Category Archives: History of science

Renaissance Science – I

To paraphrase what is possibly the most infamous opening sentence in a history of science book[1], there was no such thing as Renaissance science, and this is the is the start of a blog post series about it. Put another way there are all sorts of problems with the term or concept Renaissance Science, several of which should entail abandoning the use of the term and in a later post I will attempt to sketch the problems that exist with the term Renaissance itself and whether there is such a thing as Renaissance science? Nevertheless, I intend to write a blog post series about Renaissance science starting today.

We could and should of course start with the question, which Renaissance? When they hear the term Renaissance, most non-historians tend to think of what is often referred to as the Humanist Renaissance, but historians now use the term for a whole series of period in European history or even for historical periods in other cultures outside of Europe.

Renaissance means rebirth and is generally used to refer to the rediscovery or re-emergence of the predominantly Greek, intellectual culture of antiquity following a period when it didn’t entirely disappear in Europe but was definitely on the backburner for several centuries following the decline and collapse of the Western Roman Empire. The first point to note is that this predominantly Greek, intellectual culture didn’t disappear in the Eastern Roman Empire centred round its capitol Constantinople. An empire that later became known as the Byzantine Empire. The standard myth is that the Humanist Renaissance began with the fall of Byzantium to the Muslims in 1453 but it is just that, a myth.


Raphael’s ‘School of Athens’ (1509–1511) symbolises the recovery of Greek knowledge in the Renaissance Source: Wikimedia Commons

As soon as one mentions the Muslims, one is confronted with a much earlier rebirth of predominantly Greek, intellectual culture, when the, then comparatively young, Islamic Empire began to revive and adopt it in the eight century CE through a massive translation movement of original Greek works covering almost every subject. Writing in Arabic, Arab, Persian, Jewish and other scholars, actively translated the complete spectrum of Greek science into Arabic, analysed it, commented on it, and expanded and developed it, over a period of at least eight centuries.  It is also important to note that the Islamic scholars also collected and translated works from China and India, passing much of the last on to Europe together with the Greek works later during the European renaissances.


The city of Baghdad 150–300 AH (767 and 912 CE) centre of the Islamic recovery and revival of Greek scientific culture Source: Wikimedia Commons

Note the plural at the end of the sentence. Many historians recognise three renaissances during the European Middle Ages. The first of these is the Carolingian Renaissance, which dates to the eighth and ninth century CE and the reigns of Karl der Große (742–814) (known as Charlemagne in English) and Louis the Pious (778–840).


Charlemagne (left) and Pepin the Hunchback (10th-century copy of 9th-century original) Source: Wikimedia Commons

This largely consisted of the setting up of an education system for the clergy throughout Europe and increasing the spread of Latin as the language of learning. Basically, not scientific it had, however, an element of the mathematical sciences, some mathematics, computus (calendrical calculations to determine the date of Easter), astrology and simple astronomy due to the presence of Alcuin of York (c. 735–804) as the leading scholar at Karl’s court in Aachen.


Rabanus Maurus Magnentius (left) another important teacher in the Carolignian Renaissance with Alcuin (middle) presenting his work to Otgar Archbishop of Mainz a supporter of Louis the Pious Source: Wikimedia Commons

Through Alcuin the mathematical work of the Venerable Bede (c. 673–735), (who wrote extensively on mathematical topics and who was also the teacher of Alcuin’s teacher, Ecgbert, Archbishop of York) flowed onto the European continent and became widely disseminated.


The Venerable Bede writing the Ecclesiastical History of the English People, from a codex at Engelberg Abbey in Switzerland. Source: Wikimedia Commons

Karl’s Court had trade and diplomatic relations with the Islamic Empire and there was almost certainly some mathematical influence there in the astrology and astronomy practiced in the Carolingian Empire. It should also be noted that Alcuin and associates didn’t start from scratch as some knowledge of the scholars from late antiquity, such as Boethius (477–524), Macrobius (fl. c. 400), Martianus Capella (fl. c. 410–420) and Isidore of Seville (c. 560–636) had survived. For example, Bede quotes from Isidore’s encyclopaedia the Etymologiae.

The second medieval renaissance was the Ottonian Renaissance in the eleventh century CE during the reigns of Otto I (912–973), Otto II (955–983), and Otto III (980–1002). The start of the Ottonian Renaissance is usually dated to Otto I’s second marriage to Adelheid of Burgundy (931–999), the widowed Queen of Italy in 951, uniting the thrones of Germany (East Francia) and Italy, which led to Otto being crowned Holy Roman Emperor by the Pope in 962.


Statues of Otto I, right, and Adelaide in Meissen Cathedral. Otto and Adelaide were married after his annexation of Italy. Source: Wikimedia Commons

This renaissance was largely confined to the Imperial court and monasteries and cathedral schools. The major influences came from closer contacts with Byzantium with an emphasis on art and architecture.

There was, however, a strong mathematical influence brought about through Otto’s patronage of Gerbert of Aurillac (c. 946–1003). A patronage that would eventually lead to Gerbert becoming Pope Sylvester II.


Sylvester, in blue, as depicted in the Evangelistary of Otto III Source: Wikimedia Commons

A monk in the Monastery of St. Gerald of Aurillac, Gerbert was taken by Count Borrell II of Barcelona to Spain, where he came into direct contact with Islamic culture and studied and learnt some astronomy and mathematics from the available Arabic sources. In 969, Borrell II took Gerbert with him to Rome, where he met both Otto I and Pope John XIII, the latter persuaded Otto to employ Gerbert as tutor for his son the future Otto II. Later Gerbert would exercise the same function for Otto II’s son the future Otto III. The close connection with the Imperial family promoted Gerbert’s ecclesiastical career and led to him eventually being appointed pope but more importantly in our context it promoted his career as an educator.

Gerbert taught the whole of the seven liberal arts, as handed down by Boethius but placed special emphasis on teaching the quadrivium–arithmetic, geometry, music and astronomy–bringing in the knowledge that he had acquired from Arabic sources during his years in Spain. He was responsible for reintroducing the armillary sphere and the abacus into Europe and was one of the first to use Hindu-Arabic numerals, although his usage of them had little effect. He is also reported to have used sighting tubes to aid naked-eye astronomical observations.

Gerbert was not a practicing scientist but rather a teacher who wrote a series of textbook on the then mathematical sciences: Libellus de numerorum divisione, De geometria, Regula de abaco computi, Liber abaci, and Libellus de rationali et ratione uti.


12th century copy of De geometria Source: Wikimedia Commons

His own influence through his manuscripts and his letters was fairly substantial and this was extended by various of his colleagues and students. Abbo of Fleury (c. 945–1004), a colleague, wrote extensively on computus and astronomy, Fulbert of Chartres (c. 960–1028), a direct student, also introduced the use of the Hindu-Arabic numerals. Hermann of Reichenau (1013–1054 continued the tradition writing on the astrolabe, mathematics and astronomy.

Gerbert and his low level, partial reintroduction into Europe of the mathematical science from out of the Islamic cultural sphere can be viewed as a precursor to the third medieval renaissance the so-called Scientific Renaissance with began a century later at the beginning of the twelfth century. This was the mass translation of scientific works, across a wide spectrum, from Arabic into Latin by European scholars, who had become aware of their own relative ignorance compared to their Islamic neighbours and travelled to the border areas between Europe and the Islamic cultural sphere of influence in Southern Italy and Spain. Some of them even travelling in Islamic lands. This Scientific Renaissance took place over a couple of centuries and was concurrent with the founding of the European universities and played a major role in the later Humanist Renaissance to which it was viewed by the humanists as a counterpart. We shall look at it in some detail in the next post.

[1] For any readers, who might not already know, the original quote is, “There was no such thing as the Scientific Revolution, and this is a book about it”, which is the opening sentence of Stevin Shapin’s The Scientific Revolution, The University of Chicago Press, Chicago and London, 1996


Filed under History of science, Mediaeval Science, Renaissance Science, Uncategorized

The emergence of modern astronomy – a complex mosaic: Part LII

This is a concluding summary to my The emergence of modern astronomy – a complex mosaic blog post series. It is an attempt to produce an outline sketch of the path that we have followed over the last two years. There are, at the appropriate points, links to the original posts for those, who wish to examine a given point in more detail. I thank all the readers, who have made the journey with me and in particular all those who have posted helpful comments and corrections. Constructive comments and especially corrections are always very welcome. For those who have developed a taste for a continuous history of science narrative served up in easily digestible slices at regular intervals, a new series will start today in two weeks if all goes according to plan!

There is a sort of standard popular description of the so-called astronomical revolution that took place in the Early Modern period that goes something liker this. The Ptolemaic geocentric model of the cosmos ruled unchallenged for 1400 years until Nicolas Copernicus published his trailblazing De revolutionibus in 1453, introducing the concept of the heliocentric cosmos. Following some initial resistance, Kepler with his three laws of planetary motion and Galileo with his revelatory telescopic discoveries proved the existence of heliocentricity. Isaac Newton with his law of gravity in his Principia in 1687 provided the physical mechanism for a heliocentric cosmos and astronomy became modern. What I have tried to do in this series is to show that this version of the story is almost totally mythical and that in fact the transition from a geocentric to a heliocentric model of the cosmos was a long drawn out, complex process that took many stages and involved many people and their ideas, some right, some only half right and some even totally false, but all of which contributed in some way to that transition.

The whole process started at least one hundred and fifty years before Copernicus published his magnum opus, when at the beginning of the fifteenth century it was generally acknowledged that astronomy needed to be improved, renewed and reformed. Copernicus’ heliocentric hypothesis was just one contribution, albeit a highly significant one, to that reform process. This reform process was largely triggered by the reintroduction of mathematical cartography into Europe with the translation into Latin of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis by Jacopo d’Angelo (c. 1360 – 1411) in 1406. A reliable and accurate astronomy was needed to determine longitude and latitude. Other driving forces behind the need for renewal and reform were astrology, principally in the form of astro-medicine, a widened interest in surveying driven by changes in land ownership and navigation as the Europeans began to widen and expand their trading routes and to explore the world outside of Europe.


The Ptolemaic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

At the beginning of the fifteenth century the predominant system was an uneasy marriage of Aristotelian cosmology and Ptolemaic astronomy, uneasy because they contradicted each other to a large extent. Given the need for renewal and reform there were lively debates about almost all aspects of the cosmology and astronomy throughout the fifteenth and sixteenth centuries, many aspects of the discussions had their roots deep in the European and Islamic Middle Ages, which shows that the 1400 years of unchallenged Ptolemaic geocentricity is a myth, although an underlying general acceptance of geocentricity was the norm.

A major influence on this programme of renewal was the invention of moving type book printing in the middle of the fifteenth century, which made important texts in accurate editions more readily available to interested scholars. The programme for renewal also drove a change in the teaching of mathematics and astronomy on the fifteenth century European universities. 

One debate that was new was on the nature and status of comets, a debate that starts with Toscanelli in the early fifteenth century, was taken up by Peuerbach and Regiomontanus in the middle of the century, was revived in the early sixteenth century in a Europe wide debate between Apian, Schöner, Fine, Cardano, Fracastoro and Copernicus, leading to the decisive claims in the 1570s by Tycho Brahe, Michael Mästlin, and Thaddaeus Hagecius ab Hayek that comets were celestial object above the Moon’s orbit and thus Aristotle’s claim that they were a sub-lunar meteorological phenomenon was false. Supralunar comets also demolished the Aristotelian celestial, crystalline spheres. These claims were acknowledged and accepted by the leading European Ptolemaic astronomer, Christoph Clavius, as were the claims that the 1572 nova was supralunar. Both occurrences shredded the Aristotelian cosmological concept that the heaven were immutable and unchanging.

The comet debate continued with significant impact in 1618, the 1660s, the 1680s and especially in the combined efforts of Isaac Newton and Edmund Halley, reaching a culmination in the latter’s correct prediction that the comet of 1682 would return in 1758. A major confirmation of the law of gravity.

During those early debates it was not just single objects, such as comets, that were discussed but whole astronomical systems were touted as alternatives to the Ptolemaic model. There was an active revival of the Eudoxian-Aristotelian homocentric astronomy, already proposed in the Middle Ages, because the Ptolemaic system, of deferents, epicycles and equant points, was seen to violate the so-called Platonic axioms of circular orbits and uniform circular motion. Another much discussed proposal was the possibility of diurnal rotation, a discussion that had its roots in antiquity. Also, on the table as a possibility was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system rather than the Earth.


The Copernican Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

Early in the sixteenth century, Copernicus entered these debates, as one who questioned the Ptolemaic system because of its breaches of the Platonic axioms, in particular the equant point, which he wished to ban. Quite how he arrived at his radical solution, replace geocentricity with heliocentricity we don’t know but it certainly stirred up those debates, without actually dominating them. The reception of Copernicus’ heliocentric hypothesis was complex. Some simply rejected it, as he offered no real proof for it. A small number had embraced and accepted it by the turn of the century. A larger number treated it as an instrumentalist theory and hoped that his models would deliver more accurate planetary tables and ephemerides, which they duly created. Their hopes were dashed, as the Copernican tables, based on the same ancient and corrupt data, proved just as inaccurate as the already existing Ptolemaic ones. Of interests is the fact that it generated a serious competitor, as various astronomers produced geo-heliocentric systems, extensions of the Capellan model, in which the planets orbit the Sun, which together with the Moon orbits the Earth. Such so-called Tychonic or semi-Tychonic systems, named after their most well-known propagator, incorporated all the acknowledged advantages of the Copernican model, without the problem of a moving Earth, although some of the proposed models did have diurnal rotation.


The Tychonic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

The problem of inaccurate planetary tables and ephemerides was already well known in the Middle Ages and regarded as a major problem. The production of such tables was seen as the primary function of astronomy since antiquity and they were essential to all the applied areas mentioned earlier that were the driving forces behind the need for renewal and reform. Already in the fifteenth century, Regiomontanus had set out an ambitious programme of astronomical observation to provide a new data base for such tables. Unfortunately, he died before he even really got started. In the second half of the sixteenth century both Wilhelm IV Landgrave of Hessen-Kassel and Tycho Brahe took up the challenge and set up ambitious observation programmes that would eventually deliver the desired new, more accurate astronomical data.

At the end of the first decade of the seventeenth century, Kepler’s Astronomia Nova, with his first two planetary laws (derived from Tycho’s new accurate data), and the invention of the telescope and Galileo’s Sidereus Nuncius with his telescopic discoveries are, in the standard mythology, presented as significant game changing events in favour of heliocentricity. They were indeed significant but did not have the impact on the system debate that is usually attributed them. Kepler’s initial publication fell largely on deaf ears and only later became relevant. On Galileo’s telescopic observations, firstly he was only one of a group of astronomers, who in the period 1610 to 1613 each independently made those discoveries, (Thomas Harriot and William Lower, Simon Marius, Johannes Fabricius, Odo van Maelcote and Giovanni Paolo Lembo, and Christoph Scheiner) but what did they show or prove? The lunar features were another nail in the coffin of the Aristotelian concept of celestial perfection, as were the sunspots. The moons of Jupiter disproved the homocentric hypothesis. Most significant discovery was the of the phases of Venus, which showed that a pure geocentric model was impossible, but they were conform with various geo-heliocentric models.

1613 did not show any clarity on the way to finding the true model of the cosmos but rather saw a plethora of models competing for attention. There were still convinced supporters of a Ptolemaic model, both with and without diurnal rotation, despite the phases of Venus. Various Tychonic and semi-Tychonic models, once again both with and without diurnal rotation. Copernicus’ heliocentric model with its Ptolemaic deferents and epicycles and lastly Kepler’s heliocentric system with its elliptical orbits, which was regarded as a competitor to Copernicus’ system. Over the next twenty years the fog cleared substantially and following Kepler’s publication of his third law, his Epitome Astronomiae Copernicanae, which despite its title is a textbook on his elliptical system and the Rudolphine Tables, again based on Tycho’s data, which delivered the much desired accurate tables for the astrologers, navigators, surveyors and cartographers, and also of Longomontanus’ Astronomia Danica (1622) with his own tables derived from Tycho’s data presenting an updated Tychonic system with diurnal rotation, there were only two systems left in contention.

Around 1630, we now have two major world systems but not the already refuted geocentric system of Ptolemaeus and the largely forgotten Copernican system as presented in Galileo’s Dialogo but Kepler’s elliptical heliocentricity and a Tychonic system, usually with diurnal rotation. It is interesting that diurnal rotation became accepted well before full heliocentricity, although there was no actually empirical evidence for it. In terms of acceptance the Tychonic system had its nose well ahead of Kepler because of the lack of any empirical evidence for movement of the Earth.

Although there was still not a general acceptance of the heliocentric hypothesis during the seventeenth century the widespread discussion of it in continued in the published astronomical literature, which helped to spread knowledge of it and to some extent popularise it. This discussion also spread into and even dominated the newly emerging field of proto-sciencefiction.

Galileo’s Dialogo was hopelessly outdated and contributed little to nothing to the real debate on the astronomical system. However, his Discorsi made a very significant and important contribution to a closely related topic that of the evolution of modern physics. The mainstream medieval Aristotelian-Ptolemaic cosmological- astronomical model came as a complete package together with Aristotle’s theories of celestial and terrestrial motion. His cosmological model also contained a sort of friction drive rotating the spheres from the outer celestial sphere, driven by the unmoved mover (for Christians their God), down to the lunar sphere. With the gradual demolition of Aristotelian cosmology, a new physics must be developed to replace the Aristotelian theories.

Once again challenges to the Aristotelian physics had already begun in the Middle Ages, in the sixth century CE with the work of John Philoponus and the impetus theory, was extended by Islamic astronomers and then European ones in the High Middle Ages. In the fourteenth century the so-called Oxford Calculatores derived the mean speed theorem, the core of the laws of fall and this work was developed and disseminated by the so-called Paris Physicists. In the sixteenth century various mathematicians, most notably Tartaglia and Benedetti developed the theories of motion and fall further. As did in the early seventeenth century the work of Simon Stevin and Isaac Beeckman. These developments reached a temporary high point in Galileo’s Discorsi. Not only was a new terrestrial physics necessary but also importantly for astronomy a new celestial physics had to be developed. The first person to attempt this was Kepler, who replaced the early concept of animation for the planets with the concept of a force, hypothesising some sort of magnetic force emanating from the Sun driving the planets around their orbits. Giovanni Alfonso Borelli also proposed a system of forces as the source of planetary motion.

Throughout the seventeenth century various natural philosophers worked on and made contributions to defining and clarifying the basic terms that make up the science of dynamics: force, speed, velocity, acceleration, etc. as well as developing other areas of physics, Amongst them were Simon Stevin, Isaac Beeckman, Borelli, Descartes, Pascal, Riccioli and Christiaan Huygens. Their efforts were brought together and synthesised by Isaac Newton in his Principia with its three laws of motion, the law of gravity and Kepler’s three laws of planetary motion, which laid the foundations of modern physics.

In astronomy telescopic observations continued to add new details to the knowledge of the solar system. It was discovered that the planets have diurnal rotation, and the periods of their diurnal rotations were determined. This was a strong indication the Earth would also have diurnal rotation. Huygens figured out the rings of Saturn and discovered Titan its largest moon. Cassini discovered four further moons of Saturn. It was already known that the four moons of Jupiter obeyed Kepler’s third law and it would later be determined that the then known five moons of Saturn also did so. Strong confirming evidence for a Keplerian model.

Cassini showed by use of a heliometer that either the orbit of the Sun around the Earth or the Earth around the Sun was definitively an ellipse but could not determine which orbited which. There was still no real empirical evidence to distinguish between Kepler’s elliptical heliocentric model and a Tychonic geo-heliocentric one, but a new proof of Kepler’s disputed second law and an Occam’s razor argument led to the general acceptance of the Keplerian model around 1660-1670, although there was still no empirical evidence for either the Earth’s orbit around the Sun or for diurnal rotation. Newton’s Principia, with its inverse square law of gravity provided the physical mechanism for what should now best be called the Keplerian-Newtonian heliocentric cosmos.

Even at this juncture with a very widespread general acceptance of this Keplerian-Newtonian heliocentric cosmos there were still a number of open questions that needed to be answered. There were challenges to Newton’s work, which, for example, couldn’t at that point fully explain the erratic orbit of the Moon around the Earth. This problem had been solved by the middle of the eighteenth century. The mechanical philosophers on the European continent were anything but happy with Newton’s gravity, an attractive force that operates at a distance. What exactly is it and how does it function? Questions that even Newton couldn’t really answer. Leibniz also questioned Newton’s insistence that time and space were absolute, that there exists a nil point in the system from which all measurement of these parameters are taken. Leibniz preferred a relative model.

There was of course also the very major problem of the lack of any form of empirical evidence for the Earth’s movement. Going back to Copernicus nobody had in the intervening one hundred and fifty years succeeded in detecting a stellar parallax that would confirm that the Earth does indeed orbit the Sun. This proof was finally delivered in 1725 by Samuel Molyneux and James Bradley, who first observed, not stellar parallax but stellar aberration. An indirect proof of diurnal rotation was provided in the middle of the eighteenth century, when the natural philosophers of the French Scientific Academy correctly determined the shape of the Earth, as an oblate spheroid, flattened at the pols and with an equatorial bulge, confirming the hypothetical model proposed by Newton and Huygens based on the assumption of a rotating Earth.

Another outstanding problem that had existed since antiquity was determining the dimensions of the known cosmos. The first obvious method to fulfil this task was the use of parallax, but whilst it was already possible in antiquity to determine the distance of the Moon reasonably accurately using parallax, down to the eighteenth century it proved totally impossible to detect the parallax of any other celestial body and thus its distance from the Earth. Ptolemaeus’ geocentric model had dimensions cobbled together from its data on the crystalline spheres. One of the advantages of the heliocentric model is that it gives automatically relative distances for the planets from the sun and each other. This means that one only needs to determine a single actually distance correctly and all the others are automatically given. Efforts concentrated on determining the distance between the Earth and the Sun, the astronomical unit, without any real success; most efforts producing figures that were much too small.

Developing a suggestion of James Gregory, Edmond Halley explained how a transit of Venus could be used to determine solar parallax and thus the true size of the astronomical unit. In the 1760s two transits of Venus gave the world the opportunity to put Halley’s theory into practice and whilst various problems reduced the accuracy of the measurements, a reasonable approximation for the Sun’s distance from the Earth was obtained for the very first time and with it the actually dimensions of the planetary part of the then known solar system. What still remained completely in the dark was the distance of the stars from the Earth. In the 1830s, three astronomers–Thomas Henderson, Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve–all independently succeeded in detecting and measuring a stellar parallax thus completing the search for the dimensions of the known cosmos and supplying a second confirmation, after stellar aberration, for the Earth’s orbiting the Sun.

In 1851, Léon Foucault, exploiting the Coriolis effect first hypothesised by Riccioli in the seventeenth century, finally gave a direct empirical demonstration of diurnal rotation using a simple pendulum, three centuries after Copernicus published his heliocentric hypothesis. Ironically this demonstration was within the grasp of Galileo, who experiment with pendulums and who so desperately wanted to be the man who proved the reality of the heliocentric model, but he never realised the possibility. His last student, Vincenzo Viviani, actually recorded the Coriolis effect on a pendulum but didn’t realise what it was and dismissed it as an experimental error.

From the middle of the eighteenth century, at the latest, the Keplerian-Newtonian heliocentric model had become accepted as the real description of the known cosmos. Newton was thought not just to have produced a real description of the cosmos but the have uncovered the final scientific truth. This was confirmed on several occasions. Firstly, Herschel’s freshly discovered new planet Uranus in 1781 fitted Newton’s theories without problem, as did the series of asteroids discovered in the early nineteenth century. Even more spectacular was the discovery of Neptune in 1846 based on observed perturbations from the path of Uranus calculated with Newton’s theory, a clear confirmation of the theory of gravity. Philosophers, such as Immanuel Kant, no longer questioned whether Newton had discovered the true picture of the cosmos but how it had been possible for him to do so.


However, appearances were deceptive, and cracks were perceptible in the Keplerian-Newtonian heliocentric model. Firstly, Leibniz’s criticism of Newton’s insistence on absolute time and space rather than a relative model would turn out to have been very perceptive. Secondly, Newton’s theory of gravity couldn’t account for the observed perihelion precession of the planet Mercury. Thirdly in the 1860s, based on the experimental work of Michael Faraday, James Maxwell produced a theory of electromagnetism, which was not compatible with Newtonian physics. Throughout the rest of the century various scientists including Hendrik Lorentz, Georg Fitzgerald, Oliver Heaviside, Henri Poincaré, Albert Michelson and Edward Morley tried to find a resolution to the disparities between the Newton’s and Maxwell’s theories. Their efforts finally lead to Albert Einstein’s Special Theory of Relativity and then on to his General theory of Relativity, which could explain the perihelion precession of the planet Mercury. The completion of the one model, the Keplerian-Newtonian heliocentric one marked the beginnings of the route to a new system that would come to replace it.


Filed under History of Astronomy, History of science, Newton, Renaissance Science

Illuminating medieval science


There is a widespread popular vision of the Middle ages, as some sort of black hole of filth, disease, ignorance, brutality, witchcraft and blind devotion to religion. This fairly-tale version of history is actively propagated by authors of popular medieval novels, the film industry and television, it sells well. Within this fantasy the term medieval science is simply an oxymoron, a contradiction in itself, how could there possible be science in a culture of illiterate, dung smeared peasants, fanatical prelates waiting for the apocalypse and haggard, devil worshipping crones muttering curses to their black cats?

Whilst the picture I have just drawn is a deliberate caricature this negative view of the Middle Ages and medieval science is unfortunately not confined to the entertainment industry. We have the following quote from Israeli historian Yuval Harari from his bestselling Sapiens: A Brief History of Humankind (2014), which I demolished in an earlier post.

In 1500, few cities had more than 100,000 inhabitants. Most buildings were constructed of mud, wood and straw; a three-story building was a skyscraper. The streets were rutted dirt tracks, dusty in summer and muddy in winter, plied by pedestrians, horses, goats, chickens and a few carts. The most common urban noises were human and animal voices, along with the occasional hammer and saw. At sunset, the cityscape went black, with only an occasional candle or torch flickering in the gloom.

On medieval science we have the even more ignorant point of view from American polymath and TV star Carl Sagan from his mega selling television series Cosmos, who to quote the Cambridge History of Medieval Science:

In his 1980 book by the same name, a timeline of astronomy from Greek antiquity to the present left between the fifth and the late fifteenth centuries a familiar thousand-year blank labelled as a “poignant lost opportunity for mankind.” 

Of course, the very existence of the Cambridge History of Medieval Science puts a lie to Sagan’s poignant lost opportunity, as do a whole library full of monographs and articles by such eminent historians of science as Edward Grant, John Murdoch, Michael Shank, David Lindberg, Alistair Crombie and many others.

However, these historians write mainly for academics and not for the general public, what is needed is books on medieval science written specifically for the educated layman; there are already a few such books on the market, and they have now been joined by Seb Falk’s truly excellent The Light Ages: The Surprising Story of Medieval Science.[1]  


How does one go about writing a semi-popular history of medieval science? Falk does so by telling the life story of John of Westwyk an obscure fourteenth century Benedictine monk from Hertfordshire, who was an astronomer and instrument maker. However, John of Westwyk really is obscure and we have very few details of his life, so how does Falk tell his life story. The clue, and this is Falk’s masterstroke, is context. We get an elaborate, detailed account of the context and circumstances of John’s life and thereby a very broad introduction to all aspects of fourteenth century European life and its science.

We follow John from the agricultural village of Westwyk to the Abbey of St Albans, where he spent the early part of his life as a monk. We accompany some of his fellow monks to study at the University of Oxford, whether John studied with them is not known.


Gloucester College was the Benedictine College at Oxford where the monks of St Albans studied

We trudge all the way up to Tynemouth on the wild North Sea coast of Northumbria, the site of daughter cell of the great St Alban’s Abbey, main seat of Benedictines in England. We follow John when he takes up the cross and goes on a crusade. Throughout all of his wanderings we meet up with the science of the period, John himself was an astronomer and instrument maker.

Falk is a great narrator and his descriptive passages, whilst historically accurate and correct,[2] read like a well written novel pulling the reader along through the world of the fourteenth century. However, Falk is also a teacher and when he introduces a new scientific instrument or set of astronomical tables, he doesn’t just simply describe them, he teachers the reader in detail how to construct, read, use them. His great skill is just at the point when you think your brain is going to bail out, through mathematical overload, he changes back to a wonderfully lyrical description of a landscape or a building. The balance between the two aspects of the book is as near perfect as possible. It entertains, informs and educates in equal measures on a very high level.

Along the way we learn about medieval astronomy, astrology, mathematics, medicine, cartography, time keeping, instrument making and more. The book is particularly rich on the time keeping and the instruments, as the Abbott of St Albans during John’s time was Richard of Wallingford one of England’s great medieval scientists, who was responsible for the design and construction of one of the greatest medieval church clocks and with his Albion (the all in one) one of the most sophisticated astronomical instruments of all time. Falk’ introduction to and description of both in first class.


The book is elegantly present with an attractive typeface and is well illustrated with grey in grey prints and a selection of colour ones. There are extensive, informative endnotes and a good index. If somebody reads this book as an introduction to medieval science there is a strong chance that their next question will be, what do I read next. Falk gives a detailed answer to this question. There is an extensive section at the end of the book entitled Further Reading, which gives a section by section detailed annotated reading list for each aspect of the book.

Seb Falk has written a brilliant introduction to the history of medieval science. This book is an instant classic and future generations of schoolkids, students and interested laypeople when talking about medieval science will simply refer to the Falk as a standard introduction to the topic. If you are interested in the history of medieval science or the history of science in general, acquire a copy of Seb Falk’s masterpiece, I guarantee you won’t regret it.

[1] American edition: Seb Falk, The Light Ages: The Surprising Story of Medieval Science, W. W. Norton & Co., New York % London, 2020

British Edition: Seb Falk, The Light Ages: A Medieval Journey of Discover, Allen Lane, London, 2020

[2] Disclosure: I had the pleasure and privilege of reading the whole first draft of the book in manuscript to check it for errors, that is historical errors not grammatical or orthographical ones, although I did point those out when I stumbled over them.


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of science, Mediaeval Science, Myths of Science

The emergence of modern astronomy – a complex mosaic: Part L


By the end of the eighteenth century, Newton’s version of the heliocentric theory was firmly established as the accepted model of the solar system. Whilst not yet totally accurate, a reasonable figure for the distance between the Earth and the Sun, the astronomical unit, had been measured and with it the absolute, rather than relative, sizes of the orbits of the known planets had been calculated. This also applied to Uranus, the then new planet discovered by the amateur astronomer, William Herschel (1738–1822), in 1781; the first planet discovered since antiquity. However, one major problem still existed, which needed to be solved to complete the knowledge of the then known cosmos. Astronomers and cosmologists still didn’t know the distance to the stars. It had long been accepted that the stars were spread out throughout deep space and not on a fixed sphere as believed by the early astronomer in ancient Greece. It was also accepted that because all attempts to measure any stellar parallax down the centuries had failed, the nearest stars must actually be at an unbelievably far distance from the Earth.

Here we meet a relatively common phenomenon in the history of science, almost simultaneous, independent, multiple discoveries of the same fact. After literally two millennia of failures to detect any signs of stellar parallax, three astronomers each succeeded in measuring the parallax of three different stars in the 1830s. This finally was confirmation of the Earth’s annual orbit around, independent of stellar aberration and gave a yardstick for the distance of the stars from the Earth.

The first of our three astronomers was the Scotsman, Thomas Henderson (1798–1844).


Thomas Henderson Source: Wikimedia Commons

Henderson was born in Dundee where he also went to school. He trained as a lawyer but was a keen amateur astronomer. He came to the attention of Thomas Young (1773-1829), the superintendent of the HM Nautical Almanac Office, after he devised a new method for determining longitude using lunar occultation, that is when a star disappears behind the Moon. Young brought him into the world of astronomy and upon his death recommended Henderson as his successor.


Copy of a portrait of Thomas Young by Henry Briggs Source: Wikimedia Commons

Henderson didn’t receive to post but was appointed director of the Royal Observatory at the Cape of Good Hope. The observatory had only opened in 1828 after several years delay in its construction. The first director Fearon Fallows (1788–1831), who had overseen the construction of the observatory had died of scarlet fever in 1831 and Henderson was appointed as his successor, arriving in 1832.


The Royal Observatory Cape of Good Hope in 1857 Illustrated London News, 21 March 1857/Ian Glass Source: Wikimedia Commons

The Cape played a major role in British observational astronomy. In the eighteenth century, it was here that Charles Mason (1728–1786) and Jeremiah Dixon (1733–1779), having been delayed in their journey to their designated observational post in Sumatra, observed the transit of Venus of 1761. John Herschel (1792–1871), the son and nephew of the astronomers William and Caroline Herschel, arrived at the Cape in 1834 and carried extensive astronomical observation there with his own 21-foot reflecting telescope. cooperating with Henderson successor Thomas Maclear. In 1847, Herschel published his Results of Astronomical Observations made at the Cape of Good Hope, which earned him the Copley Medal of the Royal Society.

Manuel John Johnson (1805–1859), director of the observatory on St Helena, drew Henderson’s attention to the fact that Alpha Centauri displayed a high proper motion.


Ladder Hill Observatory St Helena Source

Proper motion is the perceived motion of a star relative to the other stars. Although the position of the stars relative to each other appears not to change over long periods of time they do. There had been speculation about the possibility of this since antiquity, but it was first Edmund Halley, who in 1718 proved its existence by comparing the measured positions of prominent stars from the historical record with their current positions. A high proper motion is an indication that a star is closer to the Earth.

Aimed with this information Henderson began to try to determine the stellar parallax of Alpha Centauri. However, Henderson hated South Africa and he resigned his position at the observatory in 1833 and returned to Britain. In his luggage he had nineteen very accurate determinations of the position of Alpha Centauri. Back in Britain Henderson was appointed the first Astronomer Royal for Scotland in 1834 and professor for astronomy at the University of Edinburgh, position he held until his death.

Initially Henderson did not try to determine the parallax of Alpha Centauri from his observational data. He thought that he had too few observations and was worried that he would join the ranks of many of his predecessors, who had made false claims to having discovered stellar parallax; Henderson preferred to wait until he had received more observational data from his assistant William Meadows (?–?). This decision meant that Henderson, whose data did in fact demonstrate stellar parallax for Alpha Centauri, who had actually won the race to be the first to determine stellar parallax, by not calculating and publishing, lost the race to the German astronomer Friedrich Wilhelm Bessel (1784–1846).


Portrait of the German mathematician Friedrich Wilhelm Bessel by the Danish portrait painter Christian Albrecht Jensen Source: Wikimedia Commons

Like Henderson, Bessel was a self-taught mathematician and astronomer. Born in Minden as the son of a minor civil servant, at the age of fourteen he started a seven-year apprenticeship as a clerk to an import-export company in Bremen. Bessel became interested in the navigation on which the company’s ships were dependent and began to teach himself navigation, and the mathematics and astronomy on which it depended. As an exercise he recalculated the orbit of Halley’s Comet, which he showed to the astronomer Heinrich Wilhelm Olbers (1758–1840), who also lived in Bremen.


Portrait of the german astronomer Heinrich Wilhelm Matthias Olbers (lithography by Rudolf Suhrlandt Source: Wikimedia Commons

Impressed by the young man’s obvious abilities, Olbers became his mentor helping him to get his work on Halley’s Comet published and guiding his astronomical education. In 1806, Olbers obtained a position for Bessel, as assistant to Johann Hieronymus Schröter (1745–1816) in Lilienthal.


Johann Hieronymus Schröter Source: Wikimedia Commons

Here Bessel served his apprenticeship as an observational astronomer and established an excellent reputation.


Schröter’s telescope in Lilienthal on which Bessel served his apprenticeship as an observational astronomer

Part of that reputation was built up through his extensive correspondence with other astronomers throughout Europe, including Johann Carl Fried Gauss (1777–1855). It was probably through Gauss’ influence that in 1809 Bessel, at the age of 25, was appointed director of the planned state observatory in Königsberg, by Friedrich Wilhelm III, King of Prussia.


Königsberg Observatory in 1830. It was destroyed by bombing in the Second World War. Source: Wikimedia Commons

Bessel oversaw the planning, building and equipping of the new observatory, which would be his home and his workplace for the rest of his life. From the beginning he planned to greatly increase the accuracy of astronomical observations and calculation. He started by recalculated the positions of the stars in John Flamsteed’s stellar catalogue, greatly increasing the accuracy of the stellar positions. Bessel also decided to try and solve the problem of determining stellar parallax, although it would be some time before he could undertake that task.

One of the astronomers with whom Bessel took up contact was Friedrich Georg Wilhelm von Struve (1793–1864), who became a good friend and his rival in the search for stellar parallax, although the rivalry was always good natured. Struve was born the son of Jacob Struve (1755–1841), a schoolteacher and mathematician, in Altona then in the Duchy of Holstein, then part of the Denmark–Norway Kingdom and a Danish citizen.


Friedrich Georg Wilhelm von Struve Source: Wikimedia Commons

Whilst he was still a youth, his father sent him to live in Dorpat (nowadays Tartu) in Estonia with his elder brother, to avoid being drafted into the Napoleonic army. In Dorpat he registered as a student at the university to study, at the wish of his father, philosophy and philology but also registered for a course in astronomy. He financed his studies by working as a private tutor to the children of a wealthy family. He graduated with a degree in philology in 1811 and instead of becoming a history teacher, as his father wished, he took up the formal study of astronomy. The university’s only astronomer, Johann Sigismund Gottfried Huth (1763–1818), was a competent scholar but was an invalid, so Struve basically taught himself and had free run of the university’s observatory whilst still a student, installing the Dolland transit telescope that was still packed in the crates it was delivered in. In 1813 he graduated PhD and was, at the age of just twenty, appointed to the faculty of the university. He immediately began his life’s work, the systematic study of double stars.


The old observatory building in Dorpat (Tartu) Source: Wikimedia Commons

Like Bessel, Struve was determined to increase the accuracy of observational astronomy. In 1820 whilst in München, to pick up another piece of observational equipment, he visited Europe’s then greatest optical instrument maker, Joseph Fraunhofer (1787–1826), who was putting the finishing touches to his greatest telescopic creation, a refractor with a 9.5-inch lens.


Joseph Fraunhofer Source: Wikimedia Commons

Struve had found his telescope. He succeeded in persuading the university to purchase the telescope, known as the ‘Great Refractor’ and began his search for observational perfection.


Frauenhofer’s Great Refractor Source: Wikimedia Commons

Like Struve, Bessel turned to Fraunhofer for the telescope of his dreams. However, unlike Struve, whose telescope was a general-purpose instrument, Bessel desired a special purpose-built heliometer, a telescope with a split objective lens, especially conceived to accurately measure the distance between two observed objects. The first  really practical heliometer was created by John Dolland (1706–1761) to measure the variations in the diameter of the Sun, hence the name. Bessel needed this instrument to fulfil his dream of becoming the first astronomer to accurately measure stellar parallax. Bessel got his Fraunhofer in 1829.


Königsberger Heliometer Source: Wikimedia Commons

One can get a very strong impression of Bessel’s obsession with accuracy in that he devoted five years to erecting, testing, correcting and controlling his new telescope. In 1834 he was finally ready to take up the task he had set himself. However, other matters that he had to attend to prevented him from starting on his quest.

The Italian astronomer Giuseppe Piazzi (1746–1826), famous for discovering the first asteroid, Ceres, had previously determined that the star 61 Cygni had a very high proper motion, meaning it was probably relatively close to the Earth and this was Bessel’s intended target for his attempt to measure stellar parallax.


Giuseppe Piazzi pointing at the asteroid Ceres Painting by Giuseppe Velasco (1750–1826). Source: Wikimedia Commons

It was also Struve’s favoured object for his attempt but, unfortunately, he was unable in Dorpat with his telescope to view both 61 Cygni and a reference star against which to measure any observable parallax, so he turned his attention to Vega instead. In 1837, Bessel was more than somewhat surprised when he received a letter from Struve containing seventeen preliminary parallax observations of Vega. Struve admitted that they were not yet adequate to actually determine Vega’s parallax, but it was obvious that he was on his way. Whether Struve’s letter triggered Bessel’s ambition is not known but he relatively soon began a year of very intensive observations of 61 Cygni. In 1838 having checked and rechecked his calculations, and dismantled and thoroughly examined his telescope for any possible malfunctions, he went public with the news that he had finally observed a measurable parallax of 61 Cygni. He sent a copy of his report to John Herschel, President of the Royal Astronomical Society in London. After Herschel had carefully studied the report and after Bessel had answered all of his queries to his satisfaction. Herschel announced to the world that stellar parallax had finally been observed. For his work Bessel was awarded the Gold Medal of the Royal Astronomical Society. Just two months later, Henderson, who had in the meantime done the necessary calculations, published his measurement of the stellar parallax of Alpha Centauri. In 1839 Struve announced his for Vega. Bessel did not rest on his laurels but reassembling his helioscope he spent another year remeasuring 61 Cygni’s parallax correcting his original figures. 

All three measurements were accepted by the astronomical community and both Henderson and Struve were happy to acknowledge Bessel’s priority. There was no sense of rivalry between them and the three men remained good friends. Modern measurements have shown that Bessel’s figures were within 90% of the correct value, Henderson’s with in 75%, but Struve’s were only within 50%. The last is not surprising as Vega is much further from the Earth than either Alpha Centauri or Cygni 61 making it parallax angle much, much smaller and thus considerably more difficult to measure.

In the sixteenth century Tycho Brahe rejected heliocentricity because the failure to detect stellar parallax combined with his fallacious big star argument meant that in a heliocentric system the stars were for him inconceivably far away. I wonder what he would think about the fact that Earth’s nearest stellar neighbour Proxima Centauri is 4.224 lightyears away, that is 3. 995904 x 1013 kilometres!



Filed under History of Astronomy, History of Optics, History of science, History of Technology

A master instrument maker from a small town in the Fränkischen Schweiz


Eggolsheim is a small market town about twenty kilometres almost due north of Erlangen in the Fränkischen Schweiz (Franconian Switzerland).


Eggolsheim Source: Wikimedia Commons

The Fränkischen Schweiz is a hilly area with many rock faces and caves in Middle Franconia, to the north of Nürnberg that is very popular with tourists, day trippers, wanderers, rock-climbers and potholers. It also has lots of old churches and castles.


Fränkische Schweiz Source Wikimedia Commons

When I first moved to Middle Franconia the Fränkischen Schweiz had the highest density of private breweries of anywhere in the world. It also has many bierkeller that during the summer months attract large crowds of visitors at the weekend. Eggolsheim is these days probably best known for its bierkeller, but in the late fifteenth century it was the birthplace of the Renaissance mathematicus, Georg Hartmann, who would become one of the leading instrument makers in Renaissance Nürnberg in the early sixteenth century.


Georg Hartmann Source: Astronomie in Nürnberg

Hartmann was born on 9 February 1489. Unfortunately, as with so many Renaissance figures, we know nothing about his background or childhood. He matriculated at the university of Ingolstadt in 1503, which is where people from Franconia often studied as there were no University in either Nürnberg or Bamberg. Johannes Werner and Johannes Stabius, two other members of Nürnberg’s Renaissance mathematical community were graduates of Ingolstadt. In 1506, Hartmann transferred to the University of Köln, where he studied mathematics and theology, graduating in 1510. As was quite common during this period he completed his studies on a journey through Italy between 1510 and 1518. He spent several years in Rome, where he was friends with Andreas Copernicus, the older brother of Nicolas, who died in Rome, possibly of leprosy or syphilis in 1518.

In 1518 Hartmann arrived in Nürnberg, where he was appointed a vicar of the St. Sebaldus Church, one of the two parish churches of the city. Unlike the modern Anglican Church, where the vicar is the principal priest of a church, in the sixteenth century Catholic Church a vicar was a deputy or replacement priest with a special function appointed either permanently or temporarily. He might, for example, be appointed to sing a daily mass in the name of a rich deceased member of the parish, who left a stipend in his will to pay for this service, as another of Nürnberg’s mathematical community, Johannes Schöner, was appointed to do in Kirchehrenbach, also in the Fränkischen Schweiz, in 1523. We don’t know what Hartmann’s specific duties in the St. Sebaldus Church were. In 1522 he was also granted the prebend of the St. Walburga Chapel in Nürnberg.

St. Sebald von Norden

St. Sebaldus in Nürnberg Source: Wikimedia Commons

This was a sinecure. It was not unusual for mathematici to receive sinecures from the Church to enable them to carry out their activities as mathematicians, instrument makers or cartographers in the service of the Church. This was certainly the case with Johannes Schöner, who was many years paid as a member of the St Joseph Beneficence in Bamberg but worked as mathematicus, printer and bookbinder for the Bishop. If this was actually so in Hartmann’s case is not known.

When he arrived in Nürnberg he became part of the, for the time, comparatively large community of mathematici, print makers, printer/publishers and instrument makers, which included both Werner and Stabius, the latter as a regular visitor, but both of whom died in 1522. I have written about this group before here and here. It also included Schöner, who only arrived in 1525, Erhard Etzlaub, Johann Neudörffer, Johannes Petreius and Albrecht Dürer.  Central to this group was Willibald Pirckheimer, who although not a mathematicus, was a powerful local figure–humanist scholar, merchant trader, soldier, politician, Dürer’s friend and patron–who had translated Ptolemaeus’ Geographia from Greek into Latin. Hartmann was friends with both Pirckheimer and Dürer, and acted as Schöner’s agent in Nürnberg, selling his globes in the city, during the time Schöner was still living in Kirchehrenbach. Like other members of this group Hartmann also stood in contact with and corresponded with many other scholars throughout Europe; the Nürnberger mathematici were integrated into the European network of mathematici.

Hartmann established himself as one of Nürnberg’s leading scientific instrument makers; he is known to have produced sundials, astrolabes, armillary spheres and globes. None of his armillary spheres or globes are known to have survived, although a few globe gores made by him are extant, an important factor when trying to assess the impact or range of an instrument maker, we can only work with that which endures the ravages of time. We know for example that Hartmann’s friend and colleague, Schöner, produced and sold large numbers of terrestrial and celestial globes but only a small handful of his globes are preserved.

A total of nine of Hartmann’s brass astrolabes are known to have survived and here Hartmann proved to be an innovator.


Hartmann astrolabe front



Hartmann astrolabe back

As far as is known, Hartmann was the earliest astrolabe maker to introduce serial production of this instrument. It is now assumed that he designed the instruments and then commissioned some of Nürnberg’s numerous metal workers to mass produce the separate parts of the astrolabe, which he them assembled and sold. Nine astrolabes might not seem a lot but compared to other known astrolabe makers, from whom often just one or two instruments are known, this is a comparatively large number. This survival rate suggests that Hartmann made and sold a large number of his mass-produced instruments.  

With his sundials the survival rate is much higher, there are seventy-five know Hartmann sundials in collection around the world. Hartmann made sundials of every type in brass, gold and ivory but is perhaps best known for his portable diptych sundials, a Nürnberg specialty. A diptych consists of two flat surfaces, usually made of ivory, connected by a hinge that fold flat to be put into a pocket. When opened the two surfaces are at the correct angle and joined by a thread, which functions as the dial’s gnomon. The lower surface contains a compass to help the user correctly orientate his dial during use.


Hartmann diptych sundial open


Hartmann diptych sundial closed


Open diptych sundial showing string gnomon and Hartmann’s name

Hartmann also made elaborate dials such as this ivory crucifix dial.


One thing that Hartmann is noted for is his paper instruments*. These are the elements for instrument printed on sheets of paper. These can be cut out and glued to thin wood backing to construct cheap but fully functioning instruments. Of course, the survival rates of such instruments are very low and in fact only one single paper astrolabe printed by Hartmann is known to have survived.


Hartmann paper astrolabe Source:History of Science Museum Oxford

However, we are lucky that several hundred sheets of Hartmann’s printed paper instruments have survived and are now deposited in various archives. There have been discussions, as to whether these were actually intended to be cut out and mounted onto wood to create real instruments or whether there are intended as sales archetypes, designed to demonstrate to customers the instruments that Hartmann would then construct out of ivory, brass or whatever.

Hartmann_Kruzifix_1529,_AGKnr4_2004,_s12 Hartmann paper crucifix


Printed paper instrument part



Apart from designing and constructing instruments Hartman was obviously engaged in writing a book on how to design and construct instrument. Several partial manuscripts of this intended work exist but the book was never finished in his lifetime. The book however does reveal his debt as an instrument designer to Johannes Stöffler’s Elucidatio fabricae usuque astrolabii.

As a manufacturer of portable sun dials with built in compasses Hartmann also developed a strong interest in the magnetic compass. Whilst living in Rome he determined the magnetic declination of the city, i.e., how much a compass needle varies from true north in that location. Hartmann also appears to have been the first to discover magnetic dip or inclination, which information he shared with Duke Albrecht of Prussia in a letter in 1544, but he never published his discovery, so it is usually credited to the English mariner Robert Norman, who published the discovery in his The Newe Attractive, shewing The Nature, Propertie, and manifold Vertues of the Loadstone; with the declination of the Needle, Touched therewith, under the Plaine of the Horizon in 1581.

The only book that Hartmann did publish in his lifetime was an edition of John Peckham’s Perspectiva communis, the most widely used medieval optic textbook, which was printed by Johannes Petreius in 1542.


Hartmann died in Nürnberg in 1564 and was buried in the St Johannes graveyard, outside the city walls, where the graves of his friend Pirckheimer, Dürer and Petreius can also be found amongst many other prominent citizens of the Renaissance city.  


Hartmann’s grave Source: Astronomie in Nürnberg


Hartmann’s epitaph Source: Astronomie in Nürnberg

  • For a detailed description of Hartmann’s printed paper instruments see: Suzanne Karr Schmidt, Interactive and Sculptural Printmaking in the Renaissance, Brill, 2017

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Filed under History of Astronomy, History of science, History of Technology, Renaissance Science

“A sea of wild, woolly thinking!”

Today’s musings on the history of science re-examine a topic that I have already dealt with several times in the past, that of presentist judgements on the heuristic used by a historical figure to find or reach their solution to a given scientific problem. In the world of scientific investigations, a heuristic is the scaffolding consisting of assumptions and presumptions that the investigator erects to direct and guide his efforts to explain a given set of phenomena. It is not necessary for a heuristic to be factually true, whatever that may mean. What  is important is that the heuristic delivers useful developments within the phenomena under investigation. Already in the sixteenth century Christoph Clavius, an excellent logician and philosopher of science pointed out that false premisses in science can nevertheless lead to correct deductions and therefore suggested falsification as a method to check scientific hypotheses; yes, Clavius was a Popperian three and a half centuries before Popper.

Johannes KeplerKopie eines verlorengegangenen Originals von 1610

Portrait of Kepler by an unknown artist, 1610 Source: Wikimedia Commons

The particular heuristics that I’m going to examine here are those on which Johannes Kepler erected his whole astronomical planetary theories, starting with his Mysterium Cosmographicum (1596) and all the way through to his Harmonices mundi (1619) and his Epitome Astronomiae Copernicanae (1617–1621). In her Measuring the Universe, Kitty Ferguson refers to Kepler’s work as follows:

His most celebrated discoveries seem like small islands of dazzling insights in a sea of wild, woolly thinking.[1]

The sea of wild, woolly thinking that Ferguson is referring to here is the heuristic that Kepler applied to his investigations to arrive at his famous conclusions concerning the shape and laws of the cosmos and also to a large part of those conclusions, which as opposed to his three laws of planetary motions today get ignored by everybody except the historians. Let us examine the collection of assumptions and presumptions under which Kepler conducted his research. Just how wild and woolly were they?

Kepler’s first and most important assumption was his devout and unquestioning belief in his Christian God. This is, of course, like a red rag to a bull to the gnu atheists, who continue to insist that religion and science should never occupy the same building let alone the same brain. This is problematic, as his belief in his God was the principle and singular driving force in all of Kepler’s scientific work. To understand this, we need to look at some more of Kepler’s assumptions. For Kepler it was obvious that his God had created the cosmos and that he had done so specifically for mankind. In his belief that God exists, and that God had created the world, Kepler differed in no way from the vast majority of his fellow Europeans in the late sixteenth and early seventeenth centuries but Kepler and not just Kepler took it further.

What is here central to the issue is Kepler’s personal perception of his God. Kepler’s God is not one of those ancient Greek or Scandinavia goods, who seem to take great pleasure in personally dicking around in the lives of selective individuals, just for the fun of it. His God is also not the fire and brimstone god of the Old Testament, who wipes out cities or murders babies. Kepler’s God is a rational, logical entity; in fact, Kepler’s God is a mathematician, which for Kepler means he is a geometer. Kepler is by no means the only natural philosophers in the Renaissance/Early Modern Period, who held this view of God. In fact, it was a common trope in the Middle Ages that produced a corresponding iconography.


God as Architect/Builder/Geometer/Craftsman, The Frontispiece of Bible Moralisee Source: Wikimedia Commons

In Kepler’s opinion his mathematician God had created his cosmos according to a completely logical, mathematical construction plan and it was Kepler’s task as an astronomer and natural philosopher to reconstruct and explicate that construction plan. He shared this view with many others in the Early Modern Period including both Galileo and Newton.

Before we go into detail, we need to pause and take stock. Kepler believed that a mathematician god had created the cosmos on mathematical principles and therefore he needs to discover and expose the mathematical patterns of his god’s construction plan. Leave out Kepler’s god and you should realise that Kepler’s assumptions and approach are no different to those used by scientists today; i.e. the cosmos is fundamentally logical and can be analysed, described and explained using mathematical models. The fact that this approach works so well led historians and philosophers to describe the so-called scientific revolution, as the mathematisation of nature but on the other side led to Eugene Wigner’s infamous essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences (1960).

Kepler set out with a series of open questions about the nature of the cosmos as it was known during his lifetime. One of his questions was why are there six planets in the heliocentric system that he believed in and why did their orbits have the distances to each other that they have? At the time, on the basis of the known facts, perfectly reasonable questions. He, sort of, stumbled into his answer. Whilst discussing, with a school class, the long-term cycle of the conjunctions of Saturn and Jupiter he realised that the diagrammatic presentation of those conjunctions over time is a perfectly symmetrical geometrical diagram.


Kepler’s original diagram trigon of the great conjunctions of Saturn and Jupiter

He wondered if the orbital distances of the planets also form some sort of symmetrical geometrical diagram. He tried various two-dimensional models without success then he his upon the three-dimensional, regular Euclidian solids. There are, and can only be, five of them, bingo! Six planets, five spaces, five Euclidian solids, do they fill out those spaces. Kepler positioned the five solids around and inside the spheres of the orbits of each pair of neighbouring planets and found they actually make a more than reasonable fit, not perfect but also not bad enough to immediately reject. He had the makings of a rational, geometrical construction plan for his cosmos.

thinking 3d005

Johannes Kepler Mysterium Cosmographicum

Kepler’s model was a good fit, but it wasn’t a perfect fit. In this situation the mediocre mathematical modeler simple accepts the imperfections, shrugs and moves on, but Kepler was not mediocre. In the situation, Kepler had two choices, he could abandon his model, or he could question his data. Kepler knew that the Ptolemaic/Copernican data he had inherited was inaccurate and corrupt, so he went in search of better data; a search that led him to Prague and working for Tycho Brahe, who had the best astronomical data available.

When Kepler finally got hold of some of Tycho’s data, it was to calculate the orbit of Mars that would eventually lead to his Astronomia nova. Kepler spent years trying to derive the most accurate orbit possible for Mars from Tycho’s data. His work was concentrated and precise and he developed several new approaches to orbit calculation in the process. At one point he had a circular orbit with just eight minutes of arc error in places; this was an amazing achievement in terms of the accepted levels of accuracy for the times, but it was neither accurate enough for Kepler’s personal standards, or in his opinion was it accurate enough to honour the accuracy of Tycho’s observations, so he worked further. As is well known he finally derived the correct elliptical orbit and with it his first two laws of planetary motion. The whole of this project was driven by Kepler’s desire to give accuracy to his Euclidian solids model.

In his Mysterium Cosmographicum Kepler had also floated the idea that his Euclidian solids model was fine-tuned by a second mathematical model the Pythagorean concept of celestial harmony. This is harmony in both its mathematical and musical meanings. This model said that the distances between the planetary orbits built a harmonious musical scale, the melody thus created only being audible to enlightened Pythagoreans. In choseing this particular approach Kepler was very much in tune with his times. The Pythagorean theory of celestial motion was very popular in the Middle Ages and in the Early Modern Perdiod Tycho Brahe designed and built his observatory Uraniborg entirely in Pythagorean harmonic proportions,


Tycho Brahe’s Uraniborg main building from the 1663 Blaeu’s Atlas Maior Source: Wikimedia Commons

whereas Newton built the Pythagorean theory into his analysis of white light. Kepler would, once again, spend years of his life following this mathematical trail, publishing the results of his research in his magnum opus, Harmonices Mundi (1619). He had investigated the ratios between all possible position or velocities of the orbits of the planets; the most famous result being his harmony law, his third law of planetary motion:

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit: i.e. for two planets with P = orbital period and R = semi-major axis P12/P22=R13/R23

Throughout the twenty-three years between the initial publication of the Mysterium Cosmographicum and the Harmonices Mundi Kepler never lost sight of his original model and in 1621 he published a second updated edition of Mysterium Cosmographicum.

Although the mathematical models that Kepler chose for his model of the cosmos are, from our point of view, more than somewhat bizarre, throughout his entire work, Kepler’s thinking was never even remotely a sea of wild, woolly thinking, just the opposite. Kepler’s thinking was always concentrated, exact, concise, logical, mathematical thinking, which consistently followed the chosen mathematical model of the subject of his research, the cosmos. His thinking contained no contradictions, imprecisions, deviations or internal errors. We might reject his heuristic, and in fact we do, but to dismiss it as wild and woolly, in the way that Kitty Ferguson and many other do, is to do Kepler a major injustice.

[1] Kitty Ferguson, Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time, Walker & Company, 1999, p. 70


Filed under History of Astronomy, History of science

The emergence of modern astronomy – a complex mosaic: Part XLIV

Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.  

Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.

Sir Francis Bacon, c. 1618

You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.

Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting. 

Source: Wikimedia Commons

The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century. 

Hans Sloane by Stephen Slaughter Source: Wikimedia Commons

This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.

The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity. 

Frans Hals – Portrait of René Descartes Source: Wikimedia Commons

The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz. 

What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.  

The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck between 1684 and 1687. Source: Wikimedia Commons

Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.


I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.

Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.

Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.

Engraving of Gottfried Wilhelm Leibniz Source: Wikimedia Commons

In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.

In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote: 

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. 

Relative, apparent, and common time […] is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…

Newton is saying that space and time have a separate existence and all objects exists within them.

In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects. 

 In his third letter to Clarke he wrote:

As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.

Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton. 

Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.


Filed under History of Astronomy, History of Physics, History of science, Newton

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

Giambattista della Porta the most polymathic of all Renaissance polymaths?

Giambattista della Porta (1535(?)–1615) is well known to historians of Renaissance science but for the general public he remains a largely unknown figure. If he is known at all,  he is often written off as an occultist, because of the title of his most well known work Magia Naturalis. In fact in the late sixteenth and early seventeenth centuries he was a highly respected and influential member of the Italian Renaissance scientific community. Although he wrote and published profusely over a wide range of scientific and related topics he made no really major discoveries and produced no major inventions and unlike his contemporaries, Kepler and Galileo, who were both well acquainted with his work, he has been largely forgotten.


Giambattista della Porta Source: Wikimedia Commons

Giambattista Della Porta were born at Vico Equense, Near Naples, probably sometime in 1535 (he created the confusion about his birth date), the third of four sons of the nobleman Nardo Antonio dell Porta of whom three survived childhood.  His parental home resembled an intellectual salon where the boys were continually exposed to and educated by visiting philosophers, mathematicians, poets and musicians. Their education was completed by private tutors, who also taught the boys the attributes of a gentleman, dancing, riding, skilled performance in tournaments and games and how to dress well. Della Porta never attended university but enjoyed life as a well educated polymathic, gentleman of leisure. If he can be considered to have had a profession, then it is that of a dramatist, he wrote more than twenty theatrical works, but it is his extensive activities in the sciences that interest us here.

Already in 1558, at the age of 23, he published the fist version of his most well known work, the Magia Naturalis in four books, a sort of encyclopaedia of the Renaissance sciences. From the beginning it was a bestseller running to five editions in Latin within the first ten years with translations into Italian (1560), French (1565), Dutch (1566) and English (1658). A vastly expanded version in twenty books was published in 1589. This final version covers a wide range of topics:


Source: Wikimedia Commons

Book 1: Of the Causes of Wonderful Things Book 2: Of the Generation of Animals Book 3: Of the Production of New Plants Book 4: Of Increasing Household-Stuff Book 5: Of Changing Metals Book 6: Of Counterfeiting Glorious StonesBook 7: Of the Wonders of the Load-Stone Book 8: Of Physical Experiments Book 9: Of Beautifying Women Book 10: Of Distillation Book 11: Of Perfuming Book 12: Of Artificial Fires Book 13: Of Tempering Steel Book 14: Of CookeryBook 15: Of Fishing, Fowling, Hunting, etc. Book 16: Of Invisible Writing Book 17: Of Strange Glasses Book 18: Of Static Experiments Book 19: Of Pneumatic Experiment Book 20: Of the Chaos

The contents range from fairly banal parlour tricks, over engineering, experimental science, horticulture and husbandry to every day things. At the very beginning della Porta is very careful to explain what exactly he mean by the term natural magic:

There are two sorts of Magick; the one is infamous, and unhappy, because it has to do with foul Spirits and consists of incantations and wicked curiosity; and this is called Socery; an art which all learned and good men detest; neither is it able to yield an truth of reason or nature, but stands merely upon fancies and imaginations, such as vanish presently away, and leave nothing behind them; as Jamblicus writes in his book concerning the mysteries of the Egyptians. The other Magick is natural; which all excellent wise men do admit and embrace, and worship with great applause; neither is there any thing more highly esteemed, or better thought of, by men of learning. The most noble Philosophers that ever were, Pythagorus, Empedocles, Democritus, and Plato forsook their own countries, and lived abroad as exiles and banished men, rather than as strangers; and all to search out and to attain this knowledge; and when they came home again, this was the Science which they professed, and this they esteemed a profound mystery. They that have been most skillful in dark and hidden points of learning, do call this knowledge the very highest point, and the perfection’s of Natural Sciences; inasmuch that if they could find out or devise amongst all Natural Sciences, any one thing more excellent or more wonderful then another, that they would still call by the name of  Magick. Others have named it the practical part of natural Philosophy, which produces her effects by the mutual and fit application of one natural thing unto another.

The association of Magick with natural philosophy is continued in della Porta’s definition of the Magician:

This is what is required to instruct a Magician, both what he must know, and what he must observe; that being sufficiently instructed in every way, he may bring very strange and wonderful things to us. Seeing Magick, as we showed before, as a practical part of natural Philosophy, it behooves a Magician and one that aspires to the dignity of the profession, to be an exact and very perfect Philosopher.

Despite the very diverse nature of the Magia Naturalis it does contain elements of genuine experimental science. For example, it contains the first experimental disproof of the widely held medieval belief that garlic disables magnets. He also experimented with the cooling properties of dissolving nitre in water. As described here by Andrea Sella (@SellaTheChemist)

As well as the Magia Naturalis della Porta wrote and published a large number of monographs on a very wide range of topics. Cryptography was a popular topic in Renaissance Europe, the most famous book being Johannes Trithemius’ Poligraphia, della Porta published his De Furtivis Literarum Notis (1563), which contain innovative cryptographical ideas.


In 1586 he published a work on physiognomy De humana physiognomonia libri IIII,


From De humana physiognomonia, 1586 Source: Wikimedia Commons

which was still being referenced in the nineteenth century, two years later a book on phytonomy (the science of the origin and growth of plants), Phytognomonica, which contains the first observations on fungal spores.


Phytognomonica, 1588 Source: Wikimedia Commons

These two books confirm della Porta’s adherence to the Renaissance doctrine of signatures. This theory claimed that it was possible to determine the nature of things based on their external appearances.

This was by no means the limit to della Porta’s publishing activities. He also wrote an agricultural encyclopaedia, separate volumes on various fruit bearing trees, books on mathematics, astronomy, meteorology, military engineering, distillation and in 1589 a book on optics, his De refractione optics. We shall return to the latter.


This incredible literary outpouring was just part of his scientific activity, in about 1560 he founded an academic society, Accademia dei Segreti (Academia Secratorum Naturae), the Academy of the Secrets of Nature, which is considered to be the earliest scientific society. The academy met regularly in della Porta’s home and membership was open to all but to become a member one had to present a new secret of nature that one had discovered. We know what some of those new secrets were as della Porta included them in the twenty volume version of his Magia Naturalis. In 1578 della Porta was summoned to Rome and investigated by the Pope. We do not know the exact grounds for this summons but he was forced to shut down his academy on suspicion of sorcery. This is to a certain extent ironic because della Porta was very careful in all his writing to avoid controversial topics particularly religious ones.

Although it was shut down the Accademia dei Segreti, would later have a major influence on another, much more renowned, early scientific academy, Federico Cesi’s Accademia dei Lincei. Cesi was a huge admirer of della Porta and as a young man travelled to Naples to visit the older natural philosopher. On his return home he founded his own academy, whose name was inspired by a line from the preface of the Magia Naturalis:

… with lynx like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them.

In 1610 della Porta became the fifth member of the Accademia dei Lincei, one year before Galileo.

Another important aspect of Renaissance science was the establishment of private natural philosophical museums also known as Wunderkammer, or cabinets of curiosity. Della Porta had, as to be expected, a particular fine cabinet of curiosity that would influence others to create their own, the Jesuit Athanasius Kircher for example.


Fold-out engraving from Ferrante Imperato’s Dell’Historia Naturale (Naples 1599), the earliest illustration of a natural history cabinet Source: Wikimedia Commons

Della Porta made minor contribution to the advance of science and engineering over a wide range of disciplines but I first ran into della Porta in the context of the history of optics and it his association with this history that I want to look at in somewhat more detail. The early seventeenth century saw both a significant turn in the theory of optics and independently of that the invention of the telescope, an instrument that would go one to revolutionise astronomy, della Porta played a minor roll in both of these things.

The invention of the telescope, by Hans Lipperhey, first became public in September 1608 and the role it would play in the future of astronomy became explosively obvious when Galileo published his Sidereus Nuncius in March 1610. Already in August 1609 della Porta wrote a letter to Federico Cesi claiming to have invented the telescope, he wrote:

I have seen the secret use of the eyeglass and it’s a load of balls [coglionaria] in any case it is taken from book 9 of my De Refractione.[1]

Here della Porta’s memory is faulty, he is after all over seventy years old, what he is referring to is not in the De Refractione but rather in Chapter 10 of Book 17 of Magia Naturalis (1589). Here we find the following suggestive description:

Concave Lenticulars will make one see most clearly things that are afar off.  But Convexes, things near at hand.  So you may use them as your sight requires.  With a Concave Lenticulars you shall see small things afar off very clearly.  With a Convex Lenticular, things nearer to be greater, but more obscurely.  If you know how to fit them both together, you shall see both things afar off, and things near hand, both greater and clearly.  I have much helped some of my friends, who saw things afar off, weakly, and what was near, confusedly, that they might see all things clearly.  If you will, you may.

The lens combination that della Porta describes here is indeed that of the Dutch or Galilean telescope but as van Helden say, and I agree with him, he is here describing some form of spectacles but not a telescope. Kepler, however, who owned a copy of Magia Naturalis credits him with being the inventor of the telescope in his Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610), where he wrote that a recent Dutch invention had been made public years earlier in Magia Naturalis. In 1641 Pierre Gassendi stated that the actual invention had been made by chance by Metius [Jacob Metius (after 1571–1628), who applied for a patent for a telescope two weeks later than Lipperhey] the idea for a similar one had been published years earlier by della Porta.

Later della Porta would graciously admit that his fellow Lynx, Galileo, had achieved much more with his telescope that he, della Porta, could have ever have hoped to do, whilst not abandoning his claim to having first conceived of the telescope.

Della Porta also played a small role in the history of the camera obscura, describing the improvement to the image obtained by placing convex lens into the pinhole, something probably first suggested by Gerolamo Cardano. He also suggested, this time as the first to do so, using a concave mirror to project the image onto a sheet of paper to facilitate drawing it. The popularity of the Magia Naturalis did much to spread knowledge of the camera obscura and its utility as a drawing instrument. Interestingly della Porta compared his camera obscura with the human eye but, unlike Kepler, failed to make the connection that the lens focuses the image on the retina. He continued to believe like everybody before him that the image in perceived in the lens itself.


First published picture of camera obscura in Gemma Frisius’ 1545 book De Radio Astronomica et Geometrica Source: Wikimedia Commons

Della Porta’s role in the turn in the theory of optics is less disputed but not so widely discussed.  Ancient Greek optics was almost exclusively about theories of vision and when taken up and developed in the Islamic Middle Ages this too remained the emphasis. Ibn al-Haytham in his work on optics showed that one could combine an intromission theory of vision with the geometric optics of Euclid, Hero and Ptolemaeus, who had all propagated an extramission theory of vision. This was a major development in the history of optics. In the thirteenth century Robert Grosseteste introduced optics as a central element in both his vision of science and his theology, which led to it being established as a mathematical discipline on the medieval university. Shortly after Roger Bacon, John Peckham and Witelo introduced al-Haytham’s theories on optics into the medieval European mainstream founding what became known as the perspectivist school of optics. Strangely there were no real further developments in the theory of optics down to the end of the sixteenth century when Johannes Kepler, almost singlehandedly, turned the study of optics from one of theories of vision to one of theories of light, thereby ending the reign of the perspectivists. I say almost singlehandedly but he did have two predecessors, who made minor contributions to this turn, Francesco Maurolico (1494–1575) and della Porta.

One major flaw in the perspectivist theory was its treatment of spherical convex lenses and spherical concave mirrors, which said that the images created by them appeared at a single focus point; this is a fallacy. This flaw was in the theory from its inception in the thirteenth century and remained unchecked and uncorrected all the way down to the end of the sixteenth century. The fact that the don’t create their images at a single focal point is, of course, the cause of spherical aberration, something that would plague the construction of telescopes and microscopes well into the eighteenth century. The man who corrected this error in optical theory was della Porta.  Using a mixture of experiments and analytical light ray tracing he came very close to the correct solution an important step towards Kepler’s light ray based theory of optics.


Della Porta’s ray tracing analysis of the reflection of a spherical concave mirror A. Mark Smith, “From Sight to Light: The Passage from Ancient to Modern Optics”, Chicago University Press, 2015 p. 349

Giambattista della Porta is an interesting example of a widespread phenomenon in the history of science. In his own times he was highly respected and regarded, throughout Europe, as a leading natural Philosopher. His books, translated into many languages, were bestsellers and that even long after his death. Johannes Kepler was a fan and Galileo disliked him because he saw him as a serious rival for the position of top dog natural philosopher, a position that Galileo very much desired for himself. However, today most people have never even heard of him and if then he is largely dismissed as a minor irrelevance or even, because of the title of his major work, as some sort of anti-science occultist. But if historians really want to understand what was going on in the scientific community of Europe in the Early Modern Period then they have to take figures like della Porta seriously and not just focus on the ‘big names’ such as Kepler and Galileo.













[1] Quoted from David Freedberg, The Eye of the Lynx: Galileo, His Friends and the Beginnings of Modern Natural History, University of Chicago Press, Chicago and London, 2002, ppb. p. 101 Albert van Helden in his The Invention of the Telescope, American Philosophical Society, Philadelphia, 1977, Reprint, 2008, translates the phrase with coglionaria as …”it’s a hoax” pp. 44-45

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Filed under History of Optics, History of science, Renaissance Science

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