Category Archives: History of science

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

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

The Penny Universities

The Hungarian mathematician Alfréd Rényi famously quipped about his colleague Paul Erdös that, “a mathematician is a machine for turning coffee into theorems”. However this theorem producing process didn’t start with Erdös in the twentieth century but became an established routine as soon the coffee house made its appearance in Restoration England in the second half of the seventeenth century.

The first coffee house in England, The Angel, opened in Oxford in 1650 closely followed by The Queen’s Lane Coffee House in 1654, which is still in existence. London’s first coffee house, owned by Pasqua Rosée opened in 1652. The Temple Bar, London’s second coffee house opened in 1656.

From the very beginning English coffee houses became the favourite haunts of the virtuosi, the new generation of natural philosophers pushing the evolution of science forward in England in the second half of the seventeenth century; the circle around Christopher Wren in Oxford and the members of the Royal Society in London quickly becoming the habitués. The famous discussion between Wren, Hooke and Halley about an inverse square law of gravity and the shape of the planetary orbits took place in a London coffee house. Later, after he moved to London in 1696, Isaac Newton would hold court in the evenings in a coffee house distributing unpublished mathematical manuscripts to favoured acolytes privileged to sit at the feet of the maestro.

However these intellectual exchanges went beyond the informal meetings of the virtuosi in their free time. The coffee house became know as the penny universities, one penny being the going price of a cup of coffee. The proprietors offered courses of study as well as lecture courses in a wide range of subjects to those willing to pay a penny. As well as foreign languages these courses covered the new sciences. William Whiston, Newton’s successor as Lucasian Professor in Cambridge, offered courses in the new natural philosophy in the coffee houses, following his fall from grace and expulsion from Cambridge because of his religious views. Francis Hauksbee, demonstrator of experiments at the Royal Society under Newton’s presidentship, also improved his income with similar courses. Abraham de Moivre, impoverished Huguenot refugee, mathematician and fervent Newtonian eked out a pittance in the coffee houses, teaching chess and mathematics and instructing punters how to calculate gambling odds.

Later in the eighteenth century the group of religious dissenters, radical liberal politicians and scientists, christened by Benjamin Franklin “The Club of Honest Whigs”, which included as well as Franklin, the chemist Joseph Priestly, the mathematician Richard Price, the natural philosopher John Canton, the military physician John Pringle and the physician Benjamin Vaughan held their regular Monday meetings in the London Coffee House in St Paul’s Churchyard.

Many were the scientific and mathematical debates and disputes that were carried out in the eighteenth century coffee houses of England.

I drink my daily cup of coffee at Amir Der KaffeeMann in Erlangen, excellent beverages personally roasted by Amir, the Persian proprietor, and for the price of a cappuccino I will entertain you with a history of science lecture of your choice.


Filed under History of science, Newton

The Internet and the history of science community

Yesterday evening I had a very pleasant evening meal in Nürnberg with Karl Galle. Now somebody reading this statement, who doesn’t know Karl, might wonder what this has to do with the title of this post. Things might become a little bit clearer if I explain that Karl is, like myself, a historian of science. Now this post is not actually about Karl but rather more how I came to be eating with him yesterday evening on the Market Square of the picturesque Renaissance city of Nürnberg. Before I give a direct answer to this implied question I first want to go back in time to those dim and distant days when the Internet didn’t exist.

When I first became seriously interested in the history of science in the 1970s, I was living in Cardiff, the capital of Wales, with no real contact to other historians of science other than through the books on the subject that I was eagerly consuming at the time and I never truly imagined that I could get to meet and converse with a real historian of science in the flesh. Occasionally I would meet up with somebody who shared my interest on some level and would then enthusiastically engage them on the subject, often whilst getting stoned or drunk or both.

In 1980 I moved to Germany more by accident than design. It was never planned, thought through or aimed for; it just happened. In 1982 I returned to university in Erlangen having dropped out of university in Cardiff in 1971. This time round I studied mathematics and philosophy with an emphasis on the history and philosophy of science. In the middle of the 1980s because the maths department were not interested in history I changed over to philosophy, English philology and history. For most of the 80s and into the 90s I also worked as an, albeit badly paid, researcher into the history of mathematical or formal logic. I was for a decade an integrated part of a history of science community. Professors, lecturers, students, doctoral students and postdocs lots of local possibility for informative exchanges. However to go beyond the local was not so simple.

In this age of cheap instant communications, I think we forget how new this all is. In the 1980s there was no Internet. Telephone calls were expensive even a long distant call within your own country would cost you an arm or a leg, so to speak, so they were outside of the possibilities of a poverty stricken student and not encouraged by employers etc. If you wanted to communicate with another historian of science in Canada for example you sat down and wrote a letter; the sending of which and any eventual reply could and often did take several weeks. Truly snail mail. If you wanted to meet non-local historians of science you either went to conferences, although travel was in those days also prohibitively expensive compared to now, or you hoped that they would come round on the lecture circuit. If your university department had the necessary funds they could invite the luminaries of the discipline to guest lectures when they were on tour. We had money and through this system I got to know and converse with such luminaries of the history of maths and logic as Martin, Davis, Joe Dauben and Ivor Grattan-Guinness amongst others.

In the early 1990s I dropped out of university because of serious mental illness, having completed about 95% of my masters degree but never passing the finishing post. Most of the next decade I had little or no contact with the history of science community although I kept up my reading on the discipline. In 2002 I returned to the fold about the same time as I acquired my first computer. The last is somewhat ironic, as compared to many of my contemporaries I came late to the computer although one of the things that I had studied intensely was the history of computing. In fact at the drop of a mega-byte I will launch into a whole lecture series on the history of computing starting with the Babylonian sexagesimal number system and going up to Alan Turing, Johnny von Neumann and beyond. On my return to being a historian of science my first public lecture was on George Boole and the contribution of Boolean algebra to the history of computing. During my absence the emergence of the Internet and the World Wide Web and completely changed the rules of the game. Being a member of the history of science community had taken on a wholly new meaning, although it took me some time to recognise and to experience this.

Initially my interest in the Internet was connected to my love of music, the first website I ever visited was The first maths or science web site was Mark Chu-Carroll’s Good Math Bad Math, which often has a history of maths content. In those days Mark was on Science Blogs and through visits to his blog I stumbled across John Wilkins, an Australian historian and philosopher of biology. John is actually responsible for the existence of this blog set up in 2009, as is here in various places well documented. Through my own blogging and my comments on other related blogs I slowly began to get to know other historians of the sciences scattered all over the world. Direct contact and instant communication that was unthinkable in the 1980s.

In 2010 John together with John Lynch, a lecturer for the history of science at Arizona State University set up the Whewell’s Ghost blog as a collective history of science blog, providing a one stop distribution point for people wishing to read posts by a diverse collection of history of science bloggers. Yours truly was invited to participate, an invitation, which I accepted with alacrity. Amongst those participants whom I didn’t already know was Rebekah “Becky” Higgitt, then a curator at the National Maritime Museum at Greenwich and now a lecturer at Kent University. Unlike myself and other participants Becky didn’t originally have her own blog but used Whewell’s Ghost as her blog. Later she would leave the nest to first found her own blog Teleskopos and then moving on to found with Vanessa Heggie the H-Word blog at the Guardian, a rare history of science blog embedded in a major science blog collective. Very early I realised that Becky and I shared similar attitudes and approaches to the history of science and I christened her, my “#histsci soul sister”. On visits to London I would come to know her personally along with her Greenwich colleague Richard Dunn.

Even before I met her in the flesh, Becky and I became good Internet friends and when I blogged something about Albrecht Dürer and Nürnberg she said that I would probably be interested in the doctoral thesis of her earlier doctoral studies colleague Karl Galle. I said I was and could she supply me with his email address. Having checked that he agreeable, she did so and I wrote an email to Karl asking if he could supply me with a pdf of his thesis. He could and did, and I read it with great interest and we continued to exchange emails. All of this took place over a couple of days. In the 1980s Becky, who I might never have got to know, would have supplied me with a postal address. I would have written a letter and posted it off hoping to maybe get a reply some weeks or even months later. If Karl had then agreed to my request he would have had to photocopy his rather substantial thesis, parcel it up and send it to me at not inconsiderable cost. It then hopefully arriving after a longer period than the letter took in the other direction. Times change!

Sometime later Karl, who lives in Cairo (the one in Egypt) came to Nürnberg to do some research connected to turning his thesis into a book and we met up for the first time, spending a happy summer’s day together rapping about things scientifically historical. This week Karl was back doing some more research, this time with his charming wife, and, as I said at the beginning of this post, we continued that conversation over things scientifically historical during a very pleasant meal sitting on a balcony overlooking the Market Place in Nürnberg.

The Frauenkirche Nürnberg our view during supper yesterday evening Source Wikimedia Commons

The Frauenkirche Nürnberg our view during supper yesterday evening
Source Wikimedia Commons

To recap, through the Internet I got to know a historian of biology living in Sydney, Australia who introduced me to a lady historian living and working in London, England, who in turn introduced me to a historian of Dürer the Nürnberger mathematician, who lives in Cairo, Egypt. I have also had the pleasure of meeting all three of these generous historians in the flesh.

This is just one set of connections that I have made through cyberspace since I decided to become a history of science blogger. I sit in a small flat, in a small village in Middle Franconia physically cut off from the rest of the world but through the medium of the Internet I am an integral part of a flourishing history of science community that is still growing and the members of which can communicate with each other instantly on a daily basis exchanging ideas or sending papers, theses or illustrations equally instantly as data files. Only physical books still have to be sent with the traditional post, although I will admit to having quite a few scans of books on my computer and iPad.

This is a situation that I would not have dreamt of when I started on my personal journey into the thickets of the history of science almost fifty years ago and one that I am very grateful to have experienced and hope to continue to enjoy for some time to come. If you know any historians of the sciences, who still haven’t discovered the Internet history of science community tell them to dive in, the waters lovely.




Filed under Autobiographical, History of science