A misleading book title that creates the wrong impression

A new biography of Johannes Kepler has just appeared and although I haven’t even seen it yet, let alone read it, it brings out the HistSci Hulk side of my personality. What really annoys me on David Love’s book, Kepler and the Universe[1], is the title or rather the subtitle, How One Man Revolutionised Astronomy. Now, I for one have for many years conducted a private campaign to persuade people not to claim that we live in a Copernican Cosmos, a standard cliché, but that we live in a Keplerian Cosmos, because it was the very different elliptical system of Kepler that helped heliocentricity to its breakthrough and not the system of Copernicus. However Love’s subtitle immediately evokes the spectre of the lone genius and for all his undoubted brilliance Kepler was not a lone genius and especially not in terms of his cosmology/astronomy.

A 1610 portrait of Johannes Kepler by an unknown artist Source: Wikipedia Commons

A 1610 portrait of Johannes Kepler by an unknown artist
Source: Wikipedia Commons

Even a cursory examination of Kepler’s road to his system will immediately reveal his intellectual debts and his co-conspirators, both willing and unwilling. First off is naturally Copernicus himself. Kepler did not conceive a heliocentric system from scratch but was, on his own admission a glowing admirer or even acolyte of the Ermländer scholar. This admiration is one of the principle reasons that we don’t truly acknowledge Kepler’s achievement but tend to dismiss it as having just dotted the ‘Is’ and crossed the ‘Ts’ in Copernicus’ system, a demonstrably false judgement. Kepler, of course, didn’t help the situation when he titled the most simple and readable version of his system, and the one that together with the Rudolphine Tables had the most influence, the Epitome Astronomiae Copernicanae. Not a smart move! Whatever, we are already at two men who revolutionised astronomy.

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń Source: Wikimedia Commons

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń
Source: Wikimedia Commons

Kepler did not discover Copernicus himself but was introduced to him by his teacher Michael Maestlin at the University of Tübingen. Usually Maestlin gets mentioned in passing as Kepler’s teacher and then forgotten but he played a very important role in Kepler’s early development. In reality Maestlin was himself one of the leading European astronomers and mathematicians in the latter part of the sixteenth century, as well as being by all accounts an excellent teacher. He was also one of the very few supporters of both Copernican astronomy and cosmology. This meant that he gave Kepler probably the best foundation in the mathematical sciences that he could have found anywhere at the time, as well as awakening his interest in Copernican thought. It was also Maestlin who decided Kepler would be better off becoming a teacher of mathematics and district mathematician rather than training for the priesthood; a decision that Kepler only accepted very, very reluctantly. Even after he had left Tübingen Maestlin continued to support the young Kepler, although he would withdraw from him in later years. Maestlin edited, corrected and polished Kepler’s, so important, first publication, the Mysterium Cosmographicum. In fact Maestlin’s contributions to the finished book were so great he might even be considered a co-author. Some people think that in later life Kepler abandoned the, for us, rather bizarre Renaissance hypothesis of the Cosmographicum, but he remained true to his initial flash of inspiration till the very end, regarding all of his later work as just refinements of that first big idea. Maestlin’s contribution to the Keplerian system was very substantial. And then there were three.

Michael Maestlin Source: Wikimedia Commons

Michael Maestlin
Source: Wikimedia Commons

Tycho! Without Tycho Brahe there would be no Keplerian System. Tycho and Kepler are the Siamese twins of elliptical astronomy joined at the astronomical data. Without Tycho’s data Kepler could never have built his system. This duality is recognised in many history of astronomy texts with the two, so different, giants of Renaissance astronomy being handled together. The popular history of science writer, Kitty Ferguson even wrote a dual biography, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens[2], a title that of course contradicts Love’s One Man. Her original title was The Nobleman and His Housedog, with the rest as a subtitle, but it seems to have been dropped in later editions of the book. The ‘housedog’ is a reference to Kepler characterising himself as such in the horoscope he wrote when he was twenty-five years old.

Portrait of Tycho Brahe (1596) Skokloster Castle Source: Wikimedia Commons

Portrait of Tycho Brahe (1596) Skokloster Castle
Source: Wikimedia Commons

Tycho invited Kepler to come and work with him in Prague when the Counter Reformation made him jobless and homeless. Tycho welcomed him back when Kepler went off in a huff at their first meeting. It was Tycho who assigned him the task of calculating the orbit of Mars that would lead him to discover his first two laws of planetary motion. It has been said that Tycho’s data had just the right level of accuracy to enable Kepler to determine his elliptical orbits. Any less accurate and the slight eccentricities would not have been discernable. Any more accurate and the irregularities in the orbits, thus made visible, would have made the discovery of the elliptical form almost impossible. It has also been said that of all the planets for which Tycho had observation data Mars was the one with the most easily discernable elliptical orbit. Serendipity seems to have also played a role in the discovery of Kepler’s system. The high quality of Tycho’s data also led Kepler to reject an earlier non-elliptical solution for the orbit of Mars, which another astronomer would probably have accepted, with the argument that it was not mathematically accurate enough to do honour to Tycho’s so carefully acquired observational data.

Tycho was anything but a one-man show and his observatory on the island of Hven has quite correctly been described as a research institute. A substantial number of astronomer, mathematicians and instrument maker came and went both on Hven and later in Prague over the almost thirty years that Tycho took to accumulate his data. The number of people who deserve a share in the cake that was Kepler’s system now reaches a point where it become silly to count them individually.

Our list even includes royalty. Rudolph II, Holly Roman Emperor, was the man, who, at Tycho’s request, gave Kepler a position at court, even if he was more than somewhat lax at paying his salary, official to calculate the Rudolphine Tables, a task that would plague Kepler for almost thirty years but would in the end lead to the acceptance of his system by other astronomers. Rudolph also appointed Kepler as Tycho’s successor, as Imperial Mathematicus, after the latter’s untimely death, thus giving him the chance to continue his analysis of Tycho’s data. Rudolph could just as easily have sacked him and sent him on his way. Tycho’s heirs did not assist Kepler in his struggle to maintain access to that all important data, which belonged to them and not the Emperor, causing him much heartache before they finally allowed him to use Tycho’s inheritance. After he had usurped his brother, Rudolph, in 1612, Matthias allowed Kepler to keep his official position and title as Imperial Mathematicus, although sending him away from court, a fact that certainly assisted Kepler in his work. Being Imperial Mathematicus gave him social status and clout.

Rudolph II portrait by Joseph Heinz the Elder Source: Wikimedia Commons

Rudolph II portrait by Joseph Heinz the Elder
Source: Wikimedia Commons

Kepler described his long and weary struggles with the orbit of Mars as a battle, but he did not fight this battle alone. In a long and fascinating correspondence with the astronomer, David Fabricius, Kepler tried out his ideas and results with a convinced supporter of Tycho’s system. Kepler would present his ideas and David Fabricius subjected them to high level and very knowledgeable criticism. Through this procedure Kepler honed, refined and polished his theories to perfection before he submitted them to public gaze in his Astronomia Nova, Knowing that they would now withstand high-level professional criticism. David Fabricius, who never met Kepler, nevertheless took a highly active role in the shaping of the Keplerian system[3].

Monument for David and Johann Fabricius in the Graveyard of Osteel

Monument for David and Johann Fabricius in the Graveyard of Osteel

Even after Kepler’s death the active participation of others in shaping his astronomical system did not cease. Jeremiah Horrocks corrected and extended the calculations of the Rudolphine Tables, enabling him to predict and observe a transit of Venus, an important stepping-stone in the acceptance of the elliptical astronomy. Horrocks also determined that the moon’s orbit was a Keplerian ellipse, something that Kepler had not done.


Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads "Ecce gratissimum spectaculum et tot votorum materiem": "oh, most grateful spectacle, the realization of so many ardent desires". It is taken from Horrocks's report of the transit

Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads “Ecce gratissimum spectaculum et tot votorum materiem”: “oh, most grateful spectacle, the realization of so many ardent desires”. It is taken from Horrocks’s report of the transit

Cassini, together with Riccioli and Grimaldi, using a heliometer determined that either the orbit of the sun around the earth or the earth around the sun, the method can’t determine which is true, is an ellipse another important empirical stepping-stone on the road to final acceptance for the system.

Giovanni Cassini Source: Wikimedia Commons

Giovanni Cassini
Source: Wikimedia Commons

Nicholas Mercator produced a new mathematical derivation of Kepler’s second law around 1670. Kepler’s own derivation was, as he himself admitted, more than a little suspect, viewed mathematically. The first and third laws had been accepted by the astronomical community fairly easily but the second law was a major bone of contention. Mercator’s new derivation basically laid the dispute to rest.

Cassini in his new role as director of the Paris observatory showed empirically that the satellite systems of both Jupiter and Saturn also obeyed Kepler’s third law extending it effectively to all orbitary systems and not just the planets of the solar system.

Lastly Newton derived Kepler’s first and second laws from his axiomatic system of dynamics giving them the true status of laws of physics. This led Newton to claim that the third law was Kepler’s but the first two were his because he, as opposed to Kepler, had really proved them

As we can see the list of people involved in revolutionising astronomy in the seventeenth century in that they replaced all the geocentric systems with a Keplerian elliptical system is by no means restricted to ‘one man’ as claimed in the subtitle to David Love’s book but is quite extensive and very diverse. There are no lone geniuses; science is a collective, collaborative enterprise.





[1] David Love, Kepler and the Universe: How One Man Revolutionized Astronomy, Prometheus Books, 2015

[2] Kitty Ferguson, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens, Walker Books, 2002

[3] For a wonderful description of this correspondence and how it contributed to the genesis of Astronmia Nova see James Voelkel’s excellent, The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001


Filed under History of Astronomy, Myths of Science, Uncategorized

Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus.

There is a strong tendency, particularly in the popular history of science, to write about or present scientists as individuals. This leads to a serious distortion of the way that science develops and in particular propagates the lone genius myth. In reality science has always been a collective endeavour with its practitioners interacting in many different ways and on many different levels. In the Renaissance, when travelling from one end of Europe to the other would take weeks and letters often even longer, one might be excused for thinking that such cooperation was very low level but in fact the opposite was the truth, with scholars in the mathematical sciences exchanging information and ideas throughout Europe. A particularly strong mathematical nexus existed in the Southern German speaking area between the cities of Nürnberg, Ingolstadt and Vienna in the century between 1450 and 1550. Interestingly two of the paintings of the Northern Renaissance artist Hans Holbein the Younger open a door into this nexus.

Holbein (c. 1497–1543) was born in Augsburg the son of the painter and draughtsman Hans Holbein the Elder. As a young artist he lived and worked for a time in Basel where he became acquainted with Erasmus and worked for the printer publisher Johann Froben amongst others. Between 1526 and 1528 he spent some time in England in the household of Thomas More and it is here that he painted the second portrait I shall be discussing. The next four years find him living in Basel again before he returned to England in 1532 where he became associated with the court of Henry VIII, More having fallen out of favour. It was at the court that he painted, what is probably his most well know portrait, The Ambassadors in 1533.

Hans Holbein The Ambassadors Source: Wikimedia Commons

Hans Holbein The Ambassadors
Source: Wikimedia Commons

The painting shows two courtiers, usually identified as the French Ambassador Jean de Dinteville and Georges de Selve, Bishop of Lavaur standing on either side of a set of shelves laden with various books and instruments. There is much discussion was to what the instruments are supposed to represent but it is certain that, whatever else they stand for, they represent the quadrivium, arithmetic, geometry music and astronomy, the four mathematical sciences taught at European medieval universities. There are two globes, on the lower shelf a terrestrial and on the upper a celestial one. The celestial globe has been positively identified, as a Schöner globe and the terrestrial globe also displays characteristics of Schöner’s handwork.

Terrestrial Globe The Ambassadors Source Wikimedia Commons

Terrestrial Globe The Ambassadors
Source Wikimedia Commons

Celestial Globe The Ambassadors Source Wikimedia Commons

Celestial Globe The Ambassadors
Source Wikimedia Commons

Johannes Schöner (1477–1547) was professor for mathematics at the Egidienöberschule in Nürnberg, the addressee of Rheticus’ Narratio Prima, the founder of the tradition of printed globe pairs, an editor of mathematical texts for publication (especially for Johannes Petreius the sixteenth centuries most important scientific publisher) and one of the most influential astrologers in Europe. Schöner is a central and highly influential figure in Renaissance mathematics.

On the left hand side of the lower shelf is a copy of Peter Apian’s Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen (published in Ingolstadt in 1527) held open by a ruler. This is a popular book of commercial arithmetic, written in German, typical of the period. Peter Apian (1495–1552) professor of mathematics at the University of Ingolstadt, cartographer, printer-publisher and astronomer was a third generation representative of the so-called Second Viennese School of Mathematics. A pupil of Georg Tannstetter (1482–1535) a graduate of the University of Ingolstadt who had followed his teachers Johannes Stabius and Andreas Stiborious to teach at Conrad Celtis’ Collegium poetarum et mathematicorum, of which more later. Together Apian and Tannstetter produced the first printed edition of the Optic of Witelo, one of the most important medieval optic texts, which was printed by Petreius in Nürnberg in 1535. The Tannstetter/Apian/Petreius Witelo was one of the books that Rheticus took with him as a present for Copernicus when he visited him in 1539. Already, a brief description of the activities of Schöner and Apian is beginning to illustrate the connection between our three cities.

Apian's Arithmetic Book The Ambassadors Source: Wikimedia Commons

Apian’s Arithmetic Book The Ambassadors
Source: Wikimedia Commons

When Sebastian Münster (1488–1552), the cosmographer, sent out a circular requesting the cartographers of Germany to supply him with data and maps for his Cosmographia, he specifically addressed both Schöner and Apian by name as the leading cartographers of the age. Münster’s Cosmographia, which became the biggest selling book of the sixteenth century, was first published by Heinrich Petri in Basel in 1544. Münster was Petri’s stepfather and Petri was the cousin of Johannes Petreius, who learnt his trade as printer publisher in Heinrich’s printing shop in Basel. The Petri publishing house was also part of a consortium with Johann Amerbach and Johann Froben who had employed Hans Holbein in his time in Basel. Wheels within wheels.

The, mostly astronomical, instruments on the upper shelf are almost certainly the property of the German mathematician Nicolaus Kratzer (1487–1550), who is the subject of the second Holbein portrait who will be looking at.

Nicolas Kratzer by Hans Holbein Source: Wikimedia Commona

Nicolas Kratzer by Hans Holbein
Source: Wikimedia Commona

Born in Munich and educated at the universities of Cologne and Wittenberg Kratzer, originally came to England, like Holbein, to become part of the Thomas More household, where he was employed as a tutor for More’s children. Also like Holbein, Kratzer moved over to Henry VIII’s court as court horologist or clock maker, although the clocks he was responsible for making were more probably sundials than mechanical ones. During his time as a courtier Kratzer also lectured at Oxford and is said to have erected a monumental stone sundial in the grounds of Corpus Christi College. One polyhedral sundial attributed to Kratzer is in the Oxford Museum for the History of Science.

Polyhedral Sundial attributed to Nicolas Kratzer Source: MHS Oxford

Polyhedral Sundial attributed to Nicolas Kratzer
Source: MHS Oxford

In 1520 Kratzer travelled to Antwerp to visit Erasmus and here he met up with Nürnberg’s most famous painter Albrecht Dürer, who regular readers of this blog will know was also the author of a book on mathematics. Dürer’s book contains the first printed instructions, in German, on how to design, construct and install sundials, so the two men will have had a common topic of interest to liven there conversations. Kratzer witnessed Dürer, who was in Antwerp to negotiate with the German Emperor, painting Erasmus’ portrait and Dürer is said to have also drawn a portrait of Kratzer that is now missing. After Kratzer returned to England and Dürer to Nürnberg the two of them exchanged, at least once, letters and it is Kratzer’s letter that reveals some new connections in out nexus.

Albrecht Dürer selfportrait Source: Wikimedia Commons

Albrecht Dürer selfportrait
Source: Wikimedia Commons

In his letter, from 1524, Kratzer makes inquires about Willibald Pirckheimer and also asks if Dürer knows what has happened to the mathematical papers of Johannes Werner and Johannes Stabius who had both died two years earlier.

Willibald Pirckheimer (1470–1530) a close friend and patron of Dürer’s was a rich merchant, a politician, a soldier and a humanist scholar. In the last capacity he was the hub of a group of largely mathematical humanist scholars now known as the Pirckheimer circle. Although not a mathematician himself Pirckheimer was a fervent supporter of the mathematical sciences and produced a Latin translation from the Greek of Ptolemaeus’ Geōgraphikḕ or Geographia, Pirckheimer’s translation provided the basis for Sebastian Münster’s edition, which was regarded as the definitive text in the sixteenth century. Stabius and Werner were both prominent members of the Pirckheimer circle.

Willibald Pirckheimer by Albrecht Dürer Source: Wikimedia Commons

Willibald Pirckheimer by Albrecht Dürer
Source: Wikimedia Commons

The two Johanneses, Stabius (1450–1522) and Werner (1468–1522), had become friends at the University of Ingolstadt where the both studied mathematics. Ingolstadt was the first German university to have a dedicated chair for mathematics. Werner returned to his hometown of Nürnberg where he became a priest but the Austrian Stabius remained in Ingolstadt, where he became professor of mathematics. The two of them continued to correspond and work together and Werner is said to have instigated the highly complex sundial on the wall of the Saint Lorenz Church in Nürnberg, which was designed by Stabius and constructed in 1502.

St Lorenz Church Nürnberg Sundial 1502 Source: Astronomie in Nürnberg

St Lorenz Church Nürnberg Sundial 1502
Source: Astronomie in Nürnberg

It was also Werner who first published Stabius’ heart shaped or cordiform map projection leading to it being labelled the Werner-Stabius Projection. This projection was used for world maps by Peter Apian as well as Oronce Fine, France’s leading mathematicus of the sixteenth century and Gerard Mercator, of whom more, later. The network expands.

Mercator cordiform world map 1538 Source: American Geographical Society Library

Mercator cordiform world map 1538
Source: American Geographical Society Library

In his own right Werner produced a partial Latin translation from the Greek of Ptolemaeus’ Geographia, was the first to write about prosthaphaeresis (a trigonometrical method of simplifying calculation prior to the invention of logarithms), was the first to suggest the lunar distance method of determining longitude and was in all probability Albrecht Dürer’s maths teacher. He also was the subject of an astronomical dispute with Copernicus.

Johannes Werner Source: Wikimedia Commons

Johannes Werner
Source: Wikimedia Commons

Regular readers of this blog will know that Stabius co-operated with Albrecht Dürer on a series of projects, including his famous star maps, which you can read about in an earlier post here.

Johannes Statius Portrait by Albrecht Dürer Source: Wikimedia Commons

Johannes Statius Portrait by Albrecht Dürer
Source: Wikimedia Commons

An important non-Nürnberger member of the Pirckheimer Circle was Conrad Celtis (1459–1508), who is known in Germany as the arch-humanist. Like his friend Pirckheimer, Celtis was not a mathematician but believed in the importance of the mathematical sciences. Although already graduated he spent time in 1489 on the University of Kraków in order to get the education in mathematics and astronomy that he couldn’t get at a German university. Celtis had spent time at the humanist universities of Northern Italy and his mission in life was to demonstrate that Germany was just as civilised and educated as Italy and not a land of barbarians as the Italians claimed. His contributions to the Nuremberg Chronicle can be viewed as part of this demonstration. He believed he could achieve his aim by writing a comprehensive history of Germany including, as was common at the time its geography. In 1491/92 he received a teaching post in Ingolstadt, where he seduced the professors of mathematics Johannes Stabius and Andreas Stiborius (1464–1515) into turning their attention from astrology for medicine student, their official assignment, to mathematical cartography in order to help him with his historical geography.

Conrad Celtis Source: Wikimedia Commons

Conrad Celtis
Source: Wikimedia Commons

Unable to achieve his ends in Ingolstadt Celtis decamped to Vienna, taking Stabius and Stiborius with him, to found his Collegium poetarum et mathematicorum as mentioned above and with it the so-called Second Viennese School of Mathematics; the first had been Peuerbach and Regiomontanus in the middle of the fifteenth century. Regiomontanus spent the last five years of his life living in Nürnberg, where he set up the world’s first scientific publishing house. Stiborius’ pupil Georg Tannstetter proved to be a gifted teacher and Peter Apian was by no means his only famous pupil.

The influence of the Nürnberg–Ingolstadt–Vienna mathematicians reached far beyond their own relatively small Southern German corridor. As already stated Münster in Basel stood in contact with both Apian and Schöner and Stabius’ cordiform projection found favour with cartographers throughout Northern Europe. Both Apian and Schöner exercised a major influence on Gemma Frisius in Louvain and through him on his pupils Gerard Mercator and John Dee. As outlined in my blog post on Frisius, he took over editing the second and all subsequent editions of Apian’s Cosmographia, one of the most important textbooks for all things astronomical, cartographical and to do with surveying in the sixteenth century. Frisius also learnt his globe making, a skill he passed on to Mercator, through the works of Schöner. Dee and Mercator also had connections to Pedro Nunes (1502–1578) the most important mathematicus on the Iberian peninsular. Frisius had several other important pupils who spread the skills in cosmography, and globe and instrument making that he had acquired from Apian and Schöner all over Europe.

Famously Rheticus came to Nürnberg to study astrology at the feet of Johannes Schöner, who maintained close contacts to Philipp Melanchthon Rheticus patron. Schöner was the first professor of mathematics at a school designed by Melanchthon. Melanchthon had learnt his mathematics and astrology at the University of Tübingen from Johannes Stöffler (1452–1531) another mathematical graduate from Ingolstadt.

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica Source: Wikimedia Commons

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica
Source: Wikimedia Commons

Another of Stöffler’s pupils was Sebastian Münster. During his time in Nürnberg Rheticus became acquainted with the other Nürnberger mathematicians and above all with the printer-publisher Johannes Petreius and it was famously Rheticus who brought the manuscript of Copernicus’ De revolutionibus to Nürnberg for Petreius to publish. Rheticus says that he first learnt of Copernicus’s existence during his travels on his sabbatical and historians think that it was probably in Nürnberg that he acquired this knowledge. One of the few pieces of astronomical writing from Copernicus that we have is the so-called Letter to Werner. In this manuscript Copernicus criticises Werner’s theory of trepidation. Trepidation was a mistaken belief based on faulty data that the rate of the precession of the equinoxes is not constant but varies with time. Because of this highly technical dispute amongst astronomers Copernicus would have been known in Nürnberg and thus the assumption that Rheticus first heard of him there. Interestingly Copernicus includes observations of Mercury made by Bernhard Walther (1430–1504), Regiomontanus partner, in Nürnberg; falsely attributing some of them to Schöner, so a connection between Copernicus and Nürnberg seems to have existed.

In this brief outline we have covered a lot of ground but I hope I have made clear just how interconnected the mathematical practitioners of Germany and indeed Europe were in the second half of the fifteenth century and the first half of the sixteenth. Science is very much a collective endeavour and historians of science should not just concentrate on individuals but look at the networks within which those individual operate bringing to light the influences and exchanges that take place within those networks.


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

The Renaissance Mathematicus “Live & Uming”

Those of you with nothing better to do can listen to a podcast of the Renaissance Mathematicus (that’s me folks!) searching for words, desperately trying to remember names, uming & ahing, thinking on his feet (I was actually sitting down the whole time) and generally stumbling his way through an eighty minute spontaneous, unrehearsed, live interview with Scott Gosnell of Bottle Rocket Science on such scintillated topics, as why the Pope got his knickers in a twist over Galileo or that notorious seventeenth century religious fanatic Isaac Newton. In fact the same boring load of old codswallop that you can read at you leisure here on this blog. As I say if you have nothing more exciting to do, such as watching paint dry or listening to the grass grow, then go listen.

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Filed under Autobiographical, History of Astronomy, History of science, Myths of Science, Renaissance Science

The Phlogiston Theory – Wonderfully wrong but fantastically fruitful

There is a type of supporter of gnu atheism and/or scientism who takes a very black and white attitude to the definition of science and also to the history of science. For these people, and there are surprisingly many of them, theories are either right, and thus scientific, and help the progress of science or wrong, and thus not scientific, and hinder that progress. Of course from the point of view of the historian this attitude or stand point is one than can only be regarded with incredulity, as our gnu atheist proponent of scientism dismisses geocentrism, the phlogiston theory and Lamarckism as false and thus to be dumped in the trash can of history whilst acclaiming Copernicus, Lavoisier and Darwin as gods of science who led as out the valley of ignorance into the sunshine of rational thought.

I have addressed this situation before on more than one occasion but as a historian of science I think that it’s a lesson that needs to be repeated at regular intervals. Because it is the American Chemical Society’s “National Chemistry Week 2015” I shall be re-examining the Phlogiston Theory whose creator Georg Ernst Stahl was born on 22 October 1659 in Ansbach, which is in Middle Franconia just down the road from where I live.

Stahl had a fairly conventional career, studying medicine at Jena University from 1679 to 1684. 1687 he became court physician to the Duke of Sachen-Weimar and in 1694 he was appointed professor of medicine at the newly founded University of Halle, where he remained until 1715 when he became personal physician to Friedrich Wilhelm I, King of Prussia. Stahl like most chemists in the Early Modern Period was a professional physician, chemistry only existing within the academic context as a sub-discipline of medicine.

To understand the phlogiston theory we need to go back and take a brief look at the development of the theory of matter since the ancient Greeks. Empedocles introduced the famous four-element theory, Earth, Water, Air and Fire, in the fifth century BCE and this remained the basic theory in Europe until the Early Modern Period. In the ninth century CE Abu Mūsā Jābir ibn Hayyān added Sulphur and Mercury to the four-elements as principles, rather than substances, to explain the characteristics of the seven metals. In the sixteenth century CE, Paracelsus took over al- Jābir’s Sulphur and Mercury adding Salt as his tria prima to explain the characteristics of all matter. In the seventeenth century, when Paracelsus’ influence was at its height, many alchemists/chemists adopted a five-element theory – Earth, Water, Sulphur, Mercury and Salt – dropping air and fire. Robert Boyle, in his The Sceptical Chymist (1661), threw out both the Greek four-element theory and Paracelsus’ tria prima, groping towards a more modern concept of element. We now arrive at the origins of the phlogiston theory.

The German Johann Joachim Becher (1635–1682), a physician and alchemist, was a big fan of Boyle and his theories and even travelled to London to learn at the feet of the master. Like Boyle he rejected both the Greek four-element theory and Paracelsus’ tria prima, in his Physica Subterranea (1667) replacing them with a two-element theory Earth and Water with Air present just as a mixing agent for the two. However he basically reintroduced Paracelsus’ tria prima in the form of three different types of Earth.

  • terra fluida or mercurial Earth giving material the characteristics, fluidity, fineness, fugacity, metallic appearance
  • terra pinguis or fatty Earth giving material the characteristics oily, sulphurous and flammable
  • terra lapidea glassy Earth, giving material the characteristic fusibility

Stahl took up Becher’s scheme of elements concentrating on his terra pinguis, making it his central substance and renaming it phlogiston. In his theory all substances, which are flammable contain phlogiston, which is given up when they burn, the combustion ceasing when the phlogiston is exhausted. The classic demonstration of this was the combustion of mercury, which turns to ash, in Stahl’s terminology (mercuric oxide in ours). If this ash is reheated with charcoal the phlogiston is restored (according to Stahl) and with it the mercury. (In our view the charcoal removes the oxygen restoring the mercury). In a complex series of experiment Stahl turned sulphuric acid into sulphur and back again, explaining the changes once again through the removal and return of phlogiston. Through extension Stahl, an excellent experimental chemist, was able to explain, what we now know as the redox reactions and the acid-base reactions, with his phlogiston theory based on experiment and empirical observation. Stahl’s phlogiston theory was thus the first empirically based ‘scientific’ explanation of a large part of the foundations of chemistry. It is a classic example of what Thomas Kuhn called a paradigm and Imre Lakatos a scientific research programme.

Viewed with hindsight the phlogiston theory is gloriously, wonderfully and absolutely wrong in all of its aspects thus leading to the scorn with which it is viewed by our gnu atheist proponent of scientism, however they are wrong to do so. I prefer Lakatos’ scientific research programme to Kuhn’s paradigm exactly because it describes the success of the phlogiston theory much better. For Lakatos it’s irrelevant whether a theory is right or wrong, what matters are its heuristics. A scientific research programme that produces new facts and phenomena that fit within the descriptive scope of the programme has a positive heuristic. One that produces new facts and phenomena that don’t fit has a negative heuristic. Scientific research programmes have both positive and negative heuristics simultaneously throughout their existences, so long as the positive heuristic outweighs the negative one the programme continues to be accepted. This was exactly the case with the phlogiston theory.

Most European eighteenth-century chemist accepted and worked within the framework of the phlogiston theory and produced a great deal of new important chemical knowledge. Most notable in this sense are the, mostly British, so-called pneumatic chemists. Working within the phlogiston theory Joseph Black (1728–1799), professor for medicine in Edinburgh, isolated and identified carbon dioxide whilst his doctoral student Daniel Rutherford (1749–1819) isolated and identified nitrogen. The Swede Carl Wilhelm Scheele (1742–1786) produced, identified and studied oxygen for which he doesn’t get the credit because although he was first, he delayed in publishing his results and was beaten to the punch by Joseph Priestley (1733–1804), who had independently also discovered oxygen labelling it erroneously dephlogisticated air. Priestley by far and away the greatest of the pneumatic chemists isolated and identified at least eight other gases as well as laying the foundations for the discovery of photosynthesis, perhaps his greatest achievement.

Henry Cavendish (1731–1810) isolated and identified hydrogen, which he thought for a time might actually be phlogiston, before going on to make the most important discovery within the framework of the phlogiston theory, the structure of water. By a series of careful experiments Cavendish was able to demonstrate that water was not an element but a compound consisting of two measures of phlogiston (hydrogen) with one of dephlogisticated air (oxygen). With the same level of precision he also demonstrated that normal air consists of four parts of nitrogen to one of oxygen or better said not quite. He constantly found something he couldn’t identify present in one one-hundredth and twentieth of the volume of nitrogen. In the nineteenth century this would finally be identified as the gas argon.

All of these discoveries are to be counted to the positive heuristic of the phlogiston theory. What weighed heavily on the negative side is the fact that as the accuracy of measurement increased in the eighteenth century it was discovered that the ashes, of mercury for example, left behind on burning were heavier than the original substance being burnt. This was troubling as combustion was supposed to be the release of phlogiston. Some supporters of the theory even suggested negative phlogiston to explain this anomaly. This suggestion, which never caught on, gets particularly mocked today, something I find somewhat strange in an age that has had to accept anti-matter and is now being asked to accept dark matter and dark energy to explain known anomalies in current theories.

Ironically it was the discoveries of oxygen and the composition of water that gave Lavoisier the necessary building blocks to dismantle the phlogiston theory and build his own competing theory, which would in the end prove successful and commit the phlogiston theory to the scrap heap of the history of chemistry. However one should never forget that it was exactly this theory that delivered him the tools he needed to do so. As I wrote in my sub-title even a theory that is wonderfully wrong can be fantastically fruitful and should be treated with respect when viewed with hindsight.



Filed under History of Chemistry, History of science, Myths of Science

A bewitching lady astronomer

Today in a day for celebrating the role that women have played and continue to play in the sciences, technology, engineering and mathematics. In the past on similar occasions I have blogged about female astronomers and I have decided today to write a short post about Aglaonice, who is possibly the oldest known lady astronomer.



Aglaonice is a semi-legendary, semi-mythical figure about whom our information is all second hand. She is associated with the witches from Thessaly, who claimed to be able to draw down the moon from its course in the heavens after depriving it of its illumination. The earliest mention of this feat in in Aristophanes The Clouds, first produced in 432 BCE.

Plutarch writing at the end of the first century CE tells us that Aglaonice knew about lunar eclipses and when they occurred. He writes, “ Always at the time of an eclipse of the Moon she pretended to bewitch it and draw it down.” In another passage he writes, “Aglaonice the daughter of Hegetor being thoroughly conversant with the periods of the Full Moon when it is subject to eclipse, and knowing beforehand when the Moon was due to be overtaken by the Earth’s shadow, imposed upon audiences of women and made them all believe that she drew down the Moon”. In late antiquity the poet Apollonius of Rhodes informs his readers that she lost a close relative after one of her performances as a punishment imposed by an outraged Moon goddess.

What is interesting in these accounts is that the moon is usually still visible during a lunar eclipse, only very occasionally does it disappear completely, so if we are to give any credence to these accounts Aglaonice must have carried out her charade during one such eclipse.

Total Lunar Eclipse 27 September 2015 Source: Wikimedia Commons

Total Lunar Eclipse
27 September 2015
Source: Wikimedia Commons

We have no idea when she is supposed to have lived but she obviously predates Plutarch writing about 100 CE and cannot be earlier than about the middle of the third century BCE, which is when the Babylonians first perfected the art of predicting lunar eclipses.

Whatever the case maybe, if Aglaonice existed at all, she must have been a truly bewitching lady astronomer.





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Filed under History of Astronomy, History of science, Ladies of Science

Science contra Copernicus

One of the most persistent and pernicious myths in the history of astronomy is that Galileo, with his telescopic observations, proved the validity of the Copernican heliocentric hypothesis and thus all opposition to it from that point on was purely based on ignorance and blind religious prejudice. Strangely, this version of the story is particularly popular amongst gnu atheists. I say strangely because these are just the people who pride themselves on only believing the facts and basing all their judgements on the evidence. Even Galileo knew that the evidence produced by his telescopic observations only disproved some aspects of Aristotelian cosmology and full scale Ptolemaic astronomy but other Tychonic and semi-Tychonic geocentric models still fit the available facts. A well as this the evidence was still a long way from proving the existence of a heliocentric model and many physical aspects spoke strongly against a moving earth. Put another way, the scientific debate on geocentrism versus heliocentrism was still wide open with geocentrism still in the most favourable position.

Apart from the inconclusiveness of the telescopic observations and the problems of the physics of a moving earth there were other astronomical arguments against heliocentricity at the time that remain largely unknown today. Christopher M. Graney[1] has done the history of astronomy community a big service in uncovering those arguments and presenting them in his new book Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo[2].


We’ll start with the general summary, as I’ve already stated in an earlier post this is an excellent five star plus book and if you have any interest in this critical period of transition in the history of astronomy then it is quite simply an obligatory text that you must read. So if you follow my advice, what are you getting for your money?

In 1651 the Jesuit astronomer Giovanni Battista Riccioli published his Almagestum Novum or New Almagest , which contains a list of 126 arguments concerning the motion of the earth, i.e. the heliocentric hypothesis, 49 for and 77 against and it is this list that provides the intellectual scaffolding for Graney’s book. Interestingly in discussion on seventeenth-century astronomy Riccioli’s book, and its list, has largely been dismissed or ignored in the past. The prevailing attitudes in the past seem to have been either it’s a book by a Jesuit so it must be religious and thus uninteresting or, as was taught to me, it’s a historical account of pre-Galilean astronomy and thus uninteresting. In fact before Graney and his wife undertook the work this list had never even been translated into English. As to the first objections only a few of Riccioli’s arguments are based on religion and as Graney points out Riccioli does not consider them to be very important compared with the scientific arguments. As to the second argument Riccioli’s account is anything but historical but reflects the real debate over heliocentrism that was taking place in the middle of the seventeenth century.

The strongest scientific argument contra Copernicus, which occupies pride of place in Graney’s book, is the so-called star size argument, which in fact predates both Galileo and the telescope and was first posited by Tycho Brahe. Based on his determination of the visible diameter of a star, Tycho calculated that for the stars to be far enough away so as to display no visible parallax, as required by a Copernican model with a moving earth, then they must be in reality unimaginably gigantic. A single star would have the same diameter as Saturn’s orbit around the sun. These dimensions for the stars didn’t just appear to Tycho to be completely irrational and so unacceptable. In a Tychonic cosmos, however, with its much smaller dimensions the stars would have a much more rational size. Should anyone think that this argument was not taken seriously, much later in the seventeenth century Christiaan Huygens considered the star size problem to be Tycho’s principle argument against Copernicus.

Many, more modern, historians dismissed the star size problem through the mistaken belief that the telescope had solved the problem by showing that stars are mere points of light and Tycho’s determined star diameters were merely an illusion caused by atmospheric refractions. In fact the opposite was true, early telescopes as used by Galileo and Simon Marius, amongst others, showed the stars to have solid disc shaped bodies like the planets and thus confirming Tycho’s calculations. Marius used this fact to argue scientifically for a Tychonic cosmos whilst Galileo tried to dodge the issue. We now know that what those early telescopic astronomers saw was not the bodies of stars but Airy discs an optical artefact caused by diffraction and the narrow aperture of the telescope and so the whole star size argument is in fact bogus. However it was first Edmond Halley at the beginning of the eighteenth century who surmised that these observed discs were in fact not real.

Graney details the whole history of the star size argument from Tycho down to Huygens revealing some interesting aspect along the way. For example the early Copernicans answered Tycho’s objections not with scientific arguments but with religious ones, along the lines of that’s the way God planned it!

Although the star size argument was the strongest scientific argument contra Copernicus it was by no means the only one and Graney gives detailed coverage of the whole range offering arguments and counter arguments, as presented by the participants in the seventeenth-century debate. Of interest particular here is Riccioli’s anticipation of the so-called Coriolis effect, which he failed to detect experimental thus rejecting a moving earth. Far from being a decided issue since 1610 when Galileo published his Sidereus Nuncius heliocentricity remained a scientifically disputed hypothesis for most of the seventeenth century.

Graney’s book is excellently written and clear and easy to understand even for the non-physicists and astronomers. He explains clearly and simply the, sometimes complex, physical and mathematical arguments and it is clear from his writing style that he must be a very good college teacher. The book is well illustrated, has an extensive bibliography and a useful index.

As a bonus the book contains two appendixes. The first is a translation (together with the original Latin text) and technical discussion of Francesco Ingoli’s 1616 Essay to Galileo, a never published but highly important document in the on going discussion on heliocentricity; Ingoli a Catholic cleric argued in favour of the Tychonic system. The second appendix is a translation (together with the original Latin text) and technical discussion of Riccioli’s Reports Regarding His Experiments with Falling Bodies. These experiments are of historical interest as they demonstrate Riccioli’s abilities, as a physicist, as he delivered the first empirical confirmation of Galileo’s laws of fall.

Graney’s book is a first class addition to the literature on the history of astronomy in the seventeenth century and an absolute must read for anyone claiming serious interest in the topic. If you don’t believe me read what Peter Barker, Dennis Danielson and Owen Gingerich, all first class historians of Early Modern astronomy, have to say on the back cover of the book.


[1] Disclosure; Chris Graney is not only a colleague, but he and his wife, Christina, are also personal friends of mine. Beyond that, Chris has written, at my request, several guest blogs here at the Renaissance Mathematicus, all of which were based on his research for the book. Even more relevant I was, purely by accident I hasten to add, one of those responsible for sending Chris off on the historical trail that led to him writing this book; a fact that is acknowledged on page xiv of the introduction. All of this, of course, disqualifies me as an impartial reviewer of this book but I’m going to review it anyway. Anybody who knows me, knows that I don’t pull punches and when the subject is history of science I don’t do favours for friends. If I thought Chris’ book was not up to par I might refrain from reviewing it and explain to him privately why. If I thought the book was truly bad I would warn him privately and still write a negative review to keep people from wasting their time with it. However, thankfully, none of this is the case, so I could with a clear conscience write the positive review you are reading. If you don’t trust my impartiality, fair enough, read somebody else’s review.

[2] Christopher M. Graney, Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo, University of Notre Dame Press; Notre Dame Indiana, 2015


Filed under Book Reviews, History of Astronomy, Myths of Science

Political correctness and the history of science

Anyone who regularly reads this blog will be already aware that the historian David Wootton has written a new book entitled The Invention of Science: A New History of The Scientific Revolution; in The Times (unfortunately behind a pay wall) Gerard DeGroot doesn’t so much review the book as perform a very nasty, vindictive hatchet job on it. DeGroot doesn’t just raise the spectre of eurocentrism in his critic he formally slaps Wootton in the face with it from the very opening paragraph of his review. This raises the question as to whether he is right to do so and whether Wootton is guilty as charged. Before I address these points I would like to briefly review what exactly eurocentrism with respect to the history of science is.

There used to be a brief standard sketch of the history of science, that probably arose some time in the Enlightenment but which owes much of its ethos to Renaissance historiography. This outline usually goes something like this. Science[1] was invented by the ancient Greeks. After the collapse of civilisation in the Dark Ages (a deliberate use of a discredited term here) science was rescued and conserved (but not changed or added to) by the Islamic Empire before being retrieved in the Renaissance by the Europeans, who then went on to create modern science in the Scientific Revolution. This piece of mythology reflected the triumphalist historiography of a colonialist Europe in the throws of dominating and exploiting large parts of the rest of the world.

During the twentieth century historians, many of them Europeans, dismantled this piece of fiction and began to explore and elucidate the histories of science of other cultures such as Egypt, Babylon, China, India and the Islamic Empire, creating in the process a much wider and infinitely more complex picture of the history of science, consisting of transfers of knowledge across space and time throughout the last approximately four thousand years. This newly acquired knowledge exposed anybody who still insisted on propagating part or all of the earlier fairy story to the charge of eurocentrism, a charge that when considering the whole of the history of science is more than justified.

Unfortunately, as I have commented in the past, this also led to an over zealous backlash on behalf of the previously wronged cultures particularly on the Internet. One only needs to state that X (a European) discovered/invented Y (some piece of science, technology, medicine, mathematics…) for some over assiduous commentator (almost always not a historian of science) to pop up saying, that’s not true Z (an Indian, Islamic, Chinese, or whatever scholar) discovered/invented Y long before X was even born. Occasionally these claims are correct but much more often they are inaccurate, exaggerated or just plain false. Any attempt to correct the informant leads inevitably to an accusation of eurocentrism. Eurocentrism has become a sort of universal weapon used indiscriminately whether it is applicable or not.

Wootton’s book deals not with a general universal history of science but as it very clearly states in its subtitle with the Scientific Revolution a historical episode that took place in Europe in the Early Modern Period. Whether one is, as a historian, a ‘revolutionary’ or a ‘gradualist’ there is no doubt that following its reintroduction into Europe during the High Middle Ages that which we call science, irrespective of its original sources, underwent a radical change that led to the emergence by, at the latest, the nineteenth century, science as we know it today. The major difference between Wootton and myself is that he thinks this process took place almost entirely within the seventeenth century whereas I see a timeframe stretching from the fourteenth century to at least the middle of the eighteenth.

Wootton is writing about a historical phenomenon that took place exclusively within Europe to accuse him of eurocentrism is to say the least perverse. If this were not a European phenomenon then the so-called Needham question would simply be nonsensical. Joseph Needham (1900-195) was the twentieth century’s greatest historian of Chinese science and instigator of the monumental, on going seven volume Science and Civilisation in China. The question that Needham posed runs as follows “Why did modern science, the mathematization of hypotheses about Nature, with all its implications for advanced technology, take its meteoric rise only in the West at the time of Galileo [but] had not developed in Chinese civilisation or Indian civilisation?” He could have equally well have posed the same question for the Islamic Empire. Many historians have tacked this question respective the three cultures and their answers are as diverse, as they are inconclusive. Some approach the question by trying to address the reasons for the decline of science and technology in China, India or the Islamic Empire whereas others try to isolate the factors that led to the Scientific Revolution in Europe. Although he doesn’t directly address the Needham question Wootton’s can be seen as an example of the latter.

If I were to be charitable to DeGroot it would appear that his main error lies in his interpretation of the word science as used by Wootton in his main title. It is clear that what Wootton intends is ‘modern science’ as used by Needham in the quote of his famous question above. DeGroot, I think disingenuously choses it to mean any form of scientific activity from anywhere and anytime in human history. We can see this conflict of interpretations in the following quotes from DeGroot:

…to assert that science was invented between certain dates in western European history automatically imposes a proprietary right – by defining science in a certain way it becomes, in essence, European.


A different intellectual climate existed in India, China and the Middle East, [in the Middle Ages] however. Outside Europe, minds were more open to progress and curiosity fired scientific enquiry. For instance great strides were made in pure and applied mathematics, optics, astronomy and medicine in the Middle East long before Columbus set sail [Wootton sees 1492 and Columbus’ first voyage as the starting point of the Scientific Revolution]. As early as the 10th century, brilliant scientists (not exclusively Muslim) were drawn to centres of learning in Baghdad, Balkh and Bukhara. These scholars considered Europe an intellectual backwater, yet hardly get a mention in this book. In other words, the so-called Scientific Revolution seems like a revolution only if we ignore what was happening outside Europe.

The first quote is a clear accusation of eurocentrism and the second is DeGroot’s attempt to justify his accusation. Nothing he writes in the second quote is wrong but also none of it has any real relevance to the book that David Wootton has written. Interesting is his attempt to deny that the Scientific Revolution ever took place. Whether you think that the very real change in the nature of science that took place in Europe in the Early Modern Period did so in the form of a revolution or more gradually over a longer timeframe to deny its very existence is to fly in the face of the historical facts. Whatever happened in the Islamic Empire between the eighth and twelfth centuries, the Golden Age of Islamic science, other than provided some of the foundations on which Kepler, Galileo, Newton et al built their new science, none of it had very much relevance to what took place in Europe in the seventeenth century.

This point is spelled out very clearly by A. Mark Smith in his recently published book, From Sight to Light, an essential volume for anybody interested in the history of optics. Smith’s book is a counter argument to David C. Lindberg’s Theories of Vision: From Al-Kindi to Kepler. Lindberg had argued that Kepler was, so to speak, the crowning glory of the European perspectivist tradition of optics that begins with the introduction of the work of Ibn al-Haytham into Europe in the thirteenth century. Following the same path, starting with ancient Greek optics, Smith, an expert on al-Haytham and Arabic optics, wants to show that Kepler is in fact a break with the perspectivist tradition and a new beginning in the theory of optics, a revolution if you will. Well aware that he might face charges of eurocentrism Smith devotes several pages of his introductions to explaining why such a charge would not be justified. He closes his explanation with the following paragraph:

The same holds for the evolution of modern optics over the sixteenth and seventeenth centuries. It may well be that certain key ideas, laws and concepts that contributed to that evolution were anticipated by Arabic or, for that matter, Indian, Chinese or Mesoamerican thinkers. And it is certainly the case that there was a lively cross-cultural marketplace of commodities and ideas between the Latin “West” and Arabic “East” throughout the Middle Ages and Renaissance. The fact remains, though, that it was in Europe that those ideas, laws, concepts were eventually assimilated, refined, channelled, and combined in such a way as to form the basis of what most of us today would characterize as modern optics. Any claim to the contrary strikes me as historically perverse. Furthermore, to contend that the evolution of modern optics over the sixteenth and seventeenth centuries happened in Europe is not to give Europe proprietary rights to that science or to accord Europe cultural exceptionalism or superiority for having developed it. I therefore strongly resist any charge of being trapped, whether wittingly or unwittingly, in some grand, master narrative or of engaging in hegemonic discourse.

If we substitute modern science for modern optics in Smith’s eloquent speech for the defence I think we can safely reject as baseless the accusations of eurocentrism that DeGroot makes against Wootton.


[1] Throughout this post I shall be using the word science as a collective noun for science, technology, medicine and mathematics to save time and effort whilst writing.


Filed under Book Reviews, History of science, Myths of Science