a trench would only increase irregularities.[14]

The problems don’t end here, Poskett writes:

La Condamine did not build the baseline himself. The backbreaking work of digging a seven-mile trench was left to the local Peruvian Indians.[15]

This is contradicted by Ferreiro who write:

Just as the three men completed the alignment for the baseline, the rest of the expedition arrived on the scene, in time for the most difficult phase of the operation. In order to create a baseline, an absolutely straight path, seven miles long and just eighteen inches wide, had to be dug into, ripped up from, and scraped out of the landscape. For the scientists, who had been accustomed to a largely sedentary life back in Europe, this would involve eight days of back breaking labour and struggling for breath in the rarefied air. “We worked at felling trees,” Bouguer explained in his letter to Bignon, “breaking through walls and filling in ravines to align [a baseline] of more than two leagues.” They employed several Indians to help transport equipment, though Bouguer felt it necessary that someone “keep an eye on them.”[16]

Poskett includes this whole story of the Peruvian Indians not digging a non-existent baseline trench because he wants to draw a parallel between the baseline and the Nazca Lines, a group of geoglyphs made in the soil of the Nazca desert in southern Peru that were created between 500 BCE and 500 CE. He writes:

The Peruvian Indians who built the baseline must have believed that La Condamine wanted to construct his own ritual line much like the earlier Inca rulers.[17]

Also:

Intriguingly some are simply long straight lines. They carry on for miles, dead straight, crossing hills and valleys. Whilst their exact function is still unclear, many historians now believe they were used to align astronomical observations, exactly as La Condamine intended with his baseline.[18]

The Nazca lines are of course pre-Inca. The ‘many historians’ is a bit of a giveaway, which historians? Who? Even if the straight Nazca lines are astronomically aligned, they by no means serve the same function as La Condamine’s triangulation baseline, which is terrestrial not celestial.  

To be fair to Poskett, without turning the baseline into a trench and without having the Indians dig it, Ferreiro draws the same parallel but without the astronomical component: 

For their part, the Indians were also observing the scientists, but to them “all was confusion” regarding the scientists’ motives for this arduous work. The long straight baseline the had scratched out of the ground certainly resembled the sacred linear pathways that Peruvian cultures since long before the Incas, had been constructing.[19]

Poskett’s conclusion to this section, in my opinion, contains a piece of pure bullshit.

By January 1742, the results were in. La Condamine calculated that the distance between Quito and Cuenca was exactly 344,856 metres. From observations made of the stars at both ends of the survey, La Condamine also found that the difference in latitude between Quit and Cuenca was a little over three degrees. Dividing the two, La Condamine concluded that the length of a degree of latitude at the equator was 110,613 metres. This was over 1,000 metres less than the result found by the Lapland expedition, which had recently returned to Paris. The French, unwittingly relying on Indigenous Andean science [my emphasis] had discovered the true shape of the Earth. It was an ‘oblate spheroid’, squashed at the poles and bulging at the equator. Newton was right.[20]

Sorry, but just because Poskett thinks that a triangulation survey baseline looks like an ancient, straight line, Peruvian geoglyph doesn’t in anyway make the French triangulation survey in anyway dependent on Indigenous Andean science. As I said, pure bullshit. 

The next section deals with the reliance of European navigators of interaction with indigenous navigators throughout the eighteenth century and is OK. This is followed by the history of eighteenth-century natural history outside of Europe and is also OK. 

At the beginning of the third quarter, we again run into a significant problem. The chapter Struggle for Existence open with the story of Étienne Geoffroy Saint-Hilaire, a natural historian, who having taken part in Napoleon’s Egypt expedition, compared mummified ancient Egyptian ibises with contemporary ones in order to detect traces of evolutions but because the time span was too short, he found nothing. His work was published in France 1818, but Poskett argues that his earliest work was published in Egyptian at the start of the century and so, “In order to understand the history of evolution, we therefore need to begin with Geoffroy and the French army in North Africa.” I’m not a historian of evolution but really? Ignoring all the claims for evolutionary thought in earlier history, Poskett completely blends out the evolutionary theories of Pierre Louis Maupertuis (1751), James Burnett, Lord Monboddo, (between 1767 and 1792) and above all Darwin’s grandfather Erasmus, who published his theory of evolution in his Zoonomia (1794–1796). So why do we need to begin with Étienne Geoffroy Saint-Hilaire?

Having dealt briefly with Charles Darwin, Poskett takes us on a tour of the contributions to evolutionary theory made in Russia, Japan, and China in the nineteenth century, whilst ignoring the European contributions. 

Up next in Industrial Experiments Poskett takes us on a tour of the contributions to the physical sciences outside of Europe in the nineteenth century. Here we have one brief WTF statement. Poskett writes:

Since the early nineteenth century, scientists had known that the magnetic field of the Earth varies across the planet. This means that the direction of the north pole (‘true north’) and the direction that the compass needle points (‘magnetic north’) are not necessarily identical, depending on where you are.[21]

Magnetic declination, to give the technical name, had been known and documented since before the seventeenth century, having been first measured accurately for Rome by Georg Hartmann in 1510, it was even known that it varies over time for a given location. Edmund Halley even mapped the magnetic declination of the Atlantic Ocean at the end of the seventeenth century in the hope that it would provide a solution to the longitude problem. 

In the final quarter we move into the twentieth century. The first half deals with modern physics up till WWII, and the second with genetic research following WWII, in each case documenting the contribution from outside of Europe. Faster than Light, the modern physics section, move through Revolutionary Russia, China, Japan, and India; here Poskett connects the individual contributions to the various revolutionary political movements in these countries. Genetic States moves from the US, setting the background, through Mexico, India, China, and Israel.  I have two minor quibbles about what is presented in these two sections.

Firstly, in both sections, instead of a chronological narrative of the science under discussion we have a series of biographical essays of the figures in the different countries who made the contribution, which, of course, also outlines their individual contributions. I have no objections to this, but something became obvious to me reading through this collection of biographies. They all have the same muster. X was born in Y, became interested in topic Z, began their studies at some comparatively local institute of higher education, and then went off to Heidelberg/Berlin/Paris/London/Cambridge/Edinburg… to study with some famous European authority, and acquire a PhD. Then off to a different European or US university to research, or teach or both, before to returning home to a professorship in their mother country. This does seem to suggest that opposed to Poskett’s central thesis of the global development of science, a central and dominant role for Europe.  

My second quibble concerns only the genetics section. One of Poskett’s central theses is that science in a given epoch is driven by an external to the science cultural, social, or political factor. For this section he claims that the external driving force was the Cold War. Reading through this section my impression was that every time he evoked the Cold War he could just have easily written ‘post Second World War’ or even ‘second half of the twentieth century’ and it would have made absolutely no difference to his narrative. In my opinion he fails to actually connect the Cold War to the scientific developments he is describing.

The book closes with a look into the future and what Poskett thinks will be the force driving science there. Not surprisingly he chooses AI and being a sceptic what all such attempts at crystal ball gazing are concerned I won’t comment here.

The book has very extensive end notes, which are largely references to a vast array of primary and mostly secondary literature, which confirms what I said at the beginning that Poskett in merely presenting in semi-popular form the current stand in the history of science of the last half millennium. There is no separate bibliography, which is a pain if you didn’t look to see something the first time it was end noted, as in subsequent notes it just becomes Smith, 2003, sending you off on an oft hopeless search for that all important first mention in the notes. There are occasional grey scale illustrations and two blocks, one of thirteen and one of sixteen, colour plates. There is also an extensive index.

So, after all the negative comments, what do I really think about James Poskett, highly praised volume. I find the concept excellent, and the intention is to be applauded. A general popular overview of the development of the sciences since the Renaissance is an important contribution to the history of science book market. Poskett’s book has much to recommend it, and I personally learnt a lot reading it. However, as a notorious history of science pedant, I cannot ignore or excuse the errors than I have outlined in my review, some of which are in my opinion far from minor. The various sections of the book should have been fact checked by other historians, expert in the topic of the section, and this has very obviously not been done. It is to be hoped that this will take place before a second edition is published. 

Would I recommend it? Perhaps surprisingly, yes. James Poskett is a good writer and there is much to be gained from reading this book but, of course, with the caveat that it also contains things that are simply wrong. 


[1] James Poskett, Horizons: A Global History of Science, Viking, 2022 

[2] Take your pick according to your personal philosophy of science.

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of botany, History of Cartography, History of Geodesy, History of Islamic Science, History of Navigation, Natural history, Renaissance Science

The sixteenth century dispute about higher order algebraic equations and their solution

The Early Modern period is full of disputes between scholars about questions of priority and accusations of the theft of intellectual property. One reason for this is that the modern concepts of copyright and patent rights simply didn’t exist then, however, that is not the topic of this post. One of the most notorious disputes in the sixteenth century concerned Niccolò Fontana Tartaglia’s discovery of the solution to one form of cubic equation and Gerolamo Cardano’s publication of that solution, despite a promise to Tartaglia not to do so, in his book Artis Magnae, Sive de Regulis Algebraicis Liber Unus, commonly known as the Ars Magna in 1545. A version of this story can be found is every general history of mathematics book and there are numerous versions to be found on the Internet. I blogged about it twelve years ago and maths teacher and historian, Dave Richeson wrote about it just last month in Quanta Magazine

Despite all of this, I am going to review a book about the story that I recently acquired and read, Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation.[1] 

Unlike most of my book reviews this is not a new book, it was originally published in Italian as, La formula segreta, in 2009 and the English translation appeared in 2020. I caught a glimpse of it on the Princeton University Press website at half price in their summer sale and on a whim decided to buy it.[2] I’m glad that I did, as it is an excellent retelling of the story using all of the original documents, which adds a whole new depth to it, not found in the popular versions. 

Toscano’s book, which is comparatively short, has six chapters each of which deals with a distinctive aspect of the sequence of historical events that he is narrating. The opening chapters introduces one of the principal characters in this story Niccolò Fontana, describing his lowly birth, his facial disfigurement delivered by a soldier during the 1512 storm of Brescia, which gave him the stutter by which he was known, Tartaglia. How the autodidactic mathematician became an abaco master, a private teacher of arithmetic, algebra, bookkeeping and elementary geometry.

The second chapter is a brief sketch of history of algebra up to the Renaissance. The elementary nature of ancient Egyptian algebra, the much more advanced nature of Babylonian algebra including the partial general solution of the quadratic equation. Partial, because the Babylonians didn’t acknowledge negative solutions. Here we have one of the few, in my opinion, failures in the book. There is no mention whatsoever of the Indian contributions to the evolution of algebra. This is important as it was Brahmagupta who, in the sixth century CE, introduced the full arithmetic of both positive and negative numbers and the full general solution of the quadratic equation. More importantly the Islamic algebraists took their knowledge of algebra from the Indians and in particular Brahmagupta. Another failure in this section is that Toscano repeats the standard myth of the House of Wisdom. Very positive is the fact that he explains the terminology of rhetorical algebra, the problems are all written out in words not symbols. He also explains that whereas we now just handle quadratic or cubic equations through the general form, in the Renaissance every variation was regarded as a separate equation. So, for example, if the x2 is missing from a cubic equation, this is a new equation that is handled separately. There are in fact, according to Omar Khayyam, fourteen different types of cubic equation. Apart from the omission of Indian algebra this whole chapter is excellent.

Toscano, The Secret Formula page 39

The third chapter takes us to the heart of the story and the event that made Tartaglia famous and would eventually lead to his bitter dispute with Cardano, the public contest with Antonio Maria Fior. In the most influential mathematics book of the era, his Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) published in Venice in 1494, Luca Pacioli (c. 1447–1517) had stated that there was no possible general solution to the cubic equation, Fior had, however, acquired a general solution to the cubic equations of the form x3 + bx = c  and thought he could turn this into capital for his career. He challenged Tartaglia to a public contest thinking he held all the trumps. Unfortunately, for him Tartaglia had also found this solution, so the contest turned into a debacle for Fior and a great triumph for Tartaglia. If you want to know the details read the book. Toscano’s account of what happened, based on the available original sources is much more detailed and informative that the usual ones. We also get introduced to Messer Zuanne Tonini de Coi, another mathematician, who doesn’t usually get mentioned in the general accounts of the story but who plays a leading role in several aspects of it. Amongst other things, he was the first who tries to get Tartaglia to divulge the partial solution of the cubic that he has discovered, and it was he, who he first told Cardano about Tartaglia’s discovery.

In chapter four we meet the villain of the story the glorious, larger than life, Renaissance polymath, Gerolamo Cardano. We get a sympathetic description of Cardano’s less than auspicious origins and his climb to success as a physician against all the odds. Toscano does not over emphasise Cardano’s oddities and he had lots of those. We now get a very detailed account, once more based on original documents, of Cardano’s attempts to woo Tartaglia and seduce the secret of the partial cubic solution out of him. Cardano’s seduction was eventually successful, and he obtained the solution but only after swearing a solemn oath to reveal the solution to nobody until Tartaglia had published in his planned book. 

Chapter five takes us to Cardano’s breaking of that oath, his, I think justifiable reasons for doing so, and Tartaglia’s understandable outrage. The chapter opens with more exchanges about Tartaglia’s solution, which Cardano hasn’t truly understood, because of an error in Tartaglia’s encrypted poetical revelation of it. Having cleared this up Tartaglia begins to panic because Cardano is planning to publish a maths book his, Practica arithmetice et mensurandi singularis (The Practice of Arithmetic and Simple Mensuration), and he fears it will include his solution, it didn’t, panic over for now. We now get introduced to Cardano’s brilliant pupil and foster son, Lodovico Ferrari. Between the two of them, starting from Tartaglia’s solution, they find the general solutions of the cubic and the quartic or biquadratic equations putting algebra on a whole new footing but are unable to publish because of Cardano’s oath to Tartaglia. However, in 1542, Cardano and Ferrari travelled to Bologna and discovered in a notebook of Scipione Dal Ferro Tartaglia’s partial solution of the cubic made twenty years earlier than Tartaglia and obviously the source of Fior’s knowledge of the solution. Cardano no longer felt constrained by his oath and in 1545, his Ars Magna was published by Johannes Petreius in Nürnberg, containing all the algebra that he and Ferrari had developed but giving full credit to Scipione Dal Ferro and Tartaglia for their contributions. Tartaglia went ballistic!

The closing chapter deals with the final act, Tartaglia’s indignation over what he saw as Cardano’s treachery and the reaction to his accusations. Tartaglia raged and Cardano remained silent. Although, he had been very vocal in obtaining the cubic solution from Tartaglia, Cardano now withdrew completely from the dispute, leaving Ferrari to act as his champion. Tartaglia and Ferrari exchanged a total of twelve pamphlets, six each, full of polemic, invective, accusations, and challenges. Tartaglia trying, the whole time, to provoke Cardano into a direct response, accusing him of ghost-writing Ferrari’s pamphlets. Ferrari, in turn, constantly challenged Tartaglia to a face-to-face public confrontation, which he steadfastly rejected. Toscano reproduces a large amount of the contents of those pamphlets, upon which he judiciously comments. It is this engagement by the author that makes the book such a good read. Tartaglia finally caved in, probably as a condition of a new job offer, and met Ferrari in the public arena in Milan, fleeing the city on the evening of the first day of the confrontation, his reputation in tatters. What exactly took place, we don’t know, as Cardano and Ferrari never commented on the meeting, and we have only Tartaglia’s account that relates that he realised that the crowd was stacked against him with Ferrari’s supporters, and he could never win and so he departed.

Given the nature of the book, it has no illustrations. However, given the authors extensive use of both primary sources as well as authoritative secondary sources, it has an impressive number of endnotes, unfortunately not footnotes. Most of these are simple references to the source quoted and here the book uses a convention that I personally dislike. These references are mostly just something like [21.e]. The authors in the bibliography are sequentially numbered and if the author of more than one text these are identified by the small case letters. So, you are interested in the origin of a quote, you go to the endnotes, find there such a number, and then leaf through the bibliography to find out who, what, why, where! I do not like! Many of the items in the bibliography are texts from Italian historians, so the English edition has a short, but high quality, extra list of English titles on the topic. There is an excellent index.

It may seem that I have revealed too much of the contents of the book to make it worth reading but I have only sketched the outline of the story as it appears in the book, a story, which as I said at the beginning is very well know, the devil is as they say in the detail. By his very extensive use of the original sources, Toscano has given the popular story a whole new dimension, making his book a totally fascinating read for anybody interested in the history of mathematics. His book is also a masterclass in how to write high quality popular history of mathematics. 


[1] Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation, Translated by Arturo Sangalli, Princeton University Press, Princeton and Oxford, 2020

[2] More accurately the dastardly Karl Galle drew my attention to it, and I couldn’t resist the temptation, as it was not only cheap but came with free p&p. When I ordered it, I had forgotten that PUP distribute their book in Europe out of the UK. I try to avoid ordering books from the UK because, since Brexit, I now have to pay customs duty on book from the UK, on top of which the German postal service adds a €6 surcharge for paying the customs duty in advance, this would, in this case almost double the cost of the book. Normally, when I receive books from the UK, I get a note in my post box and have to go to the post office to pay the money due and pick up the book. For some reason, in this case, the postman simply delivered the book despite the label saying how much I was supposed to pay and so I didn’t have to pay it. You win some, you lose some!

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Filed under Book Reviews, History of Mathematics, Renaissance Science

Astrology, data, and statistics

Is western astrology a big data science, or even the very first big data science? Data scientist Alexander Boxer thinks it is and has written a book to back up his claim, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data.[1] 

His justification for having written this book is interesting:

Over two thousand years ago, astrologers became the first to stumble upon the powerful storytelling possibilities inherent in numerical data, possibilities that become all the more persuasive when presented graphically in a chart or figure. Although it took a while for the rest of the world to catch on, the art of weaving a story out of numbers of figures, often a specific course of action, is used everywhere today, from financial forecasts to dieting advice to weather models.

And yet numbers still mislead, figures still mislead, figures still deceive, and predictions still fail–sometimes spectacularly so–even those that rely on exceptionally sophisticated mathematics. So, are the techniques being used today to parse and package quantitative information any more effective that what was devised by astrologers millennia ago?

            In order to make that assessment, it’s first necessary to have a basic understanding of what astrology is and how it works. But that sort of understanding–one that’s at least adequate to resolve some seemingly straightforward technical questions–is surprisingly hard to come by for such a long-lived and influential craft. Being frustrated in my own search for a simple yet competent overview of astrology, I decided I might just as well write one myself. This, curious reader, is the book you now hold in your hands.

Boxer is actually correct “a simple yet competent overview of astrology” doesn’t, as far as I know, exist, so has he succeeded in providing one? My answer is a qualified “yes, no, maybe, probably not!” Large parts of Boxer’s book are excellent, other parts are OK, some parts I found simply baffling, and one of his central claims is simply wrong. The biggest problem with the book, as far as I’m concerned, is that it tries to be too many different things in far too few pages. It wants to be a history of astrology from its beginnings down to the present days, at the same time being a data scientist’s, statistical analysis of fundamental aspects of astrology, as well as presenting a quasi-philosophy of science meta-analysis of some central themes of astrology, and that all whilst attempting to achieve to authors declared central aim of providing “a simple yet competent overview of [western][2] astrology.” All of this in just 263 pages of an octavo book with a medium typeface. He also largely leaves out any serious attempt to present the interpretation of a horoscope, which is actually the essence of astrology.

The excellent bits of Boxer’s book are almost all confined to the technical and mathematical aspects of casting a horoscope and to the data scientist’s statistical analysis of various aspects of astrology. There is for example a competently presented, entire chapter devoted to the nuts and bolts of mathematical astronomy, without which it is impossible to actually cast a horoscope. However, this illustrates one, in my opinion serious error in the book. In the opening chapter Boxer presents a brief greatest hits tour of what he labels the obscure beginnings of astrology. I’ve read accounts of the material he presents here that are longer than his entire book, to which I’ll return in a minute, but that is not what concerns me at the moment. Here he presents for the second time (the first one in in the introduction) one of the excellent illustrations that occur throughout the book. This is a horoscope presented on the mater and tympan of an astrolabe without the rete but with the ecliptic. Also presented are all of the relevant astronomical data, time, in various formats, celestial coordinates in all three variants, geographical coordinates and so forth. See below:

However, there is absolutely no explanation of what is being presented here. Now, I’ve spent a number of years studying this stuff, so I know roughly what I’m looking at, although I need to look up which celestial coordinate system is which, for example. A naïve reader coming to this book to learn about astrology would have no idea what they are looking at and nowhere in the book do they get this diagram explained carefully step for step. The knowledge required is contained in the book, scattered around in various sections and chapters but with no linking references to the diagrams. The celestial coordinates are, for example, explained in the chapter on mathematical astronomy, whereas the astrolabe only gets explained in dribs and drabs about one hundred pages later in the book. The Julian Day Count, one of the methods listed on the diagram to denote the time of the horoscope only gets explained on pages 225-226! The information needed to understand what is in fact an excellent diagram is scattered throughout the book like a scavenger hunt without rules or clues.

Remaining by the topic, the book is liberally illustrated with diagrams and tables to explain themes under discussion, and these are excellently done both from a pedagogical and a graphical viewpoint and this is one of the great strengths of the book. There is not a conventional bibliography but at the end of the book there is an annotated collection of source material for each section of the book. There is also a competent index. 

Following up on the all too brief sketch of the origins of western astrology and the more comprehensive introduction to the basics of astronomy, Boxer now dives into what is without doubt one of the greatest error in the book, he fell in love with Marcus Menilius’ Astronomica. After briefly dismissing our knowledge of astronomy in the last five centuries BCE, a serious error because we actually know far more that Boxer is prepared to admit. However, if he did acknowledge it, he would have to abandon his love affair with Manilius. Boxer correctly explains that although the Roman took over large parts of Alexander’s Hellenistic Empire, they were initially reluctant to adopt the Hellenistic astrology. He illustrates this with the fact that there are absolutely no astrological discussions of Julius Caesar’s assassination in 44 BCE. Enter Marcus Manilius and his Astronomica stage left. 

A brief explanation, the Astronomica is a Latin didactic poem dating to the early first century CE, which happens to be the earliest surviving, relatively complete account of western astrology.  About its probable author Marcus Manilius, we know next to nothing. 

Boxer goes complexly overboard about the Astronomica. He writes:

The Astronomica is a fascinating work in its own right, but it takes on a special significance when we recognise that this poem is, essentially, astrology’s grand unveiling on the historical stage. And like Minerva issuing from Jupiter’s skull fully grown and clad in armour, the Astronomica presents an astrology emerging from obscurity remarkably complete and fully formed. Even today, two thousand years later, there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem.

If the Astronomica is “astrology’s grand unveiling on the historical stage” then it must have got lousy reviews from the critics. Not one single author in antiquity is known to have quoted the Astronomica. There are a grand total of about thirty existing medieval manuscripts of the work none of them older than the ninth century CE. It does not feature in any other medieval literature and appears to have been largely ignored in the Middle Ages. It was (re)discovered in c. 1416 by the zealous Renaissance Humanist manuscript hunter, Poggio Bracciolini (1380–1459) and only really emerged on the European literary and scientific stage when the editio princeps was published by Regiomontanus (1436–1476) in Nürnberg in 1473. 

In his love affair with the Astronomica, Boxer seems to think that modern horoscope astrology is somehow a Roman invention. Later in the book when taking about Arabic astrology he describes Masha’allah’s theory of astrological historical cycles as the “most significant addition to astrology since Roman times.” Manilius is in fact merely describing an existing system that was created by the Hellenistic Greeks between the fifth and first centuries BCE, something that Boxer acknowledges elsewhere in his book, when he goes overboard about the wonders of ancient Alexandria.

As for the guff about “astrology emerging from obscurity remarkably complete and fully formed” and “there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem,” as already stated Manilius is reporting on an existing system not creating it. More importantly as the modern commentators point out you wouldn’t be able to cast a horoscope having read it and it contains nothing on planetary influence in astrology, the very heart of the discipline.  In fact, although they adopted astrology and used it widely until the decline of the Empire, in the sixth century, the Romans actually contributed next to nothing to the history of astrology.

However, the chapter ends with an example of Boxer’s biggest strength the data based statistical analysis of various aspect of astrology. He starts here with the personality traits that Manlius attributes to those born under a particular sun sign, setting them out in a handy table first. Using the data of different professional groups, he introduces the reader to the concept of statistical significance and shows that the astrological divisions into personality types doesn’t hold water.

Next up we have Ptolemy the most significant author in the whole of the history of western astrology. He gives an adequate sketch of Ptolemy’s contributions to astronomy, geography and astrology and shows that they are actually three aspects of one intellectual project. In his brief discussion of map projection, he makes not an error, but a misleading statement. Introducing Ptolemy’s Planisphere and the stereographic projection the key to the astrolabe he writes:

For the basic idea of a stereographic projection, imagine looking down on a globe from above its North Pole [my emphasis], and then squashing in into the equator. The visual effect ends up looking like a scoop of ice cream that’s melted onto a warm plate from the bottom out. Because there’s no limit to how far outward these maps spread, it’s customary to extend them only as far as the Tropic of Capricorn.

The following pages contain stereographic projections of the celestial sphere, the terrestrial sphere and four tympans from astrolabes taken for different latitudes. Boxer’s error is that these are taken from the South Pole as projection point. Almost all astrolabes are for the Northern Hemisphere and are projections from the South Pole, there are only a handful of Southern Hemisphere astrolabes with the North Pole as projection point. 

Boxer also makes an error in his etymology of the Name Almagest for Ptolemy’s Mathēmatikē Syntaxis. Almagest comes from the Arabic al-majistī, which in turn comes from the Greek megiste all of which mean the greatest. Boxer justifies this as follows:

The Almagest was the greatest of all ancient treatises on astronomy, just as Ptolemy was the greatest of ancient astronomers.

In fact, all of this derives from the alternative Greek name of the Mathēmatikē SyntaxisHē Megalē Syntaxis meaning The Great Treatise as opposed to a smaller work by Ptolemy on astronomy known as The Small Treatise. In other words, the Almagest is the big book on astronomy as opposed to the small book on astronomy.

Boxer has a rather negative opinion of Ptolemy’s Apotelesmatika commonly called the Tetrabiblos in Greek, or Quadripartitum in Latin, meaning four books, his big book on astrology. He finds it dry, technical, and uninspiring, unlike the Astronomica. After introducing Ptolemy’s astrological geography Boxer once again applies his statistical analysis to Ptolemy’s claims on the geographical acceptance of homosexuality comparing it with the modern data on the topic.

Boxer’s next target is the only substantial collection of actual horoscopes from antiquity, by the second century Hellenistic astrologer, Vettius Valens’ Anthologies. We move from the theoretical, Ptolemy, to the practical, Valens. Here Boxer once again reverts to his role as data scientist and gives an interesting seminar on the theme of “how unique is a horoscope? Along the way he sings a brief eulogy for ancient Alexandria as a centre for the mathematical sciences including of course astrology. He also makes a brief excursion into the philosophy of science evoking the falsifiability criterion of Karl Popper and the separation of science and pseudoscience, a couple of pages that are far too brief for what is a very complex discussion and could have been happily edited out. His work, however, on codifying the basics of a horoscope according to Valens and examining the uniqueness of the result is stimulating and a high point of the book.

Next, Boxer moves onto medieval Arabic astrology but doesn’t really. He starts, as do many authors on this topic, with the horoscopes cast to determine the right time to found the city of Baghdad and having given a brief but largely correct account of why the Abbasid caliphs adopted astrology, and the parallel transmission of astrology into Europe in the High Middle Ages, he then passes rapidly to Masha’allah’s theory of historical cycles based on the conjunctions of Jupiter and Saturn and that’s it! Arabic astrology is a massive topic and given its powerful influence on astrology as its practiced today deserves much more attention in any book claiming to provide a “simple yet competent overview of astrology.” Once again, the chapters strength lies in Boxer’s statistics-based analysis of Masha’allah’s theory, which drifts off into the theories of encryption. One thing that did piss me off was in a discussion of the use of symbols he writes:

By necessity, then, efficacy of this magic will hinge upon the fitness of these symbols to their task: Nowhere is this more evident than in mathematics. (If you don’t believe me, try adding the Roman numerals CXXXIX and DCXXIII together; or, even worse, the Greek numerals 𝛒𝛌𝛉 and 𝛘𝛋𝛄.)

This is pure bullshit! Assuming that you are cognisant with the numeral systems and the values of the symbols than these additions are no more difficult than carrying out the same sums using Hindu-Arabic numerals. Division and multiplication are, at least at first glance, more difficult but there are algorithms for both numerical systems that also make those operations as easy as the algorithms for Hindu-Arabic numerals. The major point, however, is that nobody bothered; arithmetical calculations were carried out using an abacus and the numerals were only used to write down the results. 

Having very inadequately dealt with Arabic astrology, Boxer now turns to Guido Bonatti (died around 1300). Before he gets to him, we get a brief section on the transmission from Arabic into Latin where Boxer manages to conflate and confuse two periods of translation in Toledo, one of the major centres for that work. In the twelfth century translators such as Gerard of Cremona translated the major Greek scientific works from Arabic into Latin often with the help of Jewish intermediaries. Later in the thirteenth century Alfonso X of Castille set up a school of translators in Toledo translating Hebrew and Arabic texts into Latin and Castilian, establishing Castilian as a language of learning.  Boxer goes off into an unfounded speculation about texts being translated from Greek into Syriac into Arabic into Hebrew into Castilian (here Boxer incorrectly uses the term Spanish, a language that didn’t exist at the time) into Latin, with all the resulting errors. This paragraph should have been thrown out by a good editor. We then get a couple of paragraphs of waffle about the medieval universities that appears to exist purely to point out that Abelard and Héloïse named their son astrolabe. These should have been replaced with a sensible account of the medieval universities or thrown out by the same good editor. 

We then get an account of the twelfth and thirteenth centuries war between the Guelphs and Ghibellines in Northern Italy largely to introduce Guido Bonatti, who was a Guelph astrologer and author of the Liber Astronomiae, which Boxer tells us, hyperbolically, is the most influential astrology book of the Middle Ages. Here Boxer makes two major errors. Firstly, he presents judicial astrology, which he defines as follows:

The basic premise of judicial astrology is that you ask the stars a question–a question about pretty much anything–and the stars then reveal a judgement or, in Latin, iudicium. The astrologer’s job is to interpret these judgements on your behalf. So far, so good. The odd thing about judicial astrology, however, was that for many questions, and especially the broad category of yes-or-no questions, the astrologer would determine the stars’ judgement based on their positions in the sky at the moment your question was asked.

What Boxer is actually describing is horary astrology, just one of the four branches of judicial astrology, the other three are natal astrology, mundane astrology, and elective astrology; Boxer goes on later to discuss elective astrology. Judicial astrology was opposed to natural astrology, which meant astrometeorology and astromedicine, or to give it its proper name iatromathematics, neither of which Boxer deals with, in any depth, just giving a two-line nod to astromedicine. 

Having described horary astrology, albeit under the wrong label, Boxer goes off on a rant how ridiculous it is/was. Then come two more misleading statements, he writes:

Yet however ho-hum this fatalistic outlook may have been during astrology’s early days in Stoic Rome, to deny the existence of free will was a decidedly and damnably heretical opinion in medieval Christian Europe.

[…]

As was obvious to Dante. Petrarch, and many others, astrology–and especially judicial astrology–was fundamentally incompatible with Christian doctrine. 

First off, Stoic Rome was not astrology’s early days, by that time Hellenistic astrology had been around for about four to five hundred years. Yes, Hellenistic astrology was totally deterministic and did in fact clash with the Church doctrine of free will in the beginnings of the High Middle Ages. However, Albertus Magnus and Thomas Aquinas, who laid the foundations of Church doctrine down to the present day, redefined astrology in their writings in the thirteenth century, as acceptable but non-deterministic thus removing the doctrinal clash. In terms of the impact of their work for the acceptance of astrology not just in the Middle Ages, surely it is far more influential than Bonatti’s Liber Astronomiae.

In the passage that I left out of the quote above Boxer writes, amongst other things:

Well, that’s the sort of thinking that could get you burnt at the stake in you insisted on making a fuss about it. The astrologer Cecco d’Ascoli was condemned by the Inquisition on precisely these grounds and burnt at the stake in Florence on September 16, 1327. [i.e., for practicing deterministic astrology]

This is simply not true! In 1324, Cecco d’Ascoli was admonished by the Church and punished for his commentary on the Sphere of John de Sacrobosco, nothing whatsoever to do with astrology. To avoid his punishment he fled from Bologna, where he was professor for astrology, to Florence. Here, he was condemned for trying to determine the nativity of Christ by reading his horoscope, and as a repeat offender was burnt by the Inquisition. Even under the non-deterministic interpretation of judicial astrology from Albertus Magnus and Thomas Aquinas, casting the horoscope of Christ was considered unacceptable. 

Next, Boxer introduces the Houses of Heaven and claims that, “these are astrology’s system of local coordinates the astrological analog to the modern-day quantities azimuth an elevation.” Sorry but this statement is garbage the houses are not a coordinate system, they are divisions of the ecliptic plane. Boxer introduces them here because they play a central role in Bonatti’s horary astrology. Once again Boxer the data scientist comes to the fore with the question whether it would be possible to construct an algorithm to automatically answer questions posed in horary astrology. As usually one of the best parts of the book.

Traditionally, one of the major disputes amongst astrologers in the question how exactly to determine the boundaries of the houses and Boxer now turns his attention to the various solutions presenting nine different solutions that have been used at some time in the history of astrology. 

One system that was very popular in the Renaissance and Early Modern Period was devised by Regiomontanus (1436–1476), which Boxer looks at in somewhat more detail. He starts with a very brief rather hagiographical biographical sketch, which includes the following claim:

By the time he was twenty-six, Regiomontanus had finished a complete reworking Ptolemy’s Almagest using all the newest trigonometrical methods. 

The Epitome of the Almagest was commissioned from Georg von Peuerbach, Regiomontanus’ teacher, and later colleague, by Cardinal Basilios Bessarion in 1460. Peuerbach had only completed six of the thirteen books by 1461 when he died. On his death bed he commissioned Regiomontanus to complete the work. Regiomontanus went off to Italy with Bessarion, basically as his librarian, and spent the next four years travelling through Italy collecting and copying manuscripts for Bessarion’s library. During this time, he probably completed the Epitome. Meaning he was twenty-nine. Although he might have finished it during the next two years, when we don’t know where he was or what he was doing. He intended to publish the finished book when he set up his publishing house in Nürnberg in 1471 but still hadn’t by the time he died in 1476. It was first published by Johannes Hamman in Venice in 1496

Further on Boxer writes:

Thus, when a certain archbishop in Hungary demanded an improved system for determining the Houses of Heaven–in particular one that would be more faithful to the vague instructions given by Ptolemy in his Tetrabiblos–there was only one person to ask.

            Regiomontanus accepted the challenge. In a brash and masterly treatise, he surveyed the existing methods of House division, dismissed them all as inadequate, introduced an entire new method, and provided tables for computing their boundaries at any latitude to the nearest minute of arc.

A nice story but unfortunately not exactly true. The title of the book that Regiomontanus wrote at the request, not demand, of János Vitéz Archbishop of Esztergom, for whom he had been working as a librarian since 1467 was his Tabulae directionum profectionumque. The purpose and content of the book is revealed in the title, this is not a book about the determination of the Houses, which are only secondary product of the book but about calculating directions, also called prorogratio or progression from the original Greek aphesis. A method to determine major events in the life of a horoscope subject including their death, described by Ptolemy in the Tetrabiblos, which was very popular in Renaissance astrology. 

This error by Boxer is rather bizarre because he describes the method of aphesis, albeit wrongly, whilst dealing with Manilius earlier in his book. Here he writes:

…a procedure … entailed identifying two key points on a birth horoscope: the “starter” and “destroyer.” As time elapsed from the moment of birth, the destroyer revolved along with the heavens towards the starters original position, all the while shooting evil rays at it. When the destroyer finally reached the starter, it was game over: death. The number of hours and minutes it took for the destroyer to reach the starter was then converted to the number of years and months the individual was expected to live.

A very colourful description but actually fundamentally wrong. First the astrologer has to determine the starter on the ecliptic, which is often the moment of birth but not necessarily. Then various destroyers are identified signalling major events in the life of the subjects not just their death, also on the ecliptic. Both points, started and destroyer are projected using spherical trigonometry onto the celestial equator and the number of degrees between the projected points is the time in years. Regiomontanus’ Tabulae directionum provide the mathematical apparatus to carry out this not particularly simple mathematical process. 

Which system of Houses division is still disputed amongst astrologers and Boxer possesses the impertinence to suggest they should use a particular system because he finds it mathematically the most elegant. 

The chapter closes with a short discourse on time, unequal hours, and equinoctial hours, which serves two functions to introduce the index or rule on the astrolabe which makes possible the conversion between unequal and equal hours. Boxer then states:

That the development of the mechanical clock occurred precisely when the most intricate astrological algorithms were in vogue is a historical synchronicity too striking to ignore.

[…]

In fact, the technological crossover between astrology and clock design was significant.

Here he is referring back to an earlier statement on the previous page:

This is why the earliest mechanical clocks of which the one in Prague’s old town square is the most magnificent example had astrolabe-style faces.

Source: Wikimedia Commons

Unfortunately for Boxer’s enthusiasm David S Landes, a leading historian of the clock, argues convincingly that the simple mechanical clock with a “normal” clock face preceded the astrolabe-style clock faces.

The next chapter opens with Tycho Brahe and the nova of 1572. Here once again Boxer choses to distort history for dramatic effect. He writes:

Yet, by all accounts, Tycho wanted nothing to do with Denmark’s administration, its wars, its politics, or its pageantry.

            For a nobleman like Tycho, the purpose of a university education was not to obtain a degree–that would have been unthinkably déclassé–but merely to pick up a little worldly polish of the sort that might prove serviceable in war and diplomacy. In this respect, Tycho’s education backfired spectacularly. He returned from Germany utterly captivated by the latest advances in alchemy, astronomy, and astrology.

Boxer carries on in this manner presenting Tycho as a rebel kicking against the pricks. What he neglects to mention is that although Tycho’s decision to become a professional astronomer was somewhat unorthodox, in all his endeavours Tycho received strong support from his maternal uncle Peder Oxe. Oxe was a university graduate, and a strong supporter of Paracelsian alchemical medicine, who just happened to be the Danish finance minister and Steward of the Realm, de facto prime minister, and politically by far the most powerful man in the whole of Denmark. 

Boxer closes his short section on Tycho with another piece of purple prose:

Tycho’s supernova is of tremendous historical importance because it was the first detailed observation which the old cosmological framework simply could not explain away. Something was rotten in the state of astronomy indeed. Tycho’s new star was a small crack in what had been considered a pristine crystalline firmament. There would be others–so many, in fact, that the entire system would soon collapse and shatter. It wasn’t just the heavens which had proven themselves mutable. A revolution was underway, and science, philosophy astronomy–and astrology–would never be the same.

The immutability of the heavens had been discussed and disputed by astronomers throughout Europe with respect to comets (sub– or supralunar?) since Paolo dal Pozzo Toscanelli (1397–1482) viewed them as supralunar based on his observations of the comet of 1456. The observations and reports of the 1572 supernova by many European astronomers only increased an ongoing debate. A debate that was only one part of a general trend to reform astronomy, which started around 1400 and in which everything was up for discussion. The period also saw a revival of Stoic philosophy and cosmology contra Aristotelian philosophy and cosmology. The supernova of 1572 was not the dramatic turning point that Boxer paints it as.

Boxer now delivers, what I regard as the absolute low point of the book, in that he presents the hairbrained theory of Peter Usher that Shakespeare’s Hamlet is “an elaborate astronomical analogy.” He does however backpedal and state, “I enjoy reading this quite a bit, even if I don’t find it very persuasive.” So, why include it at all?

We then move on to a very rapid sketch of the so-called astronomical revolution with the usual Copernicus=>Tycho/Kepler=>Galileo=>Newton cliché. Boxer now allows himself a real humdinger:

            Clearly Tycho’s commitment to a geocentric cosmos ran much deeper than astronomical arguments alone. IN fact, so central was the Earth’s fixity to Tycho’s philosophy that he proposed a compromise cosmology, one in which Mercury, Venus, Mars, Jupiter, and Saturn orbited the Sun, as in the Copernican system, but the Sun and Moon orbited the Earth as in the Ptolemaic system. It sounds ungainly, and Tycho may have been the only person who ever thought otherwise… [my emphasis].

Tycho may have been the only person? A handful of astronomers all independently came up with the so-called Tychonic geo-heliocentric system around the same time, as an alternative to the Copernican system, leading Tycho to accuse others of plagiarism. From about 1620 till about 1660 the majority of European astronomers thought a Tychonic model with diurnal rotation was the most probable system for the known universe.

Boxer finally gets back on course with the next section where he investigates the use of the words, astronomy, astrology, and mathematics to describe either astronomy or astrology as we know them. A very well-done section. This is followed by a section on the Gregorian calendar reform and why it was necessary, relatively good except for a false claim about Copernicus. He writes:

Copernicus cited the prospect of a more accurate calendar as one reason why he hoped (quite wrongly) that his new, Sun-centered theory of the universe might be well received by the Church.

I have no idea where Boxer found this but it’s simply not true. Copernicus’s only connection with the calendar reform was when he was approached around 1520, like many other European astronomers, to contribute to the calendar reform, he declined, stating that one first needed to accurately determine the length of the year. The chapter closes with a brief account of Kepler’s attitude and contributions to astrology, which falsely claims that he rejected astrology at the end of his life. He didn’t, he rejected traditional horoscope astrology most of his life, although he earned money with it, but believed till the end in his own system of celestial influence.

The final section of the book deals with modern forms of astrology. We have the Madame Blavatsky’s Theosophical Society and her creation of spiritual astrology. The creation of the popular twelve-paragraph newspaper horoscope and finally the creation of psychological astrology, first by the theosophist Alan Leo and developed further by psychoanalyst Carl Jung. Here Boxer delivers, what I regard as the biggest error in his entire book. He writes:

Yet the converse opinion–that every good astrologer must also be a good psychoanalyst–is pretty much the default amongst modern astrologers and their clients alike. For the professional astrologer, this represents a tremendous job promotion. A classical astrologer was, first and foremost, a human calculator, one whose most important qualification was his ability to solve long and tedious mathematical equations. [My emphasis]

Here Boxer, the mathematician, shows that he has literally not understood the difference between casting a horoscope and interpreting a horoscope. In fact, in his book he never really addresses the interpretation of horoscopes, which is the real work of a classical astrology. From the few hints that Boxer gives when discussing horary astrology (which he falsely labels judicial astrology) and elective astrology, he appears to think that you just plug in the planetary positions and the horoscopic spits out the interpretation algorithmically. Nothing could be further from the truth. 

Ptolemy writes at the beginning of the Tetrabiblos, I paraphrase, the science of the stars has two aspects, the first deals with the positions of the stars [our astronomy, his Almagest] and is precise, the second deals with their influence [our astrology, his Tetrabiblos], which is not precise. The first involves casting horoscopes and is mathematical, the second with their interpretations and is not mathematical.

If an astrologer, let us say in the sixteenth century the golden age of astrology, casts a full birth horoscope with planetary positions, houses, aspects, lunar nodes (which Boxer doesn’t deal with as being unnecessarily confusing, directions (explained wrongly by Boxer), lots of fortune (which he doesn’t even mention), etc. You have a very complex collection of material that has to be weighed up very carefully against each other. It is highly unlikely that any two professional astrologers would give the same interpretation, each arguing for their interpretation and explaining why the other interpretation is wrong. Very much of this art of interpretation is based on simplel psychology. A court astrologer, who is basically a political advisor, is going to include many psychological, political, and social factors into the interpretation that he delivers up for employer. 

I recently copyedited the translation of a chapter from a thirteenth century Arabic treatise on astrology that dealt with the interaction of the lunar nodes with the houses when practicing elective astrology. The complexity of the interpretive factors that have to be taking into consideration is mindboggling, so please don’t claim that “a classical astrologer was, first and foremost, a human calculator,” it simply isn’t true. 

If you have read this far you might come to the conclusion that my opinion of Boxer’s book is entirely negative, it isn’t. I think there is an excellent, interesting, and important book struggling to get out of a pool of confusion. Boxer’s strength is that of the data scientist and statistician and his sympathetic to astrology statistical analyses of various aspect of astrology are excellent and very much worth reading for anybody interested in the topic. His book cannot be considered a history of western astrology as he simply leaves much too much out. In fact, it is clear that those things he chooses to include are those that give him the possibility to apply his statistical analysis. Is it a “competent overview of astrology”? No, he leaves too much out, for example any competent overview of astrology must include the lunar nodes and their function in astrology and makes too many errors in his presentations of both the history of astrology and astronomy. Most importantly astrology is about the interpretation of horoscopes, a topic that he does his best to avoid.


[1] Alexander Boxer, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data

[2] Although he constantly refers to astrology rather than western astrology, he does state that his book doesn’t deal with other forms of astrology such as Indian or Chinese. 

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Filed under Book Reviews, History of Astrology, History of Astronomy

Around the World in One Thousand and Eighty-three Days 

Growing up in the UK in the 1950s, history lessons in primary school, that’s elementary school for Americans, still consisted to a large extent of a glorification of the rapidly fading British Empire. The classroom globes were still covered in swathes of pink and there, at least, the sun never set on the empire that was. Another popular theme, in this collection of fairy tales and myths, was the great period of European exploration and discovery in the Early Modern Period, in which Columbus, Vasco da Gama and Magellan were presented as larger than life, heroic, visionary adventurers, who respectively discovered America, became the first European to sail to India, and, perhaps the greatest achievement of all, circumnavigated the globe. 

At grammar school history became modern European history–Napoleon, Vienna Conference, Franco-Prussian War, unification of German, First World War, rise of Fascism and Hitler, and Second World War–my generation was after all born in and grew up in the aftermath of WWII. The “heroes” of the so-called age of discovery faded into the background, becoming nothing more than a handful of half-remembered facts–1492 Columbus sailed the ocean blue. Somewhere down the line those early tales of daring do became tarnished by inconvenient facts, such as the information that the Vikings almost certainly got to America before Columbus or that Vasco da Gama only managed to sail from Africa to India because he employed a local navigator, who knew how to get there. On the whole it was not a topic that particularly interested me in the early part of my adult life. As far as history went, it didn’t seem to me at that time to be part of the history of mathematics, boy was I wrong on that, so I largely ignored it. 

However, I was aware of the gradual dethroning of Columbus, who having been appointed governor by the Spanish Crown of the islands he had discovered was later stripped of his title because of incompetence and brutality towards the indigenous population. Also, that de Gama had had to use military force to persuade the Indians to trade with him. These men were not the saints they had been painted as in my youth. However, through it all Magellan remained a heroic role model, the first man to circumnavigate the globe. 

I first became more interested in more detail about the so-called age of discovery about fifteen years ago when I became aware that the Renaissance mathematici, who now occupied a large part of my historical activities, were not mathematicians in anything like the modern sense of the word but were, as the English term has it, mathematical practitioners. That is, that they were actively engage in particle mathematics, not to be confused with the modern term applied mathematics, which included navigation and map making, as well as the design and production of mathematical instruments for navigation, surveying, and cartography. All of these activities have, of course, a direct and important connection to those voyages of discovery. This was brought home to me when I discovered that one of my favourite mathematici, the Nürnberger Johannes Schöner (1477–1547 most well known as a pioneer in the production of printed globes, had probably produced a terrestrial globe in 1523 displaying Magellan’s circumnavigation. As I wrote in a blog post from 2010:

So, what does all of this have to do with Magellan and the first circumnavigation? As Schöner was in Kirchehrenbach in his banishment he tried to curry favour with his Bishop in that he dedicated his newest terrestrial globe to him, produced in 1523 this globe featured the route of Magellan’s circumnavigation only one year after those 18 seamen struggled back to Spain. At least we think he did! The accompanying cosmographia for the globe exists but none of the globes has survived the ravages of time. How did Schöner manage to transfer the knowledge of this epic voyage so quickly into a printed globe? In this day and age where the news of Ms Watson’s achievement is blasted around the globe in all form of media within seconds of her landfall, we tend to forget that such news sometimes took years to permeate through Europe in the 16th century. At the instigation of Cardinal Matthäus Lang a great sponsor of science in this age Maximilianus Transylvanus interviewed the survivors in Spain and published his account of the voyage in 1523 and it was this account, which Schöner, who made sure to always acquire the latest travel reports through a network of contacts, used to make his globe. I said that none of his Magellan globes have survived but there is a set of globe gores in New York that appear to be those of Schöner’s 1523 globe. Globes were printed on gores, these are strips of paper shaped like segments of an orange that were then glued on to a papier mâché sphere and coloured by hand. The set of gores in New York have Schöner’s cartographical style and Magellan’s route printed on them and although there are some dissenting voices, in general the experts think that they are Schöner’s original.

Included in this quote in the information that only a very small number of the 237 seamen, who set out on this much acclaimed voyage actually made it back to Spain, and only one of the original five ships. Moreover, Magellan was not amongst the survivors having been killed in an imperial attack on indigenous natives on the island of Mactan, who refused to accept the authority of the king of Spain. I had personally garnered this information somewhere down the line.

I became increasingly interested in the mathematical aspects of the so-called age of discovery and became embroiled in an Internet debate on the naming of America with a famous, British pop historian, who was erroneously claiming that it was far more likely that America was named after the Welsh merchant, Richard Ap Meric, an investor in John Cabot’s voyages of discovery, than after Amerigo Vespucci. Being well aware of the reasons why Waldseemüller and Ringmann had named America after Vespucci on their 1507 map of the world, I wrote a long blog post challenging this twaddle. 

As part of my study of this piece of history I acquired my first book by historian extraordinary of exploration, Felipe Fernández-Armesto, his excellent biography of Vespucci, AmerigoThe Man who Gave His Name to America.[1] This was quickly followed by his equally good biography of Columbus,[2] and somewhat later by his PathfindersA Global History of Exploration.[3] So, when it was announced that Felipe Fernández-Armesto’s latest book, he’s incredibly prolific, was to be a biography of Magellan, I immediately ordered a copy and this blog post is a review of  his STRAITSBeyond the myth of Magellan.[4]

I will start by saying that Fernández-Armesto does not disappoint, and this biography of the man and his infamous voyage is up to his usual very high standards. If you have a serious interest in the topic, then this is definitely a book you should read. Although this is a trade book rather than an academic tome, Fernández-Armesto has scrupulously researched his topic and all of the book’s statements and claims are backed up by detailed endnotes. While we are by the apparatus the book also has an extensive and very comprehensive index but no general bibliography. This is one of several new books that I have without a general bibliography, meaning that if you become interested in a referenced volume and it’s not the first reference, then you have to plough your way back through the endnotes, desperately searching for that all important first reference, which contains the details that you require to actually find the book. Staying briefly with the general description, each chapter has a frontispiece consisting of a contemporary print with a detailed descriptions that related to the following chapter. There are also five grey tone maps scattered throughout the book showing places referred to in the narrative.

One thing that Fernández-Armesto makes very clear throughout his book is that the sources for actual hard information about Magellan are very thin and those that do exist are often contradictory. Because he very carefully qualifies his statements concerning Magellan, weighing up the sources and explaining why he believes the one version rather than the other, this makes the book, whilst not a hard read, shall we say a very intense read. Put another way, Fernández-Armesto doesn’t present his readers with a smooth novel like narrative, lulling them into thinking that we know more than we do, but shows the reader how the historian is forced to construct their narrative despite inadequate sources. This is a lesson that other trade book authors could learn.

The central myth of the Magellan story that Fernández-Armesto tackles in his book is that of the inspirational figure, who set out to circumnavigate the world. Not only did Magellan personally fail to do so, a fact that is so often swept under the carpet in the simple claim that he was the first man to do so, but that he in fact never had the intention of doing so. 

In the somewhat less than first half of his book Fernández-Armesto takes the reader through the details of what we know about Magellan’s life before that infamous voyage. His origins, his life and education on the Portuguese court, his service for the Portuguese Crown both as a seaman and a soldier. His reasons for leaving Portugal and moving to Spain, where he offered his services to the Spanish Crown instead. All of this leads up to his plans for that voyage and the motivation behind it. His intended aim was not to sail around the world but to find a passage through the Americas from the Atlantic to the Pacific, or Southern Sea, as it was generally known then, and then to sail across the Pacific to the Moluccas (Spice Islands), today known as the Maluka Islands, and hopefully demonstrate that they lay in the Spanish half of the globe, as designated by the Pope’s Tordesillas Treaty. Having done so to then return to Spain by the same route. Nobody actually knew in which half of the globe the Moluccas lay, as the treaty only specified the demarcation line or meridian in the Atlantic and it was not known where the anti-meridian lay in the Pacific, which in general everybody, including Magellan, thought was much smaller than it actually is.

Due to the uncertainties that this plan, was there even a passage through the Americas joining the two oceans, was it possible to cross the Pacific by ship, did the Moluccas actually lay within the Spanish hemisphere, the negotiations to set up the voyage and the persuade the Spanish Crown to finance it were tough and complex and Fernández-Armesto takes the reader through them step by step. Having succeeded, we then set sail with Magellan on a voyage that was an unmitigated disaster every single sea mile of the way.

The somewhat more than second half of Fernández-Armesto’s narrative is a detailed account, as far as it is possible to reconstruct it, of what might be described, with only slight exaggeration, as the voyage to hell and back with long periods in purgatory. Possibly the only thing that is admirable about Magellan and the voyage is his tenacity in the constant face of doom and disaster, although that tenacity takes on more and more maniacal traits as the voyage proceeds.

Fernández-Armesto’s biography of the man and his voyage is a total demolition of the myths that have been created and propagated over the last five centuries, leaving no trace of valour, heroism, or gallant endeavour. The voyage was an unmitigated disaster perpetrated by a ruthless, driven monomaniac. At the end of his excellent tome Fernández-Armesto illustrates how the myth of Magellan and his circumnavigation was put into the world, starting almost as soon as the Victoria, the only one of the five ships to complete the circumnavigations, docked in Spain more than a thousand days after it set sail with only a handful of the crews that started that voyage. Fernández-Armesto also list some of the myriad of organisations, objects, institutes, prizes etc. that proudly bear Magellan’s name, his attitude to all this being summed up perhaps by his comment on the Order of Magellan awarded by the Circumnavigators Club of New York:

Though it seems astonishing that an award for “world understanding should be named for a failed conqueror who burned villages ad coerced and killed people. (p. 277)

As a final comment on this possibly definitive biography, I learnt in reading this book that the early explorers, Columbus, da Gamma, Magellan et al identified both themselves and their endeavours with the heroic knights in the medieval tales of chivalry and romance, riding their ships out on quests of discovery that would bring the fame, fortune, and honour. Magellan’s quest was about as far removed from this image as it was possible to get. 


[1] Felipe Fernández-Armesto, AmerigoThe Man who Gave His Name to America, Weidenfeld & Nicolson, London, 2006.

[2] Felipe Fernández-Armesto, Columbus, OUP, Oxford & London, 1991, ppb Duckworth, London, 1996

[3] Felipe Fernández-Armesto, PathfindersA Global History of Exploration, W W Norton, New York, 2006, ppb 2007

[4] Felipe Fernández-Armesto, STRAITSBeyond the myth of Magellan, Bloomsbury, London, Oxford, New York, New Delhi, Sydney, 2022

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Filed under Book Reviews, History of Navigation, Renaissance Science

Illuminating the Middle Ages

It is probably true that no period in European history had been so misconceived, misconstrued, misrepresented, as the Middle Ages. Alone the fact that a period of history that is often considered to have lasted a thousand years from 500 to 1500 CE is perceived as somehow being a single, monolithic entity is at best a joke and at worst total nonsense; one that we owe to the Renaissance Humanists, who regarding themselves as the inheritors of the glory that was the Rome of Cicero and Quintilianus labelled the time span in between antique Rome and their own age, the middle period. A period of ignorance, illiteracy, and barbaric Latin in their opinion. Although we should know better, we continue to live with the Humanists coup de grace that effectively consigned a thousand years of history to the rubbish bin, not worthy of serious consideration. 

Although I assigned dates to it above, alone trying to fix a beginning and/or an end to this period is the subject of hot debates amongst historians. Maybe, the simple answer is that it didn’t really begin or end and there is much more continuity to European history than the labels Antiquity, Middle Ages, Renaissance or Early Modern Period would at first glance imply. 

Unfortunately, whatever historians might think, do, or say, there is a very popular perception of the Middle Ages that gets regurgitated at regular intervals in novels, films, and television entertainment programmes. This is a dark, duster and barbaric period ruled over by the totalitarian, science rejecting, witch and heretic burning Church. A period of brutal wars carried out by tyrannical rulers. A period in which women are either damsels in distress, aged, wizened spinsters, whores, or witches. Peasants are filthy, downtrodden, superstitious, subhumans, who live in hovels and are subjected to the brutal whims of the tyrannical rulers and the Church. The term most often associated with this parody of the Middle Ages, and it really is pure parody, is the Dark Ages, which despite the best efforts of historians in recent decades to replace it with the Early Middle Ages is still widely used.

Two recent books on the Middle Ages have in their titles turned the tables rechristening the Middle Ages with synonyms for illumination. The first was Seb Falk’s excellent presentation of the real history of medieval science, The Light Ages, which I reviewed here. The second is Matthew Gabriele & David M Perry’s The Bright AgesA New History of Medieval Europe[1], which I shall briefly review here.  

Whereas Falk concentrates on the history of medieval science Gabriele & Perry’s book deals with the general political and religious history of Europe from the early fifth century to the early fourteenth century. What Gabriele & Perry can’t deliver in the roughly two hundred and fifty pages of their volume is a detailed historical narrative of the entire European history of the nine hundred years that their book covers; they would probably require two and a half thousand pages for that. What they deliver is an episodic narrative of the period, which sketches very informatively the main developments, illustrating the ups and downs, twists and turns of European history that took place over this almost millennium. 

Whilst the narrative style of the two authors is light and breezy making their book a comparatively easy read and they also succeed in effectively demolishing a lot of myths about the medieval period, the book left me wanting more than they delivered. However, before I explain my reservations a couple of positive aspects of the book.

The first in in terms of the contents. Whereas, it is common in discussions of the Middle Ages to talk, as I did above, of the Church, meaning the Catholic Church, as if there was only one version of Christianity throughout the period, the authors show how different dominant political groups adhered to different interpretations of Christianity, during the Early Medieval Period and that a monolithic Catholic Church was a quite late development.

The second very positive aspect is the clear demonstration that there was more continuity between the decline of the Roman Empire and its political structures and the Early Modern Period than the ‘fall’ of popular perception.

For me the third big plus point is in the bibliography or rather the extensive further reading recommendations. The book is a trade book, not an academic one, aimed at a fairly wide audience and as such has not foot or end notes and no conventional bibliography. However, at the end there is a twenty-page Further Reading section, which chapter for chapter give annotated recommendation for deeper exploration of the topic dealt with in that chapter.

Now my personal reservations. Firstly, maybe it’s my problem, but a lot of the time I found that the authors were assuming too much previous knowledge for the level of text that they are trying to present in their book. For my taste it is neither an introductory text nor an advanced one, but an uneasy hybrid stuck somewhere in between. 

My second reservation is, in my opinion, more important. The book is very heavily tilted towards the two themes of religion and politics in the medieval period, which of course are very much intertwined for most of the period under discussion and this makes the book very narrow in its presentation of the period. There is next to nothing on agriculture, technology, trade, science, or finance, all areas which underwent important developments during the Middle Ages and helped to shape the future. Seb Falk has naturally covered the science and John Farrell the technology in his The Clock and the CamshaftAnd Other Medieval Inventions We Still Can’t Live Without, which I reviewed here. However, I feel that they should at least have been addressed in Garbriele & Perry’s volume.

As it stands The Bright Ages is good on the areas it covers and is definitely worth a read but in my opinion it could and should have been so much more.


[1] Matthew Gabriele & David M Perry, The Bright AgesA New History of Medieval Europe, Harper, New York, 2021.

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A Clock is a Thing that Ticks

As I have mentioned a few times in the past, I came late to the computer and the Internet. No Sinclairs, Ataris, or Commadores in my life, my first computer was a Bondi Blue iMac G3. All of which is kind of ironic, because by the time I acquired that G3, I was something of an expert on the history of computing and computing devices. Having acquired my G3, I then took baby steps into the deep waters of the Internet. My initial interest was in music websites starting with the Grateful Dead. Did I mention that I’m a Dead Head? One day I stumbled across Mark Chu-Carroll’s Good Math, Bad Math blog, which in turn introduced me to the Science Blogs collective of which it was a part. Here I discovered, amongst other, the Evolving Thoughts blog of John Wilkins. Who, more than any other, was responsible for me starting my own blog. Another blog that I started reading regularly was Uncertain Principles by the American physicist Chad Orzel, who wrote amusing dialogues explain modern physics to his dog Emmy. A publisher obviously thought they were good, they were, and they soon appeared as a book, How to Teach Physics to Your Dog (Scribner, 2010), launching his career as a writer of popular science books. This was followed by How to Teach Relativity to Your Dog (Basic Books, 2012) with the original book now retitled as How to Teach [Quantum] Physics to Your Dog. Leaving the canine world, he then published Eureka: Discovering Your Inner Scientist (Basic Books, 2014) followed by Breakfast With EinsteinThe Exotic Physics of Everyday Objects (BenBella Books, 2018). 

All of the above is a longwinded introduction to the fact that this is a review of Chad Orzel’s latest A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks[1].

Astute, regular readers might have noticed that I reviewed Davis Rooney’s excellent volume on the history of timekeeping About TimeA History of Civilisation in Twelve Clocks (Viking, 2021) back in September last year and they might ask themselves if and how the two books differ and whether having read the one it is worth reading the other? I follow both authors, and they follow each other, on Twitter and there were several exchanges during last year as to whether they were covering the same territory with their books. However, I can honestly report that if one is interested in the history of time keeping then one can read both books profitably, as they complement rather than copy each other. Whereas Rooney concentrates on the social, cultural, and political aspects of measuring time, Orzel concentrates on the physics of how time was measured.

The title of this blog post is the title of the introductory chapter of Orzel’s book. This definition I viewed with maximum scepsis until I read his explication of it:

At the most basic level a clock is a thing that ticks.

The “tick” here can be the audible physical tick we associate with a mechanical clock like the one in Union’s Memorial Chapel, caused by collision between gear teeth as a heavy pendulum swings back and forth. It can also be a more subtle physical effect, like the alternating voltage that provides the time signal for the electronic wall clock in our classrooms. It can be exceedingly fast, like the nine-billion-times-a-second oscillations of the microwaves used in the atomic clock that provides the time signals transmitted to smartphones via the internet, or ponderously slow like the changing position of the rising sun on the horizon.

In every one of these clocks, though, there is a tick: a regular repeated action that can be counted to mark the passage of time. 

I said above that what distinguishes Orzel’s book is a strong emphasis on the physics of timekeeping. To this end, the book had not one, but two interrelated but separate narratives. There is the main historical narrative in language accessible to every non-expert reader describing forms of timekeeping, their origins, and developments. The second separate narrative, presented on pages with a grey stripe on the edge, takes the willing reader through the physics and technical aspects behind the timekeeping devices described in the historical narrative. Orzel is a good teacher with an easy pedagogical style, so those prepared to invest a little effort can learn much from his explanations. This means that the reader has multiple possibilities to approach the book. They can read it straight through taking in historical narrative and physics explication as they come, which is what I did. They can also skip the physics and just read the historical narrative and still win much from Orzel’s book. It would be possible to do the reverse and just read the physics, skipping the historical narrative, but I, at least, find it difficult to imagine someone doing this. Other possibilities suggest themselves, such as reading first the historical narrative, then going back and dipping into selected explanations of some of the physics. I find the division of the contents in this way a very positive aspect of the book. 

Orzel starts his journey through time and its measurement with the tick of the sun’s annual journey. He takes us back to the Neolithic and such monuments as the Newgrange chamber tomb and Stonehenge which display obvious solar orientations. The technical section of this first chapter is a very handy guide to all things to do with the solar orbit. The second chapter stays with astronomy and the creation of early lunar, lunar-solar and solar calendars. Here and in the following chapter which deals with the Gregorian calendar reform there are no technical sections. 

In Chapter 4, The Apocalypse That Wasn’t, Orzel reminds us of all the rubbish that was generated in the months leading up to the apocalypse supposedly predicted by the Mayan calendar in 2012. In fact, all it was the end of one of the various Mayan cycles of counting days. Orzel gives a very good description of the Mayan number system and their various day counting cycles. An excellent short introduction to the topic for any teacher. 

Leaving Middle America behind, in the next chapter we return to the Middle East and the invention of the water clock or clepsydra. He takes us from ancient Egypt and the simplest form of water clock to the giant tower clock of medieval China. The technical section deals with the physics of the various systems that were developed to produce a constant flow in a water clock. In the simplest form of water clock, a hole in the bottom of a cylinder of water, the rate of flow slows down as the mass of water in the cylinder decreases. 

Chapter 6 takes us to the real tick tock of the mechanical clock from its beginnings up to the pendulum clock. Interestingly there is a lot of, well explained, physics in the narrative section, but the technical section is historical. Orzel gives us a careful analysis of what exactly Galileo did or did not do, did or did not achieve with his pendulum experiments. The chapter closes with the story how the pendulum was used to help determine the shape of the earth.

The next three chapters take as deep into the world of astronomy. For obvious reasons astronomy and timekeeping have always been interwoven strands. We start with what is basically a comparison of Mayan astronomy, with the Dresden Codex observations of Venus, and European astronomy. In the European section, after a brief, but good, section on Ptolemy and his epicycle- deferent model, we get introduced to the work of Tycho Brahe.

The rules of the history of astronomy says that Kepler must follow Tycho and that is also the case here. After Kepler’s laws of planetary motion, we arrive at the invention of the telescope, the discovery of the moons of Jupiter and the determination of the speed of light. If you want a good, accurate, short guide to the history of European astronomy then this book is for you. 

Chapter nine starts with a very brief introduction to the world of Newtonian astronomy before taking the reader into the problem of determining longitude, a time difference problem, and the solution offered by the lunar distance method as perfected by Tobias Mayer. Here, the technical section explains why the determination of longitude is a time difference problem, how the lunar distance method works, and why it was so difficult to make it work.

Of course, in a book on the history of timekeeping, having introduced the longitude problem we now have John Harrison and the invention of the marine chronometer. I almost cheered when Orzel pointed out that although Harrison provided a solution, it wasn’t “the” solution because his chronometer was too complex and too expensive to be practical. The technical section is a brief survey of the evolution of portable clocks. The chapter closes with a couple of paragraphs in which Orzel muses over the difference between “geniuses” and master craftsmen, a category into which he places both Mayer and Harrison. I found these few lines very perceptive and definitely worth expanding upon. 

Up till now we were still in the era of local time determined by the daily journey of the sun. Orzel’s next chapter takes us into the age of railways, and telegraphs and the need for standardised time for train timetables and the introduction of our international time zone system. The technical section is a fascinating essay on the problems of synchronising clocks using the telegraph and having to account for the delays caused by the time the signal needs to travel from A to B. It’s a hell of a lot more complex than you might think.

We are now firmly in the modern age and the advent of the special theory of relativity. Refreshingly, Orzel does most of the introductory work here by following the thoughts of Henri Poincaré, the largely forgotten man of relativity. Of course, we get Albert too.  The technical section is about clocks on moving trains and will give the readers brains a good workout. 

Having moved into the world of modern physics Orzel introduces his readers to the quantum clock and timekeeping on a mindboggling level of accuracy. We get a user-friendly introduction to the workings of the atomic clock. This was the first part of the book that was completely new to me, and I found it totally fascinating. The technical section explains how the advent of the atomic clock has been used to provide a universal time for the world. The chapter closes with a brief introduction to GPS, which is dependent on atomic clocks.

Einstein returns with his general theory of relativity and a technical section on why and how exactly gravity bends light. A phenomenon that famously provided the first confirmation of the general theory.

Approaching the end, our narrative takes a sharp turn away from the world of twentieth century physics to the advent and evolution of cheap wrist and pocket watches. In an age where it is taken for granted that almost everyone can afford to carry an accurate timekeeper around with them, it is easy to forget just how recent this phenomenon is. The main part of this chapter deals with the quartz watch. A development that made a highly accurate timepiece available cheaply to everyone who desired it. Naturally, the technical section deals with the physics of the quartz clock. 

The book closes with a look at The Future of Time. One might be forgiven for thinking that modern atomic clocks were the non plus ultra in timekeeping, but physicists don’t share this opinion. In this chapter Orzel describes various project to produce even more accurate timepieces.

Throughout the book are scattered footnote, which are comments on or addition to the text. The book is illustrated with grey scale drawing and diagrams that help to explicate points being explained. There is a short list of just seven recommended books for further reading. I personally own six of the seven and have read the seventh and can confirm that they are all excellent. There is also a comprehensive index.

Chad Orzel is a master storyteller and despite the, at times, highly complex nature of the narrative he is spinning, he makes it light and accessible for readers at all levels. He is also an excellent teacher and this book, which was originally a course that he teaches, would make a first-class course book for anybody wishing to teach a course on the history of timekeeping from any level from say around middle teens upwards. Perhaps combined with Davis Rooney’s About TimeA History of Civilisation in Twelve Clocks, as I find that the two books complement each other perfectly. Orzel’s A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks is a first-rate addition to the literature on the topic and highly recommendable. 


[1] Chad Orzel, A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks, BenBella Books, Dallas, TX, 2022

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Chronology, history, or prophecy?

Bible chronology is a fascinating Early Modern intellectual phenomenon that combines science, history, and theology. Put simply, it is basically the attempt, assuming the Old Testament to be true and historically accurate, to develop the time frame of that history bringing into accord with what was known of the histories of the ancient cultures and calculate backwards to the point of God’s creation of the world. Although aware of its existence for a long time I paid it little heed because there were/are so many other things that interest me and occupy my time. This changed when the so-called gnu-atheists, whom I regard as smug ignoramuses, who give atheism a bad name, started to mock the Irish mathematician and theologian, James Ussher, Archbishop of Armagh, and Primate of All Ireland, on the “earth’s birthday”, 22 October, the date that Ussher calculated for the day of creation in his Bible chronology. A date well known amongst Protestants because it was enshrined in the Book of Common Prayer. I took up cudgels on Ussher’s behalf and wrote a blog post, In defence of the indefensible, pointing out that in the framework within which Ussher was working his calculations were in fact totally rational. In this post I wrote amongst other things:

Ussher was by no means the only prominent Bible chronologist of the 16th and 17thcenturies the most famous being the philologist and historian Joseph Justus Scaliger and of course Isaac Newton; others such as Johannes Kepler and Phillip Melanchthon also dabbled.

Now, it is well known that I am interested in everything that Isaac Newton indulged in during his long and unbelievably productive life, but that unbelievable productivity is exactly the problem. Newton wrote literally millions of words over a vast range of topics. If James Brown could crown himself, the hardest working man in show business, then Newton could crown himself the hardest working man in the history of science. Although I did write a brief post sketching Newton’s involvement in Bible chronology entitled, Newton was one too, the topic got put very definitely on the back burner.  I wrote another post on Bible chronology, about Joseph Justus Scaliger’s involvement, Counting the days, because his Julian Year Count, converted to the Julian Day Count became, in the nineteenth century, the universal dating system for astronomers.

Returning to Newton’s impossibly vast intellectual output, most people over the decades and centuries since his death concentrated on his mathematics, astronomy, and physics, actually by far the smallest part, whilst quietly ignoring the rest. There have been notable exceptions, which I’m not going to list here, but they were on the whole piecemeal. In more recent times the historian Rob Iliffe set up the Newton Project to systematically edit, comment upon, and make available Newtons vast inheritance, initially in Cambridge, and then somewhat ironically moving the whole to Oxford University, where it still current resides. There is a parallel Chymistry of Isaac Newton project at Indiana University. The Newton Project has been producing first class results and publishing first class material, such as Iliffe’s Priest of NatureThe Religious Worlds of Isaac Newton (OUP, 2019) for some time now and one of the most recent publications is Cornelius J Schilt, Isaac Newton and the Study of ChronologyProphecy, History, and Method (Amsterdam University Press, 2021), which could also be titled everything you ever wanted to know about Bible chronology in general and Isaac Newton’s involvement in it in particular. Yes, it really is that comprehensive!

The first thing to note is that this is a very serious piece of academic research and not in anyway a popular book. However, Schilt writes in a clear accessible style, so that anybody, who is interested, and is prepared to invest the effort can read the book with profit, even if they come to the topic as Bible chronology virgins, so to speak.

 A short introduction sets out the purpose of Schilt’s research, the problems that it entailed and a brief guide to the sections of the book. It closes with an unusually feature of the book. Instead of the usual massive bibliography at the end of the book, each section, and I will explain the sections shortly, closes with an, often extensive, bibliography for that section. The book is divided into four sections, each of which deals with a different aspect of Newton’s work and Schilt’s research into that work.

The first section is a comparatively short and concise, but highly informative, explanation of what exactly Bible chronology was in the Early Modern period. It illustrates how individual Bible chronologist approached the topic and what they hoped to achieve through their work. Having explained Bible chronology, Schilt closes the section with the question, Isaac Newton … Chronologist? Here Schilt discusses Newton’s two published chronology text, the first during his lifetime and heavily criticised and the second put together from his convolute of manuscripts by his acolytes after his death. Here Schilt touches upon, for the first time, the sheer volume of manuscripts and manuscript fragments on the topic, none of them noticeable finished, that Newton left behind in a total chaos, when he died, for historians to try and make some sort of sense out of. This section closes with an extremely extensive bibliography. If one just wished to read an introduction to Bible chronology and not Newton’s work in particular, then this section provides an excellent one. 

In the second section, Schilt introduces the reader to the mind of Isaac Newton and how it worked when he was producing his chronological work. We start with his library, the books he owned. The books that he read to inform himself about ancient history. Primary text by ancient authors for their historical content. Books by contemporary authors for information about which other ancient books he should read. Lists of books that he wished to acquire to further his knowledge. This is followed by Newton’s note taking habits. Here we run into major problems of which I was already aware from other areas of Newton’s work, mathematics, physics, astronomy. Newton was anything but organised in his note taking, using random sheets of paper, using the same sheet two-times years apart etc. etc. How Newton marked passages in books, not by underlining but by dogearing pages bending them over so far that the corner pointed to the passage in question.

The section closes out with a discussion of the fact Newton was an outsider, an independent scholar with no connections to others working in the same or related fields. Newton worked for himself not with others.

The second section makes very obvious that on a meta-level throughout the book we also get a very clear picture of how the researcher, Schilt, worked. He doesn’t just present the results of his research but outlines in detail how he extracted his results from the chaos that is both Newton’s papers and his approaches to his work over the years. This meta-level continues throughout the book and gives powerful insights into how to approach such a research task and carry it through to completion.

The third section takes the reader into the development history of Newton’s earliest chronological treatise, Theologiae gentilis origines philosophicae, known as Origines for short created literally over decades. This is simply not a working manuscript but an extensive collection of manuscripts, fragments, paragraphs, chapters, outlines. Schilt takes his reader through his analysis of what belongs where and why. Explaining his reasons for dating various pieces of writing and why he thinks over separately produced manuscripts belong to the Origines.

The reader gets presented with a master class in academic research detective work.

In the fourth and final section, Schilt does the same for the Chronology of Ancient Kingdoms Amended, as he did for Origines in section three. This is the manuscript on which Newton was working when he died, and which was edited and published by John Conduitt and Martin Folkes. Schilt also delivers a deep analysis as to why Newton was involved in chronological studies at all. Another master class in academic research detective work. As with the first two sections two and three both have their own bibliographies. 

I’m not going to go into any details of what Newton is trying the achieve with his chronological work, you’ll have to read the book for that, but his work is very different from that of the other Bible chronologists that the reader meets in section one. At the end of that first segment Schilt poses the question, is Newton a chronologist. His conclusion at the end of the fourth section is no he isn’t really. Newton’s chronology serves the higher purpose of helping him to analyse the Bible prophecies a central concern of his whole approach to religion. 

The book closes with “Some Concluding Remarks” which gives a one sentence summary of the book better then any I could create:

In this book, I have purposely presented the narrative of Newton’s chronological studies from the bottom up, as a quest in search of the real Chronology of Ancient Kingdoms Amended and the real Newton

This he does brilliantly. He goes on the point out that given the vast quantity of manuscript material that Newton left behind when he died and which became spread out all over the world when Newton’s papers were sold off in public auction in the 1930s, his work and the work in general of the Newton Project and the Chymistry of Isaac Newton project, has only become possible because of digitation of the material making it available to researchers.

The book is excellently presented, it closes with another general bibliography and an excellent index. Each of the four sections starts with a clear and informative short abstract explaining its contents. It has extensive footnotes, not the dreaded endnotes. There are illustrations that are just excerpts from manuscripts, which, however, are interesting as they often show Newton actively editing his work. There are also diagrammatical presentations of Schilt’s reconstructions of the order in which individual pieces of work were created and how various manuscripts fit together (see above).

I suspect Schilt’s book is compulsory reading for any serious student of the whole Newton, i.e., not just those interested in the maths and physics and also for scholars of Bible chronology. However, I think it can also be read by those more generally interested in Newton the man, a complex, puzzling and totally fascinating figure. Schilt has opened another window on that conundrum that is J M Keynes’ “the  last of the magicians” Woolsthorpe’s finest, Isaac Newton. 

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