Category Archives: Book Reviews

A flawed survey of science and the occult in the Early Modern Period

There is no shortage of good literature on the relationships between science and magic, or science and astrology, or science and alchemy during the Early Modern Period so what is new in Mark A. Waddell’s Magic, Science, and Religion in Early Modern Europe[1]? Nothing, because it is not Waddell’s aim to bring something new to this material but rather to present an introductory textbook on the theme aimed at university students. He sets out to demonstrate to the uninitiated how the seemingly contradictory regions of science, religion and magic existed in the Early Modern Period not just parallel to but interwoven and integrated with each other.  Waddell’s conception is a worthy one and would make for a positive addition to the literature, his book is however flawed in its execution.


Image with thanks from Brian Clegg

The book actually starts well, and our author sets out his planned journey in a lengthy but clear and informative introduction. The book itself is divided into clear sections each dealing with a different aspect of the central theme. The first section deals with the Renaissance discoveries of hermeticism and the cabala and the concept of natural magic, as a force to manipulate nature, as opposed to demonic magic. Although limited by its brevity, it provides a reasonable introduction to the topics dealt with. My only criticisms concerns, the usual presentation of John Dee as a magus, whilst downplaying his role as a mathematician, although this does get mentioned in passing. However, Waddell can’t resist suggesting that Dee was the role model for Marlowe’s Faustus, whereas Faustus is almost certainly modelled on Historia von D. Johann Faustus, a German book containing legends about the real Johann Georg Faust (c. 1480–c. 1541) a German itinerant alchemist, astrologer, and magician of the German Renaissance. A note for authors, not just for Waddell, Dee in by no means the only Renaissance magus and is not the role model for all the literary ones.

Waddell’s second section deals with demonic magic, that is magic thought to draw its power from communion with the Devil and other lesser demons. As far as I can tell this was the section that most interested our author whilst writing his book. He manages to present a clear and informative picture of the period of the European witch craze and the associated witch hunts. He deals really well with the interrelationship between the belief in demonic witchcraft and the Church and formal religion. How the Church created, propagated and increasingly expanded the belief in demonic magic and witches and how this became centred on the concept of heresy. Communion with the devil, which became the central theme of the witch hunts being in and of itself heretical.

Following this excellent ´section the book starts to go downhill. The third section of the book deals with magic, medicine and the microcosm. Compared with the good presentation of the previous section I can only call this one a mishmash. We get a standard brief introduction to medieval academic medicine, which Waddell labels premodern, with Hippocrates, Galen and a nod to Islamic medical writes, but with only Ibn Sīnā mentioned by name. This is followed by a brief description of the principles of humoral medicine. Waddell correctly points out the academic or learned doctors only represent one group offering medical assistance during this period and gives a couple of lines to the barber-surgeons. It is now that the quality of Waddell’s presentation takes a steep nosedive.

Having correctly pointed out that medieval academic medicine was largely theoretical he then, unfortunately, follows the myth of “and then came Andy”! That is, we jump straight into Andreas Vesalius and his De fabrica, as I quote, “the beginnings of what we would understand as a rigorous and empirical approach to the study of anatomy.” Strange, only two weeks ago I wrote a post pointing out that Vesalius didn’t emerge out of the blue with scalpel raised high but was one step, albeit a very major one, in a two-hundred-year evolution in the study of anatomy. Of course, Waddell dishes up the usual myth about how seldom dissection was before Vesalius and corpses to dissect were rare etc, etc. Whereas, in fact, dissection had become a regular feature of medical teaching at the European universities over that, previously mentioned two-hundred-year period. Waddell closes his Vesalius hagiography with the comment that Vesalius’ De fabrica “was a crucial step in the more widespread reform of medical theory and practice that took place over the next 150 years” and although his book goes up to the middle of the eighteenth century, we don’t get any more information on those reforms. One of his final comments on Vesalius perpetuates another hoary old myth. He writes, “Vesalius made it permissible to question the legacy of antiquity and, in some cases, to overturn ideas that had persisted for many hundred years.” Contrary to the image created here, people had been challenging the legacy of antiquity and overturning ideas since antiquity, as Edward Grant put it so wonderfully, medieval Aristotelian philosophy was not Aristotle’s philosophy. The same applies to all branches of knowledge inherited form antiquity.

Having dealt with Vesalius, Waddell moves on to the philosophy of microcosm-macrocosm and astro-medicine or as it was called iatromathematics, that is the application of astrology to medicine. His basic introduction to the microcosm-macrocosm theory is quite reasonable and he then moves onto astrology. He insists on explaining that, in his opinion, astrology is not a science but a system of non-scientific rules. This is all well and good but for the people he is dealing with in the Early Modern Period astrology was a science. We then get a guide to astrology for beginners which manages right from the start to make some elementary mistakes. He writes, “You might know what your “sign” is, based on when you were born […]. These refer to the twelve (or according to some, thirteen) signs of the Western zodiac, which is the band of constellations through which the Sun appears to move over the course of a year.” The bullshit with thirteen constellations was something dreamed up by some modern astronomers, who obviously know nothing about astrology, its history or the history of their own discipline for that matter, in order to discredit astrology and astrologers. The only people they discredited were themselves. The zodiac as originally conceived by the Babylonians a couple of millennia BCE, mapped the ecliptic, the apparent annual path of the Sun around the Earth, using seventeen constellations. These were gradually pared down over the centuries until the Western zodiac became defined around the fifth century BCE as twelve equal division of the ecliptic, that is each of thirty degrees, starting at the vernal or spring equinox and preceding clockwise around the ecliptic. The most important point is that these divisions, the “signs”, are not constellations. There are, perhaps unfortunately, named after the constellations that occupied those positions on the ecliptic a couple of millennia in the past but no longer do so because of the precession of the equinoxes.

Although, Waddell gives a reasonable account of the basics of astro-medicine and also how it was integrated with humoral medicine but then fails again when describing its actual application. A couple of examples:

There were cases of surgeons refusing to operate on a specific part of the body unless the heavens were aligned with the corresponding zodiac sign, and it was not uncommon for learned physicians to cast their patient’s horoscope as part of their diagnosis.


Though the use of astrology in premodern medicine was common, it is less clear how often physicians would have turned to astrological magic in order to treat patients. Some would have regarded it with suspicion and relied instead on genitures alone to dictate their treatment, using a patient’s horoscope as a kind of diagnostic tool that provided useful information about that person’s temperament and other influences on their health. Astrological magic was a different thing altogether, requiring the practitioner to harness the unseen forces and emanations of the planets to heal their patient rather than relying solely on a standard regimen of care.

This is a book about the interrelationships between magic, religion and science during the Early Modern period, but Waddell’s lukewarm statements here, “there were cases of surgeons refusing to operate…, not uncommon for learned physicians…” fail totally to capture the extent of astro-medicine and its almost total dominance of academic medicine during the Renaissance. Beginning in the early fifteenth century European universities established the first dedicated chairs for mathematics, with the specific assignment to teach astrology to medical students.

During the main period of astrological medicine, the most commonly produced printed products were wall and pocket calendars, in fact, Gutenberg printed a wall calendar long before his more famous Bible. These calendars were astronomical, astrological, medical calendars, which contained the astronomical-astrological data that enabled physicians and barber-surgeons to know when they should or should not apply a particular treatment. These calendars were universal, and towns, cities and districts appointed official calendar makers to produce new calendars, every year. Almost no physician or barber-surgeon would consider applying a treatment at an inappropriate time, not as Waddell says, “cases of surgeons refusing to operate.” Also, no learned physicians in this time would begin an examination without casting the patient’s horoscope, to determine the cause, course and cure for the existing affliction. The use of what Waddell calls astrological magic, by which he means astrological talismans, by learned physicians was almost non-existent. This is aa completely different area of both astrology and of medicine.

Within the context of the book, it is obvious that we now turn to Paracelsus. Here Waddell repeats the myth about the name Paracelsus, “The name by which he is best known, Paracelsus, is something of a mystery, but historians believe that it was inspired by the classical Roman medical writer Celsus (c. 25 BCE–c. 50 CE). The prefix “para-“ that he added to that ancient name has multiple meanings in Latin, including “beyond,” leading some to speculate that this was a not-so-modest attempt to claim a knowledge of medicine greater than that of Celsus.” This is once again almost certainly a myth. Nowhere in his voluminous writings does Paracelsus mention Celsus and there is no evidence that he even knew of his existence. Paracelsus is almost certainly a toponym for Hohenheim meaning ‘up high’, Hohenheim being German for high home. By the way, he only initially adopted Paracelsus for his alchemical writings. The rest of his account of Paracelsus is OK but fails to really come to grips with Paracelsus’ alchemy.

To close out his section on medicine, Waddell now brings a long digression on the history of the believe in weapon salve, a substance that supposedly cured wounds when smeared on the weapon that caused them, an interesting example of the intersection between magic and medicine. However, he misses the wonderful case of a crossover into science when Kenhelm Digby suggested that weapon salve could be used to determine longitude.


The next section A New Cosmos: Copernicus, Galileo, and the Motion of the Earth, takes us into, from my point of view, a true disaster area:

In this chapter, we explore how the European understanding of the cosmos changed in the sixteenth and seventeenth centuries. It was on the single greatest intellectual disruptions in European history, and in some ways we are still feeling its effects now, more than 450 years later. The claim that our universe was fundamentally different from what people had known for thousands of years led to a serious conflict between different sources of knowledge and forms of authority, and forced premodern Europe to grapple with a crucial question: Who has the right to define the nature of reality?

This particular conflict is often framed by historians and other commentators as a battle between science and religion in which the brave and progressive pioneers of the heliocentric cosmos were attacked unjustly by a tyrannical and old-fashioned Church. This is an exaggeration, but not by much. [my emphasis]

Waddell starts with a standard account of Aristotelian philosophy and cosmology, in which he like most other people exaggerates the continuity of Aristotle’s influence. This is followed by the usual astronomers only saved the phenomena story and an introduction to Ptolemy. Again, the continuity of his model is, as usual, exaggerated. Waddell briefly introduces the Aristotelian theory of the crystalline spheres and claims that it contradicted Ptolemy’s epicycle and deferent model, which is simply not true as Ptolemy combined them in his Planetary Hypothesis. The contradiction between the two models is between Aristotle’s astronomical mathematical homocentric spheres used to explain the moments of the planets (which Waddell doesn’t mention), which were imbedded in the crystalline spheres, and the epicycle-deferent model. Waddell then hypothesises a conflict between the Aristotelian and Ptolemaic system, which simply didn’t exist for the majority, people accepting a melange of Aristotle’s cosmology and Ptolemy’s astronomy. There were however over the centuries local revivals of Aristotle’s homocentric theory.

Now Copernicus enters stage right:

Copernicus had strong ties to the Catholic Church; he was a canon, which meant he was responsible for maintaining a cathedral (the seat of a bishop or archbishop), and some historians believe he was ordained as a priest as well.

If a student writes “some historians” in a paper they normally get their head torn off by their teachers. Which historians? Name them! In fact, I think Waddell would have a difficult time naming his “some historians”, as all the historians of astronomy that I know of, who have studied the question, say quite categorically that there is no evidence that Copernicus was ever ordained. Waddell delivers up next:

Most probably it [De revolutionibus] was completed by the mid-1530s, but Copernicus was reluctant to publish it right away because his work called into question some of the most fundamental assumptions about the universe held at the time.

It is now generally accepted that Copernicus didn’t published because he couldn’t provide any proofs for his heliocentric hypothesis. Waddell:

He did decide to circulate his ideas quietly among astronomers, however, and after seeing his calculations were not rejected outright Copernicus finally had his work printed in Nuremberg shortly before his death.

Here Waddell is obviously confusing Copernicus’ Commentariolus, circulated around 1510 and  Rheticus’ Narratio prima, published in two editions in Danzig and Basel, which I wouldn’t describe as circulated quietly. Also, neither book contained  calculations. Waddell now tries to push the gospel that nobody really read the cosmological part of De revolutionibus and were only interested in the mathematics. Whilst it is true that more astronomers were interested in the mathematical model, there was a complex and intensive discussion of the cosmology throughout the second half of the sixteenth century. Waddell also wants his reader to believe that Copernicus didn’t regard his model as a real model of the cosmos, sorry this is simply false. Copernicus very definitely believed his model was a real model.

 Moving on to Tycho Brahe and the geo-heliocentric system Waddell tells us that, “[Tycho] could not embrace a cosmology that so obviously conflicted with the Bible. It is not surprising, then, that the Tychonic system was adopted in the years following Brahe’s death in 1601”

At no point does Waddell acknowledge the historical fact that also the majority of astronomers in the early decades of the seventeenth century accepted a Tychonic system because it was the one that best fit the known empirical facts. This doesn’t fit his hagiographical account of Galileo vs the Church, which is still to come.

Next up Waddell presents Kepler and his Mysterium Cosmographicum and seems to think that Kepler’s importance lies in the fact that he was ac deeply religious and pious person embraced a heliocentric cosmos. We then get an absolute humdinger of a statement:

There is more that could be said about Kepler, including the fact that he improved upon the work of Copernicus by proposing three laws of planetary motion that are still taught in schools today. For the purpose of this chapter, however, Kepler is significant as someone who embraced heliocentricity and [emphasis in the original] faith.

With this statement Waddell disqualifies himself on the subject of the seventeenth century transition from a geocentric cosmos to a heliocentric one. Kepler didn’t propose his three laws he derived them empirically from Tycho’s observational data and they represent the single most important step in that transition.

We now have another Waddell and then came moment, this time with Galileo. We get a gabled version of Galileo’s vita with many minor inaccuracies, which I won’t deal with here because there is much worse to come. After a standard story of the introduction of the telescope and of Galileo’s improved model we get the following:

[Galileo] presented his device to the Doge (the highest official in Venice) and secured a truly impressive salary for life from the Venetian state. Mere weeks later he received word from the court of the Medici in Galileo’s home in Tuscany, that they wanted a telescope of their own. The Venetian leaders, however had ordered Galileo to keep his improved telescope a secret, to be manufactured only for Venetian use, and Galileo obliged, at least temporarily.

When they bought Galileo’s telescope they thought, erroneously, that they were getting exclusive use of a spectacular new instrument. However, it soon became very clear that telescopes were not particularly difficult to make and were freely available in almost all major European towns. They were more than slightly pissed off at the good Galileo but did not renege on their deal. The Medici court did not request a telescope of their own, but Galileo in his campaign to gain favour by the Medici, presented them with one and actually travelled to Florence to demonstrate it for them. We now move on to the telescopic discoveries in which Waddell exaggerates the discovery of the Jupiter moons. We skip over the Sidereus Nuncius and Galileo’s appointment as court philosophicus and mathematicus in Florence, which Waddell retells fairly accurately. Waddell now delivers up what he sees as the great coup:

The problem was that the moons of Jupiter, while important, did not prove the existence of a heliocentric cosmos. Galileo kept searching until he found something that did: the phases of Venus.

The discovery of the phases of Venus do indeed sound the death nell for a pure geocentric system à la Ptolemy but not for a Capellan geo-heliocentric system, popular throughout the Middle Ages, where Mercury and Venus orbit the Sun, which orbits the Earth, or a full Tychonic system with all five planets orbiting the Sun, which together with the Moon orbits the Earth. Neither here nor anywhere else does Waddell handle the Tychonic system, which on scientific, empirical grounds became the most favoured system in the early decades of the seventeenth century.

We then get Castelli getting into deep water with the Grand Duchess Christina and, according to Waddell, Galileo’s Letter to the Grand Duchess Christina. He never mentions the Letter to Castelli, of which the Letter to the Grand Duchess Christina was a later extended and improved version, although it was the Letter to Castelli, which got passed on to the Inquisition and caused Galileo’s problems in 1615. Waddell tells us:

In 1616 the Inquisition declared that heliocentrism was a formal heresy.

In fact, the eleven Qualifiers appointed by the Pope to investigate the status of the heliocentric theory delivered the following verdict:

( i ) The sun is the centre of the universe (“mundi”) and absolutely immobile in local motion.

( ii ) The earth is not the centre of the universe (“mundi”); it is not immobile but turns on itself with a diurnal movement.

All unanimously censure the first proposition as “foolish, absurd in philosophy [i.e. scientifically untenable] and formally heretical on the grounds of expressly contradicting the statements of Holy Scripture in many places according to the proper meaning of the words, the common exposition and the understanding of the Holy Fathers and learned theologians”; the second proposition they unanimously censured as likewise “absurd in philosophy” and theologically “at least erroneous in faith”.

However, the Qualifiers verdict was only advisory and the Pope alone can official name something a heresy and no Pope ever did.

Waddell gives a fairly standard account of Galileo’s meeting with Cardinal Roberto Bellarmino in 1616 and moves fairly rapidly to the Dialogo and Galileo’s trial by the Inquisition in 1633. However, on the judgement of that trial he delivers up this gem:

Ultimately, Galileo was found “vehemently suspect of heresy,” which marked his crime as far more serious than typical, run-of-the-mill heresy.

One really should take time to savour this inanity. The first time I read it, I went back and read it again, because I didn’t think anybody could write anything that stupid. and that I must have somehow misread it. But no, the sentence on page 131 of the book reads exactly as I have reproduced it here. Maybe I’m ignorant, but I never knew that to be suspected of a crime was actually “far more serious” than actually being found guilty of the same crime. One of my acquaintances, an excellent medieval historian and an expert for medieval astronomy asked, “WTF is run-of-the-mill heresy?” I’m afraid I can’t answer her excellent question, as I am as perplexed by the expression, as she obviously is.

Enough of the sarcasm, the complete sentence is, of course, total bollocks from beginning to end. Being found guilty of suspicion of heresy, vehement or not, is a much milder judgement than being found guilty of heresy. If Galileo had been found guilty of heresy, there is a very good chance he would have been sentenced to death. The expression “run-of-the-mill heresy” is quite simple total balderdash and should never, ever appear in any academic work.

Waddell now draws his conclusions for this section, and they are totally skewed because he has simple ignored, or better said deliberately supressed a large and significant part of the story. In the final part of this section, “Science versus Religion?”, he argues that the Church was defending its right to traditional truth against Galileo’s scientific truth. He writes:

This was not a fight between winners and losers, or between “right” and “wrong.” Instead, this is a story about power, tradition, and authority, about who gets to decide what is true and on what grounds.


Organised religion, exemplified here by the Catholic Church, had an interest in preserving the status quo [emphasis in original] for many reasons, some of which were undeniably self-serving.


The ideas of Aristotle and Ptolemy were still taught in virtually every European university well into the seventeenth century, making the Church’s allegiance to these ideas understandable. At the same time, the Church also recognised another source of authority, the Christian scriptures, which stated clearly that the Earth did not move. On both philosophical and theological grounds, then, the Church’s position on the immobility of the Earth was reasonable by the standards of the time.  

The above quotes have more relationship to a fairy tale than to the actual historical situation. Due to the astronomical discoveries made since about 1570, by1630 the Catholic Church had abandoned most of the Aristotelian cosmology and never adopted  Aristotelian astronomy. They fully accepted that the phases of Venus, almost certainly observed by the Jesuit astronomers of the Collegio Romano before Galileo did, refuted the Ptolemaic geocentric astronomy. Instead by 1620 the Church had officially adopted the Tychonic geo-heliocentric astronomy, not, as Waddell claims, on religious grounds but because it best fit the known empirical facts. Despite efforts since 1543, when Copernicus published De revolutionibus, nobody, not even Galileo, who had tried really hard, had succeeded in finding any empirical evidence to show that the Earth moves. Waddell’s attempt to portrait the Church as at best non-scientific or even anti.scientific completely ignores the fact that Jesuit and Jesuit educated mathematicians and astronomer were amongst the best throughout the seventeenth century. They made significant contributions to the development of modern astronomy before the invention of the telescope, during Galileo’s active period, in fact it was the Jesuits who provided the necessary scientific confirmation of Galileo’s telescopic discoveries, and all the way up to Newton’s Principia. Their record can hardly be described as anti-scientific.

The Church’s real position is best summed up by Roberto Bellarmino in his 1615 letter to Foscarini, which is also addressed to Galileo:

Third, I say that if there were a true demonstration that the sun is at the centre of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. 

Put simple prove your theory and we the Church will then reinterpret the Bible as necessary, which they in fact did in the eighteenth century following Bradley’s first proof that the Earth does actually move.

Waddell then goes off on a long presentist defence of Galileo’s wish to separate natural philosophy and theology, which is all well and good but has very little relevance for the actual historical situation. But as already stated, Waddell is wrong to claim that the phases of Venus prove heliocentrism. Worse than this Galileo’s Dialogo is a con. In the 1630s the two chief world systems were not Ptolemy and Copernicus, the first refuted and the second with its epicycle-deferent models, which Galileo continues to propagate, abandoned, but the Tychonic system and Kepler’s ecliptical astronomy, which Waddell like Galileo simply chose to ignore.

One last comment before I move on. Somewhere Waddell claims that Galileo was the first to claim that the Copernicus’ heliocentric model represented reality rather than simply saving the phenomena. This is historically not correct, Copernicus, Tycho and Kepler all believed that their models represented reality and by 1615, when Galileo first came into confrontation with the Church it had become the norm under astronomers that they were trying to find a real model and not saving the phenomena.

Waddell’s account of the early period of the emergence of modern astronomy sails majestically past the current historical stand of our knowledge of this phase of astronomical history and could have been written some time in the first half of the twentieth century but should not be in a textbook for students in the year 2021.

With the next section we return to some semblance of serious state-of-the-art history. Waddell presents and contrasts the mechanical philosophies of Pierre Gassendi and René Descartes and their differing strategies to include their God within those philosophies. All pretty standard stuff reasonably well presented. The section closes with a brief, maybe too brief, discourse on Joseph Glanvill’s attempts to keep awareness of the supernatural alive against the rationalism of the emerging modern science.

The penultimate section deals with the transition from the Aristotelian concept of an experience-based explanation of the world to one based on experiments and the problems involved in conforming the truth of experimental results. In my opinion he, like most people, gives far too much attention/credit to Francis Bacon but that is mainstream opinion so I can’t really fault him for doing so. I can, however, fault him for presenting Bacon’s approach as something new and original, whereas Bacon was merely collating what had been widespread scientific practice for about two centuries before he wrote his main treatises. Specialist historians have been making this public for quite some time now and textbooks, like the one Waddell has written, should reflect these advances in our historical awareness.

Waddell moves on to alchemy as another source of experimentation that influenced the move to an experiment-based science in the seventeenth century. To be honest I found his brief account of alchemy as somewhat garbled and meandering, basically in need of a good editor. He makes one error, which I found illuminating, he writes:

Aristotle in particular had taught that all metals were composed of two principles: Mercury and Sulphur

Aristotle thought that metals were composed of two exhalations, one is dry and smoky, the other wet and steamy. These first became widely labeled as Mercury and Sulphur in the ninth century writings of the Arabic alchemist Jābir ibn-Hayyān, who took it from the mid-ninth century work, the Book of the Secrets of Creation by Balīnūs. I find this illuminating because I don’t know things like this off by heart, I just knew that Mercury-Sulphur was not from Aristotle, and so have to look them up. To do so I turned to Principe’s The Secrets of Alchemy. Now, according to Waddell’s bibliographical essays at the end of the book, Principe is his main source for the history of alchemy, which means he read the same paragraph as I did and decided to shorten it thus producing a fake historical statement. When writing history facts and details matter!

Having introduced alchemy we now, of course, get Isaac Newton. Waddell points out that Newton is hailed as the epitome of the modern scientist, whereas in fact he was a passionate exponent of alchemy and devoted vast amounts of time and effort to his heterodox religious studies. The only thing that I have to criticise here is that Waddell allocates Newton and his Principia to the mechanical philosophy, whereas his strongest critics pointed out that gravity is an occult force and is anything but conform with the mechanical philosophy. Waddell makes no mention of this here but strangely, as we will see does so indirectly later.

The final section of the book is a discussion of the enlightenment, which I found quite good.  Waddell points out that many assessments of the enlightenment and what supposedly took place are contradicted by the historical facts of what actually happened in the eighteenth century.

Waddell draws to a close with a five-page conclusion that rather strangely suddenly introduces new material that is not in the main text of the book, such as Leibniz’s criticism that Newton’s theory of gravity is not mechanical. It is in fact more a collection of after thoughts than a conclusion.

The book ends with a brief but quite extensive bibliographical essay for each section of the book, and it was here that I think I found the reason for the very poor quality of the A New Cosmos section, he writes at the very beginning:

Two important studies on premodern astronomy and the changes it experienced in early modern Europe are Arthur Koestler’s The Sleepwalkers: A History of Man’s Changing Vision of the Universe (Penguin Books, 1990) and Thomas Kuhn’s The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (Harvard University Press, 1992)

The Sleepwalkers was originally published in 1959 and The Copernican Revolution in 1957, both are horribly outdated and historically wildly inaccurate and should never be recommended to students in this day and age.

All together Waddell’s tome  has the makings of a good and potentially useful textbook for students on an important set of themes but it is in my opinion it is spoilt by some sloppy errors and a truly bad section on the history of astronomy in the early modern period and the conflict between Galileo and the Catholic Church.

[1] Mark A. Waddell, Magic, Science, and Religion in Early Modern Europe, Cambridge University Press, Cambridge & London, 2021


Filed under Book Reviews, History of Alchemy, History of Astrology, History of Astronomy, History of medicine, History of science, Renaissance Science

Review of a book I have not read and have absolutely no intention of wasting money on!

Since this blog post was written, Professor Screech has recognised and acknowledged that he erred in his book and has made changes in the text reflecting the criticism in this post, which are already in the ebook version and will soon appear in a new print edition. To what extent he has made changes, I cannot at the moment say, but I shall be receiving a print copy of the amended book and will report when I have read it. The OUP blog post discussed here has already been amended.

Timon Screech is an art historian, who is professor for Japanese art of the Early Modern Period at SOAS in London. He is the author of numerous books and in his newest publication has decided to turn his hand to the history of astronomy at the beginning of the seventeenth century, namely the early years following the invention of the telescope, the result is a train wreck! The offending object is, The Shogun’s Silver Telescope: God, Art and Money in the English Quest for Japan, 1600–1625. OUP, 2020.


If, as I state in the title to this blog post, I have not read this book, and in fact have no intentions of wasting my time and money in doing so, how can I claim that it is a train wreck? OUP have been kind enough to provide a description of the book on the Internet and Professor Screech has posted a lecture on YouTube in which he elucidates the central thesis of his work. These contain enough statements that make it very clear that that central thesis is a festering heap of dodo dung.

The OUP description opens thus:

Over the winter of 1610-11, a magnificent telescope was built in London. [my emphasis] It was almost two metres long, cast in silver and covered with gold. This was the first telescope ever produced in such an extraordinary way, worthy of a great king or emperor. Why was it made and who was it going to?

The origins of telescopes are shrouded in mystery. All that is known for sure is that the first one to be patented had been built in Middleburgh, in the Dutch Republic, in October 1608. [my emphasis] The English were soon making their own under the name of “prospective glasses,” for seeing “prospects” or distant views. One had been shown to King James I of England and Scotland in May 1609. The English and Dutch were not alone, for, famously, Galileo obtained a telescope some months later and conducted experiments in Venice. In March 1610, he published his seminal study, The Starry Messenger (so-called in English, though the text is in Latin). King James’s ambassador to Venice sent a copy to the king post-haste, with a letter emphasising the extraordinary importance of the object.

The telescope in question was very probably not built in London but imported from Holland, as was the one shown to James I&VI in 1609. The origins of the telescope, whilst complex, are, of course, not shrouded in mystery; there is in fact quite a lot of very good historical research on the subject. The Dutch city, where Hans Lipperhey (1569–1619) made the telescope mentioned in the next sentence lived, is Middelburg and not Middleburgh, which apparently is a town in the State of New York. Now history is not an exact academic discipline but an interpretative one. From the usually limited facts available the historian tries their best to recreate as accurately as possible that part of the past he is dealing with. Important in this process is that they get the known facts right. We know from that historical research on the origins of the telescope that Lipperhey applied to the States General for a patent for his instrument in Den Hague on 2 October 1608. However, we also know that on 15 December 1608 his request for a patent was denied. Actually, Sir Henry Wotton the English ambassador to Venice sent two copies of Galileo’s Sidereus Nuncius to London on the day it was published, 12 March 1610.

Up till now the OUP’s account has only been inaccurate and sloppy but now they leave the realm of bad history and enter the world of fantasy or perhaps wishful thinking

The telescope built in London the next year was made for King James I. It was not his to keep but was to be sent in his name to one of the world’s supreme potentates—one the English were desperate to please. This was the Shogun of Japan, Tokugawa Ieyasu.

Why send a telescope? English trade with Asia was the monopoly of the East India Company, founded a decade before, and they were very anxious to open markets in Japan. It was with a telescope that Galileo had made his findings, and although his discoveries were received with enthusiasm in some quarters, this was not the case in others. The Papacy, famously, could not accept his key finding, namely that the earth orbits the sun— [my emphasis] heliocentricity contradicted Scripture, which states that the sun moves. Later Galileo would be summoned before the Inquisition for this, as telescopes became a central battleground between Rome and the Protestant churches. [my emphasis] It had evidently dawned on the East India Company, and perhaps on King James himself, that here was the perfect a way to court Japanese favour. They would show the shogun the latest scientific instrument, and in doing so embarrass the Iberians. Spain and Portugal were already trading successfully in Japan, accompanied by Jesuit missionaries, to whom the English had the highest aversion: the Jesuits were blamed for many things, including Guy Fawkes and the Gunpowder Plot of 1605. In Japan, they spent as much time teaching astronomy as theology. A telescope would prove that they were teaching falsehoods, and that the Jesuits were a danger to Japan. [my emphasis]

First up, we have the usual false claim about the Sidereus Nuncius that it provided proof of the heliocentric hypothesis, it didn’t, and Galileo knew well that it didn’t. As a historian one gets tired of busting the same myths over and over again, but once more for those who haven’t been paying attention. The new telescopic discoveries made by 1610, not just by Galileo, disproved two aspects of Aristotelian cosmology, that the heavens were perfect and celestial bodies perfect spheres, and that all celestial bodies orbit a common centre. However, it offered no evidence to truly support or refute any of the three main contending models of the cosmos, geocentricity, heliocentricity and geo-heliocentricity. The later discovery of the phases of Venus eliminated a pure geocentric model, but that was made public well after the Shogun shiny new telescope was on its way to Japan, so needn’t be considered here.

I have looked at the phrase, as telescopes became a central battleground between Rome and the Protestant churches numerous times, from various standpoints and different angles and all that occurs to me is, what the fuck is that supposed to mean? It is simply put baloney, balderdash, poppycock, gibberish, hogwash, drivel, palaver, mumbo jumbo, rubbish, or even more simply, total and utter crap! I’m not even going to waste time, space and effort in trying to analyse and refute it, it doesn’t deserve it. Somebody please flush it down the toilet into the sewers, where it belongs.

The final emphasised sentence is the whole crux of Screech’s argument, as we shall see, it refers to the fact that the Jesuit astronomers in Japan in 1611 were teaching that the cosmos was geocentric, as this was certainly the accepted scientific view of the vast majority of European astronomers in 1611, including those in London, I think claiming that they were teaching falsehoods is historically simply wrong.

OUP now explain how the telescope was delivered to the Shogun in Japan and make a clear statement of Screech’s central thesis:

The telescope was taken out in a flotilla of four vessels in spring 1611. Command was given to John Saris, who had already lived several years in Asia, as the most senior English merchant. Now on his second trip East, he was told to push further on, all the way to Japan, where no English ship had yet gone. Oddly, the Company was aware of one Englishman already living in Japan. This was William Adams, who had gone on a Dutch ship. Many people in London remembered him, and word was that he had married a great Japanese lady. Saris took only one of his ships to Japan (the others went home with nearer Asian goods), arriving in Japan in summer 1613. Adams was contacted and within a few months he and Saris took the telescope to the Shogun’s castle, presenting it together in September at a grand ceremony. The Japanese records show to this. Saris enjoyed success in opening trade with Japan, and by December 1614 was safely back in London. Adams preferred to stay.

Once the English had provided proof that “European astronomy,” as explained in Japan for many years, was all wrong, the Roman Catholic missions lost their value. [my emphasis] They were closed down forthwith, and the Jesuit missionaries were expelled. Their old enemies put to flight, the English looked forward to unfettered trade with what was perhaps the world’s richest country, somewhat grudgingly agreeing to share this with the Dutch.

You will be amazed as to how John Saris provided proof that “European astronomy,” as explained in Japan for many years, was all wrong.

We now turn to our author’s own presentation of his thesis in a 45-minute YouTube video. I shall only be commenting on the relevant statements from this.

(starting at approx. 23 mins) In 1610 Galileo had conducted his extraordinary discoveries.

Actually, he made a large part of them in 1609, he published them in 1610.

The first telescope referred to in England is also in 1609, when one was shown to King James.…We also know that one was on public display in London shortly after the Clove [Saris’ ship] left England [1611] In other words they are still very rare, very special things. Not that many people can get hold of them.  

Screech is obviously not aware of the fact that Thomas Harriot had been making and using telescopes in London since 1609 and by 1611, the group centred on Harriot (Harriot, Christopher Tooke his lens grinder, Sir William Lower and John Prydderch (or Protheroe)) were making and comparing astronomical observation. In fact, Harriot was using telescopes before Galileo.

Even in 1618, a telescope is still a rather unusual thing

Sorry, but no it wasn’t, not in scientific circles

The Japanese record says something that the English record doesn’t say that the telescope was, using their own measurements, about ten feet long. So, it was extremely long and that must have meant that it was actually quite powerful. Possibly more powerful than the one Galileo used. It was two years later so lenses might have improved. Galileo could of course see the rings of Saturn with his.  

There is quite a lot to unpack here, which illustrates that Screech actually knows nothing about the early history of the telescope. For a telescope in 1611, ten feet is quite long not extremely long, telescopes later in the century reached lengths of fifty and sixty feet. However, length does not equal magnification power. For a Dutch or Galilean telescope, the magnification equals the focal length of the objective lens divided by the focal length of the eyepiece lens. So, if the Shogun’s telescope’s objective had a focal length of 120 inches and the eyepiece one of 1 inch, then it would have a magnification of 120. However, if the objective focal length was 8 feet and the eyepiece one 2 feet, its magnification would be only 4. These are not real numbers, just illustrative examples.

Galileo had a four-foot telescope with a magnification of c. 30, meaning an objective with focal length of c. 46.5 inches and an eyepiece focal length of c. 1.5 inches. The next problem is the higher the magnification of a Dutch telescope the smaller the field of vision. A magnification of about 30 is the upper limit for a usable Dutch telescope, anything above that is basically useless. Galileo made most of his discoveries with a telescope with a magnification of about 20. There was also no real improvement in lens making between 1609 and 1611. The telescope delivered to the Shogun was almost certainly of poorer quality than those used by Galileo, who was at the time producing some of the best lenses in Europe. 

The telescope is then presented and Ieyasu and Adams have a big discussion about and about what it means and what did it mean? Galileo, of course, as we all know ran into big problems with the Church, not because he discovered the rings of Saturn, which they didn’t care very much about but because he discovered that the Earth is not the centre of the world.  [my emphasis] Church history, of course, early Ptolemaic astronomy teaches that the Earth is the centre of the world and the Sun revolves around it, which obviously you would think standing on Earth and watching the Sun move. We still say the Sun rises and sets and goes by the clouds. We use these expressions today although they are, of course, astronomical completely incorrect. So, the Church had a problem because the Bible explicitly says that the Sun moves, and you can’t suddenly say that it doesn’t.

The Catholic Church took a great interest in astronomy and Catholic astronomers, many of them Jesuits or Jesuit trained, took a great interest in all of Galileo’s discoveries including the indecipherable something that later turned out to be the rings of Saturn. Galileo, of course, did not then or at any later time discover that the Earth is not the centre of the world. The conflict between the Bible and the heliocentric hypothesis did not became an issue for the Church before 1615!

Now, the Church didn’t care too much about this because heliocentricity was an extremely abstruse thing. Copernicus was even a Roman Catholic priest and he did his discoveries while living with a Roman Catholic bishop in Poland. But Copernicus book has been called the book that nobody ever read, if you get hold of a copy it’s impossible to read it’s in Latin, it’s completely impossible to understand. So, Copernicus’s discovery of heliocentricity had not really bothered anyone. The thing about the telescope is that any person using a telescope can see for themselves that heliocentricity is correct. This would give the Church considerable worries and that’s why they…it was Galileo pulled before the Inquisition; Copernicus had died peacefully in bed. [my emphasis]

Before I start to dismantle it, one should reflect that this heap of garbage was written by a professor for history at a world-famous institute for higher education. I weep. I’m almost ashamed to admit that my father taught history at the same institution.

Where to start? We start with a couple of simple facts. There is nothing abstruse about the heliocentric hypothesis and Copernicus was not a Roman Catholic priest. He was a canon of the Cathedral of Frombork, who never took holy orders. I do hope that Owen Gingerich doesn’t see this video. The expression the book that nobody read is a quote from Arthur Koestler’s popular history of astronomy, The Sleepwalkers. Gingerich spent several decades searching out all the extant copies of the first and second editions of Copernicus’ De revolutionibus and analysing the readers’ annotations and marginalia to show that an awful lot of people did read it and did so meticulously. He published the results of his long year endeavours in his, An Annotated Census of Copernicus’ De Revolutionibus (Brill, 2002), a very useful reference book for historians of astronomy. He then published an entertaining autobiographical book detailing some of the adventures he experienced compiling his census, The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus (Walker & Company, 2004). There was of course a very lively discussion about De revolutionibus and the heliocentric hypothesis amongst European astronomers between its publication in 1543 and 1611. If Professor Screech is too lazy to plough his way through Gingerich’s Census then might I suggest he reads, Pietro Daniel Omodeo, Copernicus in the Cultural Debates of the Renaissance: Reception, Legacy, Transformation (Brill, 2014) & Jerzy Dobrzycki ed., The Reception of Copernicus’ Heliocentric Theory (D Reidel, 1972). He might actually learn something.

Once again, I find myself flabbergasted by a Screech statement, if you get hold of a copy it’s impossible to read it’s in Latin, it’s completely impossible to understand. This man is an academic historian or at least so he claims. Of course, it’s in bloody Latin that was the academic language of communication in the sixteenth century that all professional astronomers used. Also, for a sixteenth century astronomer the book is perfectly understandable.

Once again Screech takes us into cloud cuckoo land, The thing about the telescope is that any person using a telescope can see for themselves that heliocentricity is correct. I have to ask, when looking through this magic telescope, did the observer see little green Martians holding up a neon sign reading, you are now viewing a heliocentric cosmos? It would be 182 years after the publication of De revolutionibus and 117 after the invention of the telescope before somebody was able, using a telescope, to prove that the Earth orbits the Sun, when in 1725 Molyneux and Bradley detected stellar aberration, delivering the first real empirical evidence for heliocentricity. Empirical evidence for diurnal rotation would first come 126 years later, when Foucault demonstrated his pendulum in 1851!

Screech seems to have problems with chronology; he writes, This would give the Church considerable worries and that’s why they…it was Galileo pulled before the Inquisition; Copernicus had died peacefully in bed. Screech’s story takes place between 1611 and 1613. Galileo’s first run in with the Church, concerning heliocentricity, was in 1615/16 and he was first “pulled” before the Inquisition in 1633.

So, the English had clearly turned up with an object, which was a wonderful thing to see in its own right, but it will also confuse and embarrass the Roman Catholic Church [my emphasis].

No, it wouldn’t! 

And this is where Spain and Portugal come in, hopefully the present given by the king will neutralise the Dutch and show that the English were better than the Dutch but the Spanish and the Portuguese had been there much longer than the Dutch had been there for decades and most of the Spanish are buying and selling, are merchants. But, of course, there are a large number of priests, and the merchants tend to stick to the ports because that’s where they do business but the priest wander all over the place and the priest had had this absolute dream of building a church in Kyoto, which was the capital city at the time, and they had succeeded in doing it.  […] Of course, the missionaries mostly Jesuits […] where seeking conversions. […] But the Jesuits also taught in Japan astronomy and this was absolutely crucial because various Japanese rituals surrounding the court and not the Shogun but the actual Emperor of Japan, it was very important to predict eclipses. This is really key to Japanese political thinking, and over the course of a lunar calendar that went out of sync Japanese astronomers had become less and less able to predict eclipses and the Jesuits could do it. This was also a reason why Christian missions were accepted in China, not to teach the gospel but to teach astronomy. [my emphasis]

I admit, quite freely, that I know nothing about Japanese astronomy in the Early Modern Period, but I do know that this was the function that the Jesuits fulfilled in China in the seventeenth century, which gave them access to Chinese society at the highest levels. They even ran the Chinese office or ministry for astronomy for large parts of that century. This being the case I assume that Screech is correct in saying the same for Japan.

The English had suddenly turned up and they say to the Japanese, all that astronomy they’ve been teaching you for the last fifty years, telling you how important it is, it’s wrong. It’s not only wrong, they know its wrong and they’re teaching you lies. And this must have been what Ieyasu heard in those hours after Saris left the room, while he has in his hands his silver telescope. [my Emphasis]

Just exactly how did the English tell Ieyasu this? As I have already pointed out, he could not have possibly got this information simply by looking through the telescope, as Screech claims, this is pure bullshit.  Screech has obviously never tried to observe the heavens with a replica of an early seventeenth century Dutch or Galilean telescope. If you have never ever used one, and Ieyasu very obviously hadn’t, the very small field of vision means that you see almost nothing. If you are trying to use one without a tripod or some other support, then every slightest tremor of your hand or arms sends the image skittering across the skies. Even worse for Ieyasu, early telescopes suffered from both spherical and chromatic aberration meaning that the image was blurred and had coloured fringes. Add to this that early lenses were of very poor quality and so the images were anything but good and you’re not really going to impress anybody. Almost certainly. Saris and Adams demonstrated the telescope as a terrestrial telescope, as had Lipperhey during his first demonstration in Den Hague in the last September week in 1608.  So, what about Saris and Adams as a source of astronomical information. Saris was a merchant trader and not an astronomer and there is nothing to indicate that he would have been up to date on the actual astronomical/cosmological discussions, let alone that he would have been a, for that time rare, supporter of heliocentricity. Adams is even more unlikely to have been informed of all things astronomical. He had been living in Japan since 1600, so the telescope would have been just as much a novelty for him as it was for Ieyasu. He was however a navigator so he would have had a basic knowledge of astronomy. However, navigators, even today learn geocentric astronomy, so once again no information forthcoming from that quarter.

Saris was given as a result of this permission to open a trading station in Japan and Ieyasu even said you can trade anywhere in my dominions that you wish. […]

Saris sailed back to England at the end of 1613 […] Within months, actually within weeks, even possibly within days of Saris leaving Ieyasu issues an instruction all Jesuit churches must be torn down all priests must leave the country and there was tremendous destruction. And in the early months of 1614 running through into the autumn, was what is often known as the great exile as a vast number of Japanese Christians fled. Mostly they went to the Philippines under Spanish protection or they went to Goa under Portuguese protection. We don’t know the number involved probably in the thousands. Fifty or sixty priest and friars left too […]

Why did it happen then, the Spanish and the Portuguese had been in Japan for fifty year and suddenly in one winter they were told to leave because the English turned up with their telescope.

Screech has turned a correlation into a cause and effect, with a fallacious chain of reasoning based on a series of falsehoods. Analysed rationally the whole argument falls together like a house of cards that was erected with soggy sheets of toilet paper. If we add some more astronomical and historical context then Screech’s whole heap of fact vacant waffle collapses even further.

 Screech informs us that the Japanese, like the Chinese, were interested in the Jesuit’s knowledge of astronomy because of their ability to accurately predict eclipses, which in Asian culture had a massive socio-political and cultural significance. What Screech doesn’t appear to know is that eclipse prediction models are, by nature, fundamentally geocentric as they are based on the relative positions of the Sun and Moon on the ecliptic, the Sun’s apparent path around the Earth. So, the revelation that the solar system is heliocentric and not geocentric, would in this case have no relevance whatsoever.

Next, it pays to take a look at the Jesuits, the early history of the telescope and Asia. Would they have feared, or did they fear the revelations of the telescope? Historically the exact opposite is the case. The Jesuit astronomers of the Collegio Romano, were making telescopic astronomical observations at least as early as Galileo and it was these astronomers, working together with Galileo, who provided the very necessary scientific confirmation of all of his discoveries. Having done so, they threw a large banquet in his honour in Rome. This doesn’t quite fit Screech’s narrative but there is more.

Almost all the telescopes, with possibly only the exception of King James’ present for Ieyasu, introduced into Asia,–India, China and even Japan–in the early part of the seventeenth century were brought there by the Jesuit missionaries. Mainly, like the silver telescope, as presents to impress but also for their own astronomical work. Jesuit missionaries bound for Asia were prepared for their mission at the University of Coimbra in Portugal. We know that from 1615 to 1617 the Jesuit astronomer, Giovanni Paolo Lembo (1570–1618), one of those Collegio Roman astronomers who confirmed Galileo’s discoveries, not only taught those trainee missionaries astronomy but also lens grinding and telescope construction, to enable them to make their own instruments in Asia. The Jesuits were also the first to introduce the heliocentric hypothesis into Asia, which they did in China, in Chinese, during the course of the seventeenth century.

Having completely demolished Screech’s totally crackbrained thesis, could there be another reason why the Jesuits were expelled from Japan shortly after the arrival of the English traders, apart from pure coincidence?

What Screech doesn’t explain in his lecture, maybe he does in his book, but I doubt it, is that there had been serious stress between the Jesuits and the rulers of Japan for several years before the arrival of the English. Toyotomi Hideyoshi, who unified Japan in the mid 1580s was suspicious of the activities of the Catholics and in 1587 he banned Catholicism in Japan. In 1597 twenty-six Christians–six Franciscan missionaries, three Japanese Jesuits and seventeen Japanese laymen–were crucified. Toyotomi Hideyoshi died in 1598 and was succeeded by Tokugawa Ieyasu, who also distrusted the Catholics but wished to trade with both Spain and Portugal. The Protestant Dutch provided a counterbalance, so that the Iberian Catholics did not have a trade monopoly. The arrival of the English in 1613, meant that Ieyasu now had two Protestant European trading partners, who would compete because they didn’t like each other, but who both promised not to try and convert the Japanese to Christianity. Ieyasu could now get rid of the despised Catholics, which he then did in 1614. Simple, factual historical explanation without a cock and bull story about a magical telescope that revealed the heliocentric nature of the cosmos when one simply looked through it.

I find it both fascinatingly gruesome but also frightening and ultimately very depressing that a professor of history from a world-renowned university can propagate a thesis based on the early history of the telescope and the history of the most important transition in the history of astronomy, apparently without bothering to learn anything about either discipline. It appears that his sources were something along the lines of the 1920s Boy’s Own Big Book: Galileo’s Persecution by the Nasty Catholics and Enid Blyton’s Guide to the History of Astronomy for Under Fives.

Screech’s only achievement is that with his, The thing about the telescope is that any person using a telescope can see for themselves that heliocentricity is correct, he delivers one of the mind bogglingly stupid history of science statements that I have ever read.

 The main thesis of his book, which he presents in the lecture analysed here, is an abomination and an insult to every historian of the telescope and/or astronomy. Even worse is the fact that OUP, a major academic publisher, published and are promoting this heap of crap, without having subjected it to any sort of control of the accuracy of its historical content. If OUP possessed even a shred of decency, they should withdraw this book from the market, pulp it and issue a public apology to the history of science community.



Filed under Book Reviews, History of Astronomy

Reading Euclid

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

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


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

Reading Maths01

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

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

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

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

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

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

Reading Maths01

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

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

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

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

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

Reading Maths02

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

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

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

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

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

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

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

Reading Maths03

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

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

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

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A book is a book is a book is a book


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


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

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

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

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

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

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

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

My name is Thony and I am a bookaholic.

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

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

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


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

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


Filed under Autobiographical, Book Reviews

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


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

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


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

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

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


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


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


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

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


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

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

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

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

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

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

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

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

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


Filed under Book Reviews, History of Mathematics

A book or many books?

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

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

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


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


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

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


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

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

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


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

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

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


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

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

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

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


Filed under Book Reviews, History of Mathematics

A Different Royal Society

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

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

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

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

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

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

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

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

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

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

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

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

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


Filed under Book Reviews, Uncategorized

A scientific Dutchman

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5] I have after all a reputation to uphold


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

Our medieval technological inheritance.

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

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

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


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

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

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


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


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

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


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

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

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

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

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

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

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

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

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

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


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