Category Archives: History of Navigation

Measure for measure

The Brexit vote in the UK has produced a bizarre collection of desires of those Leavers eager to escape the poisonous grasp of the Brussels’ bureaucrats. At the top of their list is a return of the death penalty, a piece of errant stupidity that I shall leave largely uncommented here. Not far behind is the wish to abandon the metric system and to return to selling fruit and vegetables in pounds and ounces. This is particularly strange for a number of reasons. Firstly the UK went metric in 1965, six years before it joined the EU. Secondly EU regulations actually allows countries to use other systems of weights and measures parallel to the metric system, so there is nothing in EU law stopping greengrocers selling you a pound of carrots or bananas. Thirdly the country having gone metric in 1965, anybody in the UK under the age of about fifty is going to have a very hard time knowing what exactly pounds and ounces are.

Most readers of this blog will have now gathered that I have spent more than half my life living in Germany. Germany is of course one of the founding states of the EU and as such has been part of it from the very beginning in 1957. The various states that now constitute Germany also went metric at various points in the nineteenth century, the earliest in 1806-15, and the latest in 1868. However the Germans are a very pragmatic folk and I can and do buy my vegetables on the market place in Erlangen in pounds and half pounds. The Germans like most Europeans used variation of the predecessors to the so-called Imperial system of weights and measures and simple re-designated the pound (Pfund in German) to be half a kilo. The Imperial pound is actually approximately 454 grams and for practical purposes when buying potatoes or apples the 46-gram difference if negligible. Apparently the British are either too stupid or too inflexible to adopt such a pragmatic solution.

At the beginning of the month Tory dingbat and wanna be journalist Simon Heffer wrote an article in The Telegraph with the glorious title, Now that we are to be a sovereign nation again, we must bring back imperial units. I haven’t actually read it because one has to register in order to do so and I would rather drink bleach than register with the Torygraph. I shall also not link to the offending article, as it will only encourage them. Heffer charges into the fray thus:

But I know from my postbag that there is another infliction from the decades of our EU membership that many would like to be shot of, and that was the imposition of the metric system on large parts of our life. 

Consumer resistance ensured that our beer is still served in pints (though not in half-pint and pint bottles when bought in supermarkets: brewers please note), and that our signposts are still marked in miles.

As pointed out above it was not the EU who imposed the metric system on British lives but the British government before the UK joined the EU. According to EU regulations you can serve drinks in any quantities you like just as long as the glasses are calibrated, so keeping the traditional pint glasses and mugs in British pubs was never a problem. Alcohol is sold in Germany in a bewildering range of different size glasses depending on the local traditions. My beer drinking German friends (the Germans invented the stuff, you know) particularly like pints of beer because they say that they contain a mouthful more beer that a half litre glass. Sadly many bars in Franconia have gone over to selling beer in 0.4litre glasses to increase their profits, but I digress.

UK signposts are still marked in miles because the government could not afford the cost of replacing all of them when the UK went metric. Expediency not national pride was the motivation here.

Just before Heffer’s diatribe disappears behind the registration wall he spouts the following:

But we have been forced on to the Celsius temperature scale, which is less precise than Fahrenheit

When I read this statement I went back to check if the article had been published on 1 April, it hadn’t! Is the international scientific community aware of the fact that they have been conned into using an inaccurate temperature scale? (I know that scientist actually use the Kelvin temperature scale but it’s the same as the Celsius scale with a different zero point, so I assume by Heffer’s logic(!) it suffers from the same inaccuracy). Will all of those zillions of experiments and research programmes carried out using the Celsius/Kelvin scale have to be repeated with the accurate Fahrenheit scale? Does Simon Heffer actually get paid for writing this crap?


Anders Celcius Portrait by Olof Arenius Source: Wikimedia Commons


Daniel Gabriel Fahrenheit

Like myself on being confronted with the bring back imperial weights and measures madness lots of commentators pointed out that the UK went metric in 1965 but is this true? No, it isn’t! The UK actually went metric, by act of parliament over one hundred years earlier in 1864! The nineteenth century contains some pretty stirring history concerning the struggles between the metric and imperial systems and we will now take a brief look at them.

As soon as it became in someway necessary for humans to measure things in their environment it was fairly obvious that they would use parts of their body to do so. If we want a quick approximate measure of something we still pace it out or measure it with the length of an arm or the span of our fingers. So it was natural that parts of the body became the units of measurement, the foot, the forearm, the arm span and so on and so forth. This system of course suffers from the fact that we are not all the same size. My foot is shorter than yours; my forearm is longer than my partners. This led cultures with a strong central bureaucracy to develop standard feet and forearms. The various Fertile Crescent cultures developed sophisticated weights and measures systems, as did the Roman Empire and it is the latter that is the forefather of the imperial system. The Roman foot was between 29.5 and 30 cm, the pace was 2.5 feet and the Roman mile was 5000 feet. The word mile comes from the Latin for thousand, mille. The Roman military, which was very standardised, carried the Roman system of weights and measures to large parts of Europe thus establishing their standards overall.

With the collapse of the Roman Empire their standardised system of weights and measures slowly degenerated and whilst the names were retained their dimensions varied from district to district and from town to town. In the eighth and ninth centuries Karl der Große (that’s Charlemagne for the Brits) succeeded in uniting a substantial part of Europe under his rule. Although he was uneducated and illiterate he was a strong supporter of education and what passed at the time for science and amongst his reforms he introduced a unified system of weights and measures for his entire empire, another forefather of the imperial system. Things are looking quite grim for the anti-European supporters of the imperial system; it was born in Rome the birthplace of the EU and was reborn at the hands of a German, nothing very British here.

Karl’s attempt to impose a unified system of weights and measures on his empire was not a great success and soon after his death each district and town went back to their own local standards, if they ever left them. Throughout the Middle Ages and deep into the Early Modern Period traders had to live with the fact that a foot in Liège was not the same as a foot in Venice and a pound in Copenhagen was not a pound in Vienna.

This chaos provided work for the reckoning masters producing tables of conversions or actually doing the conversions for the traders, as well as running reckoning schools for the apprentice traders where they taught the arithmetic and algebra necessary to do the conversions, writing the textbooks for the tuition as well. The lack of unity in currency and mensuration in medieval Europe was a major driving force in the development algebra – the rule of three ruled supreme.

At the beginning of the seventeenth century Simon Stevin and Christoph Clavius introduced decimal fractions and the decimal point into European mathematics, necessary requirements for a decimal based metric system of mensuration. Already in the middle of the seventeenth century just such a system emerged and not from the dastardly French but from a true blue English man, who was an Anglican bishop to boot, polymath, science supporter, communicator, founding member of the Royal Society and one of its first secretaries, John Wilkins (1614–1672).

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Asked by the society to devise a universal standard of measure he devoted four pages of his monumental An Essay towards a Real Character and a Philosophical Language (1668) to the subject.


Title Page Source: Wikimedia Commons

He proposed a decimal system of measure based on a universal measure derived from nature for use between ‘learned men’ of various nations. He considered atmospheric pressure, the earth’s meridian and the pendulum as his universal measure, rejecting the first as susceptible to variation, the second as immeasurable and settled on the length of the second pendulum as his measure of length. Volume should be the cubic of length and weight a cubic standard of water. To all extents and purposes he proposed the metric system. His proposal fell, however, on deaf ears.


European units of length in the first third of the 19th century Part 1


European units of length in the first third of the 19th century Part 2

As science developed throughout the seventeenth and eighteenth century it became obvious that some sort of universal system of measurement was a necessity and various people in various countries addressed to subject. In 1790 the revolutionary Assemblée in France commissioned the Académie to investigate the topic. A committee consisting of Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Nicolas de Condorcet, all leading scientific figures, recommended the adoption of a decimal metric system based on one ten-millionth of one quarter of the Earth’s circumference. The proposal was accepted by the Assemblée on 30 March 1791. Actually determining the length of one quarter of the Earth circumference turned into a major project fraught with difficulties, which I can’t do justice to here in an already overlong blog post, but if you are interested then read Ken Adler’s excellent The Measure of All Things: The Seven-Year Odyssey That Transformed The World.


Standard meter on the left of the entrance of the french Ministère de la Justice, Paris, France. Source: Wikimedia Commons

However Britain needed a unified system of mensuration, as they still had the problem that every town had different local standards for foot, pound etc. John Herschel the rising leading scientific figure wanted a new decimal imperial system based on the second pendulum but in the end parliament decide to stick with the old imperial system taking a physical yard housed in the Houses of Parliament as the standard for the whole of the UK. Unfortunately disaster struck. The Houses of Parliament burnt down in 1834 and with it the official standard yard. It took the scientists several years to re-establish the length of the official yard and meanwhile a large number were still advocating for the adoption of the metric system.


The informal public imperial measurement standards erected at the Royal Observatory, Greenwich, London, in the 19th century: 1 British yard, 2 feet, 1 foot, 6 inches, and 3 inches. The inexact monument was designed to permit rods of the correct measure to fit snugly into its pins at an ambient temperature of 62 °F (16.66 °C) Source: Wikimedia Commons

The debate now took a scurrile turn with the introduction of pyramidology! An English writer, John Taylor, developed the thesis that the Great Pyramid was constructed using the imperial system and that the imperial system was somehow divine. Strangely his ideas were adopted and championed by Charles Piazzi Smyth the Astronomer Royal of Scotland and even received tacit and indirect support from John Herschel, who rejected the pyramidology aspect but saw Taylor’s pyramid inch as the natural standard of length.

However wiser heads prevailed and the leaders of the British Victorian scientific community made major contributions to the expansion of the metric system towards the SI system, used internationally by scientists today. They applied political pressure and in 1864 the politicians capitulated and parliament passed the Metric (Weights and Measures) Act. This permitted the use of weights and measures in Britain. Further acts followed in 1867, 1868, 1871 and 1873 extending the permitted use of the metre. However the metric system could be used for scientific purposes but not for business. For that, Britain would have to wait another one hundred and one years!

Interestingly, parallel to the discussion about systems of mensuration in the nineteenth century, a discussing took place about the adoption of a single prime meridian for cartographical, navigational, and time purposes. In the end the two main contenders were the observatories in Paris and Greenwich. Naturally neither Britain nor France was prepared to concede to the other. To try and solve the stalemate it was suggested that in exchange for Paris accepting Greenwich as the prime meridian London should adopt the metric system of measurement. By the end of the nineteenth century both countries had nominally agreed to the deal without a formal commitment. Although France fulfilled their half of this deal sometime early in the twentieth century, Britain took until 1965 before they fulfilled their half.

Should the Leavers get their wish and the UK returns to the imperial system of measurement then they will be joining an elite group consisting of the USA, Myanmar and Liberia, the only countries in the world that don’t have the metric system as their national system of measurement for all purposes.


Filed under History of Mathematics, History of Navigation, History 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

Retelling a story – this time with all the facts

Before 1995 probably only a handful of people interested in the history of navigation had ever heard of the English clockmaker John Harrison and the role he played in the history of attempts to find a reliable method of determining longitude at sea. This situation changed radically when Dava Sobel published her book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time[1] in that year. This volume caught the public imagination and very rapidly became one of the most successful popular history of science and technology books of all time. It was followed just three years later by a lavishly illustrated expanded edition. Just one year after that followed the equally lavish television documentary film based on the book. By the year 2000 at the latest John Harrison had become a household name and a British scientific hero on a level with Newton and Darwin.

P.L. Tassaert's half-tone print of Thomas King's original 1767 portrait of John Harrison, located at the Science and Society Picture Library,

P.L. Tassaert’s half-tone print of Thomas King’s original 1767 portrait of John Harrison, located at the Science and Society Picture Library,

All of this would have been well and good if Sobel had actually adhered to the first three words of her subtitle, The True Story…, but unfortunately she sacrificed historical accuracy to the expediency of telling a good story, basically reducing a complex historical narrative to the fairy tale of a poor honest hero, John Harrison, overcoming adversity to finally triumph against the evil machination of his dishonest scheming opponent the Astronomer Royal, Nevil Maskelyne. Sobel’s lurid narrative proved, as already stated, commercially very successful but left its readers with a highly distorted view of what actually took place in the long eighteenth century in the endeavours to find a method of determining longitude and the role that the various people involved played in those endeavours. In particular Nevil Maskelyne was left in the popular public imagination looking rather like the devil’s evil cousin.


Rev. Dr Nevil Maskelyne Source Wikimedia

Rev. Dr Nevil Maskelyne
Source Wikimedia

About five years ago a major historical research project, under the auspices of the Arts & Humanities Research Council, was set up by Cambridge University and the National Maritime Museum in Greenwich on the history of the British Board of Longitude, the official body set up to oversee and direct the search for a method to determine longitude at sea in the eighteenth century. Led by Simon Schaffer for the University of Cambridge and Richard Dunn and Rebekah Higgitt for the National Maritime Museum this project featured a cast of excellent doctoral and post doctoral researchers some of whose findings can be found on the excellent Longitude Project Blog. To date this research project has produced a remarkable list of achievements. Alongside a volume of papers on the much maligned Nevil Maskelyne, which has just appeared and which I am looking forward very much to reading,


the whole of the Board of Longitude archive has been digitized and made available online to researchers. Currently on at the Museum in Greenwich is a major exhibition Ships, Clocks and Stars: The Quest for Longitude, which you can still visit if you hurry, it closes on the 4th of January 2015. If you are uncertain whether or not it’s worth visiting, it has just been awarded the British Society for the History of Science Great Exhibitions Award for 2014! If like myself you are unable for some reason to make the journey to Greenwich do not despair you can bring the exhibition into your own living room by acquiring the accompanying book Finding Longitude: How Ships, clocks and stars helped solve the longitude problem[2] by Richard Dunn and Rebekah Higgitt, a review of which is the actually subject of this post.

Finding Longitude001

My review is actually very simple this book is magnificent. If you have any interest in the histories of navigation, sea voyages, astronomy, clocks, John Harrison, Nevil Maskelyne, Tobias Mayer, and a whole ship’s cargo of other related and interrelated topics then buy this book! I guarantee you that you won’t regret it for one second. It combines thorough research, first class scholarship, excellent writing, unbelievably lavish illustrations, fascinating narratives and historical accuracy in one superb and, for what it is, surprisingly low priced large format volume. Unlike Sobel’s, from a historians standpoint, ill-starred volume, this work really does tell the true story of the solution of the longitude problem with all its complex twists and turns giving all the participants their dues. Although written for the general reader this book should also find a home on the bookshelves of any working historian of navigation, astronomy, horology, sea voyages or just the science and technology of the long eighteenth century.

This book will take you on a voyage through the choppy waters of eighteenth century science, politics and technology and deliver you up on the shores of the nineteenth century much more knowledgeable then you were when you boarded ship and entertain and delight you along the way. It will also make for a first class Christmas present.

[1] Dava Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Fourth Estate, London, 1995

[2] Richard Dunn & Rebekah Higgitt, Longitude: How Ships, clocks and stars helped solve the longitude problem, Collins and Royal Museums Greenwich, London 2014


Filed under Book Reviews, History of Cartography, History of Navigation, History of science

Planetary Tables and Heliocentricity: A Rough Guide

Since it emerged sometime in the middle of the first millennium BCE the principal function of mathematical astronomy was to provide the most accurate possible predictions of the future positions of the main celestial bodies. This information was contained in the form of tables calculated with the help of the mathematical models, which had been derived by the astronomers from the observed behaviour of those bodies, the planets. The earliest Babylonian models were algebraic but were soon replaced by the Greeks with geometrical models based on spheres and circles. To a large extent it did not matter if those models were depictions of reality, what mattered was the accuracy of the prediction that they produced; that is the reliability of the associated tables. The models of mathematical astronomy were judge on the quality of the data they produced and not on whether they were a true reproduction of what was going on in the heavens. This data was used principally for astrology but also for cartography and navigation. Mathematical astronomy was a handmaiden to other disciplines.

Before I outline the history of such tables, a brief comment on terminology. Data on the movement of celestial bodies is published under the titles planetary tables and ephemerides (singular ephemeris). I know of no formal distinction between the two names but as far as I can determine planetary tables is generally used for tables calculated for quantitatively larger intervals, ten days for example, and these are normally calculated directly from the mathematical models for the planetary movement. Ephemeris is generally used for tables calculated for smaller interval, daily positions for example, and are often not calculated directly from the mathematical models but are interpolated from the values given in the planetary tables. Maybe one of my super intelligent and incredibly well read readers knows better and will correct me in the comments.

The Babylonians produced individual planetary tables, in particular of Venus, but we find the first extensive set in the work of Ptolemaeus. He included tables calculated from his geometrical models in his Syntaxis Mathematiké (The Almagest), published around 150 CE, and to make life easier for those who wished to use them he extracted the tables and published them separately, in extended form with directions of their use, in what is known as his Handy Tables. This publication provided both a source and an archetype for all future planetary tables.

The important role played by planetary tables in mathematical astronomy is illustrated by the fact that the first astronomical works produced by Islamic astronomers in Arabic in the eighth-century CE were planetary tables known in Arabic as zījes (singular zīj). These initial zījes were based on Indian sources and earlier Sassanid Persian models. These were quickly followed by those based on Ptolemaeus’ Handy Tables. Later sets of tables included material drawn from Islamic Arabic sources. Over 200 zījes are known from the period between the eighth and the fifteenth centuries. Because planetary tables are dependent on the observers geographical position most of these are only recalculation of existing tables for new locations. New zījes continued to be produced in India well into the eighteenth-century.

With the coming of the European translators in the twelfth and thirteenth centuries and the first mathematical Renaissance the pattern repeated itself with zījes being amongst the first astronomical documents translated from Arabic into Latin. Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was originally better known in Europe for his zīj than for The Compendious Book on Calculation by Completion and Balancing” (al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala), the book that introduced algebra into the West. The Toledan Tables were created in Toledo in the eleventh-century partially based on the work of Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī, known in Latin as Arzachel. In the twelfth-century they were translated in Latin by Gerard of Cremona, the most prolific of the translators, and became the benchmark for European planetary tables.

In the thirteenth- century the Toledan Tables were superseded by the Alfonsine Tables, which were produced by the so-called Toledo School of Translators from Islamic sources under the sponsorship of Alfonso X of Castile. The Alfonsine Tables remained the primary source of planetary tables and ephemerides in Europe down to the Renaissance where they were used by Peuerbach, Regiomontanus and Copernicus. Having set up the world’s first scientific press Regiomontanus produced the first ever printed ephemerides, which were distinguished by the accuracies of their calculations and low level of printing errors. Regiomontanus’ ephemerides were very popular and enjoyed many editions, many of them pirated. Columbus took a pirate edition of them on his first voyage to America and used them to impress some natives by accurately predicting an eclipse of the moon.

By the fifteenth-century astronomers and other users of astronomical data were very much aware of the numerous inaccuracies in that data, many of them having crept in over the centuries through frequent translation and copying errors. Regiomontanus was aware that the problem could only be solved by collecting new basic observational data from which to calculate the tables. He started on such an observational programme in Nürnberg in 1470 but his early death in 1475 put an end to his endeavours.

When Copernicus published his De revolutionibus in 1543 many astronomers hoped that his mathematical models for the planetary orbits would lead to more accurate planetary tables and this pragmatic attitude to his work was the principle positive reception that it received. Copernicus’ fellow professor of mathematic in Wittenberg Erasmus Reinhold calculated the first set of planetary tables based on De revolutionibus. The Prutenic Tables, sponsored by Duke Albrecht of Brandenburg Prussia (Prutenic is Latin for Prussian), were printed and published in 1551. Ephemerides based on Copernicus were produced by Johannes Stadius, a student of Gemma Frisius, in 1554 and by John Feild (sic), with a forward by John Dee, in 1557. Unfortunately they didn’t live up to expectations. The problem was that Copernicus’ work and the tables were based on the same corrupted data as the Alfonsine Tables. In his unpublished manuscript on navigation Thomas Harriot complained about the inaccuracies in the Alfonsine Tables and then goes on to say that the Prutenic Tables are not any better. However he follows this complaint up with the information that Wilhelm IV of Hessen-Kassel and Tycho Brahe on Hven are gathering new observational data that should improve the situation.

As a young astronomer the Danish aristocrat, Tycho Brahe, was indignant that the times given in both the Alfonsine and the Prutenic tables for a specific astronomical event that he wished to observe were highly inaccurate. Like Regiomontanus, a hundred years earlier, he realised that the problem lay in the inaccurate and corrupted data on which both sets of tables were based. Like Regiomontanus he started an extensive programme of astronomical observations to solve the problem, initially at his purpose built observatory financed by the Danish Crown on the island of Hven and then later, through force of circumstances, under the auspices of Rudolph II, the Holy Roman German Emperor, in Prague. Tycho devoted almost thirty years to accruing a vast collection of astronomical data. Although he was using the same observational instruments available to Ptolemaeus fifteen hundred years earlier, he devoted an incredible amount of time and effort to improving those instruments and the methods of using them, meaning that his observations were more accurate by several factors than those of his predecessors. What was now needed was somebody to turn this data into planetary tables, enter Johannes Kepler. Kepler joined Tycho in Prague in 1600 and was specifically appointed to the task of producing planetary tables from Tycho’s data. Contrary to popular belief he was not employed by Tycho but directly by Rudolph.

Following Tycho’s death, a short time later, a major problem ensued. Kepler was official appointed Imperial Mathematicus, as Tycho’s successor, and still had his original commission to produce the planetary tables for the Emperor, however, legally, he no longer had the data; this was Tycho’s private property and on his death passed into the possession of his heirs. Kepler was in physical possession of the data, however, and hung on to it during the protracted, complicated and at times vitriolic negotiations with Tycho’s son in law, Frans Gansneb Genaamd Tengnagel van de Camp, over their future use. In the end the heirs granted Kepler permission to use the data with the proviso that any publications based on them must carry Tengnagel’s name as co-author. Kepler then proceeded to calculate the tables.

Put like this, it sounds like a fairly straightforward task, however it was difficult and tedious work that Kepler loathed intensely. It was not made any easier by the personal and political circumstances surrounding Kepler over the years he took to complete the task. Wars, famine, usurpation of the Emperor’s throne (don’t forget the Emperor was his employer) and family disasters all served to make his life more difficult.

Finally in 1626, twenty-six years after he started Kepler had finally reduced Tycho’s thirty years of observations into planetary tables for general use, now he only had to get them printed. Drumming up the financial resources for the task was the first hurdle that Kepler successfully cleared. He then purchased the necessary paper and settled in Linz to complete the task of turning his calculations into a book. As the printing was progressing all the Protestants in Linz were ordered to leave the city, Kepler, being Imperial Mathematicus, and his printer were granted an exemption to finish printing the tables but then Wallenstein laid siege to the city to supress a peasants uprising. In the ensuing chaos the printing shop and the partially finished tables went up in flames.

Leaving Linz Kepler now moved to Ulm where, starting from the beginning again, he was finally able to complete the printing of the Rudophine Tables, named after the Emperor who had originally commissioned them but dedicated to the current Emperor, Ferdinand II. Although technically not his property, because he had paid the costs of having them printed Kepler took the finished volumes to the book fair in Frankfurt to sell in September 1627.

Due to the accuracy of Tycho’s observational data and the diligence of Kepler’s mathematical calculations the new tables were of a level of accuracy never seen before in the history of astronomy and fairly quickly became the benchmark for all astronomical work. Perceived to have been calculated on the basis of Kepler’s own elliptical heliocentric astronomy they became the most important artefact in the general acceptance of heliocentricity in the seventeenth century. As already stated above systems of mathematical astronomy were judged on the data that they produced for use by astrologers, cartographers, navigators et al. Using the Rudolphine Tables Gassendi was able to predict and observe a transit of Mercury in 1631, as Jeremiah Horrocks succeeded in predicting and observing a transit of Venus for the first time in human history based on his own calculations of an ephemeris for Venus using Kepler’s tables, it served as a confirming instance of the superiority of both the tables and Kepler’s elliptical astronomy, which was the system that came to be accepted by most working astronomers in Europe around 1660. The principle battle in the war of the astronomical systems had been won by a rather boring set of mathematical tables, Johannes Kepler’s Tabulae Rudolphinae.

Rudolphine Tables Frontispiece

Rudolphine Tables Frontispiece




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

Cartographical Claptrap!

The AEON magazine website has a long essay[1] by Kurt Hollander simply titled Middle Earth that takes as its subject not the fantasy realm of J. R. R. Tolkien but the equator, the imaginary line marking the middle of the Earth’s sphere. Unfortunately this essay is severely marred by a series of errors, myths and falsities about the history of cartography and geodesy. I have selected some of the worst here for critical analysis and correction.

Our author gets off to a flying start with the biggest geodesic myth of them all:

Medieval Christian mapmakers, familiar only with a small corner of the planet, worked within strict horizons that were fixed by the Church’s interpretation of the Bible. Their Earth was flat.

My friend Darrin Hayton (@dhayton) has written several posts on the excellent PACHS blog over the years criticising the people who still insists on propagating the myth that the Europeans in the Middle Ages believed that the world was flat. Just once more for those that haven’t been listening, they didn’t. That the world was a sphere was probably first recognised by the Pythagoreans in the sixth century BCE and almost all educated people accepted this fact from at the latest the fourth century BCE up to the present.

First created in the 7th century, the Christian orbis terrarum (circle of the Earth) maps, known for visual reasons as ‘T-and-O’ maps, included only the northern hemisphere.

T and O maps actually have their roots in Greek geography and cartography and only display part of the northern hemisphere because that was all that their creators knew about.

The T represented the Mediterranean ocean, which divided the Earth’s three continents — Asia, Africa, and Europe — each of which was populated by the descendants of one of Noah’s three sons. Jerusalem usually appeared at the centre, on the Earth’s navel (ombilicum mundi), while Paradise (the Garden of Eden) was drawn to the east in Asia and situated at the top portion of the map. The O was the Ocean surrounding the three continents; beyond that was another ring of fire.

Given that the Greeks, the originators of the geography on which the T and O maps are based, lived in the Mediterranean Sea (not ocean!) they were of course well aware of the fact that it is not T shaped. The T on T and O maps actually represents in schematic form the Mediterranean and the Don and Nile rivers, as the dividing lines between the three known continents.

For the Catholic Church, the Equator marked the border of civilisation, beyond which no humans (at least, no followers of Christ) could exist. In The Divine Institutes (written between 303 and 311CE), the theologian Lactantius ridiculed the notion that there could be inhabitants in the antipodes ‘whose footsteps are higher than their heads’. Other authors scoffed at the idea of a place where the rain must fall up. In 748, Pope Zachary declared the idea that people could exist in the antipodes, on the ‘other side’ of the Christian world, heretical..

As has been pointed out by numerous people writing about the flat earth myth, Lactantius had almost no supporters of his theories.

This medieval argument was still rumbling on when Columbus first sailed southwest from Spain to the ‘Indies’ in 1492. Columbus, who had seen sub-Saharans in Portuguese ports in west Africa, disagreed with the Church: he claimed that the Torrid Zone was ‘not uninhabitable’.

Our author appears to be prejudiced against the Portuguese. Throughout the fifteenth century in a series of expeditions, started by Henry the Navigator (1394 – 1460), a succession of Portuguese explorers had been venturing further and further down the West African coast reaching the Gulf of Guinea, which lies on the equator, in 1460. These expeditions reached a climax in 1488, four years before Columbus set sail to the Indies, when Bartolomeu Dias rounded the tip of South Africa proving that one could reach the Indian Ocean by sea and pathing the way for Vasco de Gama’s 1497 voyage to India.

Although he never actually crossed the Equator, he did go beyond the borders of European maps when he inadvertently sailed to the Americas. To navigate, Columbus used, among others, the Imago Mundi (1410), a work of cosmography written by the 15th-century French theologian Pierre d’Ailly, which included one of the few T-and-O maps with north situated at the top.

The importance of Pierre d’Ailley’s Imago Mundi for Columbus lay not in the orientation of its T and O map but in the fact that d’Ailley severely underestimated the circumference of the globe thus making Columbus’ attempt to sail westward to the Indies seem more plausible than it in reality was.

Columbus’s eventual ‘discovery’ of America stretched the horizons of the European mind. The Equator was gradually reimagined: no longer the extreme limit of humanity, a geographical hell on Earth, it became simply the middle of the Earth.

In particular, Cobo has problems with the direction that mapmaking has taken. In 150AD, Ptolemy drew the first world map with north placed firmly at the top.

Earlier Greek geographers such as Eratosthenes, who also drew world maps, almost certainly also drew their maps with north at the top. Ptolemaeus is not the beginning but the culmination of Greek cartography.

This orientation has become the standard one for maps everywhere. The preeminence of north derives from the use of Polaris, also known as the North Star, as the guiding light for sailors.

This is a piece of pure fantasy on the part of out author. To quote Jerry Brotton from his excellent A History of the World in Twelve Maps, “Why north ultimately triumphed as the prime direction in the Western geographical tradition, especially considering its initial negative connotations for Christianity […], has never been fully explained. Later Greek maps and early medieval sailing charts, or portolans, were drawn using magnetic compasses, which probably established the navigational superiority of the north-south axis over an east-west one; but even so there is little reason why south could not have been adopted as the simplest point of cardinal orientation instead, and indeed Muslim mapmakers continued to draw maps with south at the top long after the adoption of the compass.”[2] I would add to this the fact that many European Renaissance maps also had south at the top.

Yet Polaris, or any other star for that matter, is not a fixed point. Because of the Sun and Moon’s gravitational attraction, the Earth actually moves like a wobbling top. This wobble, known to astronomers as the precession of the Equator, represents a cyclical shift in the Earth’s axis of rotation. It makes the stars seem to migrate across the sky at the rate of about one degree every 72 years. This gradual shift means that Polaris will eventually cease to be viewed as the North Star, and sailors will have to orient themselves by other means.

In 1569, the Flemish cartographer Gerardus Mercator, the first to mass-produce Earth and star globes,

Geradus Mercator (1512 – 1594) was not the first to mass-produce Earth and star globes Johannes Schöner  (1477 – 1547) was.

devised a system for projecting the round Earth onto a flat sheet of paper.

Our author, probably unintentionally or at least I hope so, creates the impression that Mercator was the first to devise a map projection from the sphere onto a flat sheet of paper; he, of course, wasn’t. This achievement is usually credited to Eratosthenes in the third century BCE. Ptolemaeus’ Geographia (about 150 CE) outlines three different map projections.

His ‘new and augmented description of Earth corrected for the use of sailors’ made the Earth the same width at the Equator and the poles, thus distorting the size of the continents. Although Mercator created his projection (still used today in almost all world maps) for navigation purposes, his scheme led to a bloated sense of self for the northern countries, located at the top of the map, while diminishing the southern hemisphere’s sense of size and importance.

Our author is rather vague about how or why this distortion occurs. Because the distance between the parallels of longitude in the Mercator projection increases the further one moves from the equator, landmasses become distorted in area (larger than they are in reality) the further they are away from the equator. Because the major landmasses in the northern hemisphere are further removed from the equator than those in the southern hemisphere they take on an illusionary physical dominance.

Might I, not so politely, suggest to Mr Hollander that if he wishes to write about the history of cartography in the future that he indulges in some proper research of the subject before he puts finger to keyboard.

[1] I’m not sure whether I should thank or curse Richard Carter FCD (@friendsofdarwin) for drawing my attention to this essay. Whichever, he is to blame for the existence of this post.

[2] Jerry Brotton, A History of the World in Twelve Maps, Allen Lane, London, 2012, p. 11


Filed under History of Cartography, History of Navigation, History of science, Myths of Science, Renaissance Science

Isaac Newton: The Last Lone Genius?

The Friday before last, with much advanced publicity, the BBC broadcast a new documentary film biography of Isaac Newton with the title The Last Magician. This phrase is part of a famous quote by John Maynard Keynes, “not the first scientist but the last magician”, describing his feeling upon reading the Newtonian alchemical manuscripts that he acquired at the auction of the Portsmouth family Newton papers in 1936.  This of course together with the advanced advertising for the programme signalled that we were due for a fresh dose of “did you know that Newton was a secret alchemist?” A phenomenon that Rebekah “Becky” Higgitt has blogged on informatively in the past.

Based on quotes from Newton’s own writings and correspondence as well of those of his contemporaries the programme was in its basics factually correct. As usual for BBC historical documentaries it was well-produced and excellently filmed and thus pleasant to watch. The basic structure was the direct quotes being spoken by actors in costume and commented upon by five more or less experts. These were the historians of science Rob Iliffe head of the Newton Papers editing project and a genuine Newton expert, Patricia Fara author of an excellent book on the changing image of Newton down the centuries and Lisa Jardine expert on Renaissance history of science, as well as popular science writer James Gleick author of a competent popular Newton biography and astrophysicist turned novelist Stuart Clark.

Given all of these preconditions it should have been an excellent hours entertainment for a historian of science like myself, unfortunately it turned out to be a major disappointment for two reasons. The programme deliberately created two principle impressions that were and are fundamentally wrong.

The first of these turned up in the pre-programme publicity but also featured prominently fairly early in the documentary in what seems at first glance to be a fairly harmless statement:

By the age of 21, he had rejected 2,000 years of scientific orthodoxy

This brief phrase contains two claims one implicit and one explicit. The implicit claim is how wonderful Newton was to take such a bold step when he was only 21 years old. Anyone who has spent anytime at all looking at the history of mathematics knows that mathematicians tend to be very precocious. Pascal wrote the paper that gained him entry to the top flight of seventeenth century mathematics at the age of sixteen. In the nineteenth century the teenage William Rowan Hamilton was trotted out in public like a circus pony to display his brilliance. The stories are legion and there is absolutely nothing unusual in Newton intellectual development it’s par for the course for a highly talented mathematician.

As Becky put it very succinctly in a tweet what they are actually saying here is that there had been no science since Aristotle, which is of course complete rubbish. The scientific orthodoxy of the day, which was by the way on the verge of disappearing, of which more shortly, came into being in the thirteenth century when Albertus Magnus and his pupil Thomas Aquinas created a synthesis of Catholic theology and Aristotle’s philosophy with the addition of Ptolemaic geocentric astronomy. This synthesis is known as Scholastic or Aristotelian physics or natural philosophy. However as Edward Grant, one of the leading experts on medieval science, points out Aristotelian philosophy is not Aristotle’s philosophy. It is also important to note that Aristotelian philosophy was never carved in stone but in fact changed and developed continuously over the next four hundred years. Examples of major changes are the work of the Oxford Calculatores and the Paris Physicists in the fourteenth century. The Aristotelian physics of the fifteenth century is a very different beast to that of the thirteenth century. The geocentric astronomy produced in the middle of the fifteenth century by Peuerbach and Regiomontanus differed substantially from that of the first Ptolemaic translations of the twelfth century.

Added to all this change and development the first seeds of what would become modern science began to poke their slender stems out of the substrate of scientific innovation around the beginning of the fifteenth century. By 1661 when Newton went up to university Keplerian heliocentric astronomy had become the new orthodoxy and Aristotelian physics was being pushed out by the new physics developed by mathematicians such as Tartaglia and Benedetti in the sixteenth century and Stevin, Galileo, Borelli, Descartes, Pascal, Huygens and others in the seventeenth. One should bear in mind that the Leopoldina, the Accademia del Cimento, the Royal Society and the Acadédemie des Sciences all institutions dedicated to the propagation and development of the new science were founded in 1652, 1657, 1660 and 1666 respectively. The young Newton did not like some Carrollian hero draw his Vorpal Blade to slay the Jabberwock of ancient Greek science but like any bright young academic would do jumped on the band wagon of modern science that was speeding full speed ahead into the future.

We now turn to what I see as the most serious failing of the documentary expressed in the question posed in the title of this post. For the best part of an hour the documentary banged on about Newton’s solitude, his isolation his lone path to the secrets of nature. We were presented with the ultimate lone genius of the history of science. It went so far that the only other contemporary researchers mentioned by name were Descartes in passing and Hooke purely in a negative light. The way that the programme was structured created a totally false impression of Newton’s scientific endeavours.

We actually know very little about Newton’s time as a student though it is safe to say that he was more the type to curl up in front of the fire with a good book on a Friday evening than to go to the latest rave at which ever student hostelry was in that term. As a fellow we know that he communicated and worked together with other scholars such as Isaac Barrow so to talk of total solitude as the documentary did is wrong. After he emerged from obscurity at the beginning of the 1670s with his reflecting telescope and his famous paper on the phenomenon of colours he was in no way isolated. Even if Cambridge was somewhat off the beaten track in those days Newton corresponded with other scholars in Britain and also abroad as can easily be seen in his voluminous correspondence as edited by Turnbull. He was also often visited by other mathematical scholars such as Halley or John Collins. When he left Cambridge to go to London he became positively gregarious. Maintaining a town house with his niece Catherine Barton, a renowned social beauty, as his housekeeper where he received and entertained visitors. At the Royal Mint, which he attended daily, he was surrounded by a large staff. After 1703 he presided over the weekly meetings of the Royal Society and on other evenings surrounded by his acolytes he held court in one or other of the then fashionable London coffee bars.

More important for me was the totally false impression created by the documentary of Newton’s mathematical and scientific work. Anyone being introduced to Newton for the first time would come away with the impression that he revolutionised mathematics, physics and astronomy in a superhuman solo endeavour completely isolated from the rest of the late seventeenth century intellectual world.

We got presented with Newton in 1666 creating a completely new branch of mathematics, he only actually started it then and it took a number of years to develop. At no point was any other mathematician mentioned. The fact that Newton either, directly or indirectly, knew of and built on the previous work in this field of Kepler, Cavalieri, Fermat, Pascal, Descartes, van Schooten, Barrow and others was quietly swept under the carpet. Even worse no mention what so ever of Leibniz who independently developed the same mathematics almost at the same time from the same sources. This of course led eventually to the most notorious priority dispute in the history of science involving many of the leading mathematicians of Europe.

The same thing occurred with the presentation of his work in optics, no mention of Kepler, Schiener, Descartes, Grimaldi, Gregory, Hooke, Huygens or anybody for that matter. Isaac apparently did it all alone in isolation.

This form of presentation continued with his greatest work the Principia. We got each of the famous laws of motion presented individually but no hint of the fact that the first was taken from Beeckman by way of Descartes, the second from Huygens and the third from his readings in alchemy. We were told that he derived the law of gravity from his three laws but no mention was made of the fact that the concept of the law of gravity was common, much discussed intellectual property in academic circles at the time. No mention of the contributions made to the substance of the Principia by the work of Kepler, Galileo, Cassini, Halley and above all Flamsteed. We had the strange spectacle of Hooke famous accusation of Newton having stolen his law of gravity and plagiarised him delivered in a passionate speech to the Royal Society in 1660 but no mention what so ever that Hooke’s accusation had more than a little substance. Hooke and Newton had corresponded on the subject in the early 1680s and Hooke had already formulated a concept of universal gravity before Newton. This correspondence was with certainty one of the spurs that led Newton to write the Principia although Hook’s claims as to the extent of his contribution are wildly exaggerated.

Isaac Newton did not live and work in an intellectual vacuum as was very strongly implied either deliberately or accidently through bad scripting by this documentary. He was part of a strong multi-faceted scientific community who supplied both the scaffolding and a significant part of substance of Newton’s life work in mathematics, physics and astronomy. He was in no way a lone genius but a highly significant cog in a large intellectual endeavour.

There was a time some decades back when some historians of science went so far as to decry the Principia as purely a work of synthesis with only a very small original contribution from Newton. This view was shown to be exaggerated and invalid and has been dropped but the opposite point of view implied by this documentary of the Principia as being alone the work of Newton’s genius is even more false.

Before I close there are a couple of small points from the film that I think should be mentioned. As is all too often the case we had the tired old statement that after Newton became President of the Royal Society he produced no more original scientific work. This was as always made without explicit comment but with a strong implicit negative aura. Dear people, when Isaac Newton became President of the Royal Society in 1703 he was already sixty years old. He had written and published two of the most important major scientific works in the history of mankind, his Principia and his Optics, as well as vast quantities of, largely unpublished, absolutely world-class mathematics, which he did however circulate in manuscript amongst his acolytes. What more did you expect him to do (FFS)?

I noted four major scientific/historical errors during the film, a fairly low quota; there may have been others. We of course get introduced to Newton’s reflecting telescope, the invention that first made him known to the world at large, but then we get informed that this instrument played a major role in marine navigation in the eighteenth century. Now whilst it is true that the reflecting telescope, mostly Gregorian’s and not Newtonian’s, had become the instrument of choice for astronomers by the middle of the eighteenth century they were for several good reasons not used for navigation on ships. Firstly reflecting telescopes whilst in principle smaller than refracting ones don’t telescope and so are more massive and cumbersome than the classical marine telescope. Secondly until the nineteenth century reflecting telescopes had metal mirrors made of so-called speculum metal an alloy that unfortunately was very susceptible to corrosion necessitating regular re-polishing. The salt-water atmosphere of sea voyages would have been very adverse for such mirrors requiring almost daily re-polishing and thus completely impractical.

The next error I spotted was a real howler. A voice over informed the viewer that, “for centuries light was considered the purest form of energy in the universe.” Really? Although etymologically derived from an ancient Greek word the physics concept of energy was first appeared in the nineteenth century, as did the recognition that light is a form of energy. Nuff said.

Moving along the historical time scale in the opposite direction voice over informed us the Newton’s Principia made possible the accurate prediction of comets and eclipses. Now the former is indeed true although the credit should properly go to Halley who first showed that some comets were periodical and obeyed Newton’s law of gravity. The latter is however again a real history of science howler. The Babylonians could accurately predict lunar eclipses in about the fifth century BCE and the ability to accurately predict solar eclipses was also developed in antiquity. No need to wait for Newton.

My final error is the one that as a historian of science causes me the most concern. Whilst discussing Newton’s alchemy voice over stated correctly Newton’s alchemical belief that light and matter are both products of some as yet undiscovered primal alchemical substance. The claim was immediately made that Newton had anticipated Einstein’s famous E = MC2! This claim being, to my surprise, repeated by Rob Iliffe an excellent historian of science. Now I’m not a big fan of the Kuhn/Feyerabend principle of the incommensurability of scientific theories. This says that one can’t compare scientific theories because the definitions of the concepts that they contain differ and are thus not comparable. Newton’s concept of force is not Maxwell’s concept of force for example. However I think that here we have a genuine case of incommensurability. The metaphysical concepts behind Newton’s alchemical theory and the metaphysical concepts behind Einstein’ theory of relativity are in no way comparable. It is not even comparing apples with oranges; it’s comparing apples with bicycles!

On the whole I think what was superficially a very good and certainly an excellently produced documentary failed miserably as a piece of history of science for the reasons that I have outlined above. Maybe I’m being too harsh but on the whole I don’t think so. For me the very strong emphasis of the biography of Newton as some sort of lone genius whether intended or an accidental product of ill considered scripting made this documentary next to worthless as a contribution to popular history of science.




Filed under History of Astronomy, History of Mathematics, History of Navigation, History of Optics, History of Physics, History of science, Myths of Science, Newton

The Virgin Queen was in reality John Dee in drag.

The rumbling you can hear in the background is the HISTSCI HULK playing skittles with some skyscrapers. He’s all riled up and wants to place a big green foot in Carole Jahme’s butt and propel her into publishing purgatory. What has Ms Jahme done to provoke the wrath of the big green HISTSCI destroyer? Damon Albarn’s so-called Opera Dr Dee is being revived in London and Ms Jahme wrote an introductory preview posted last Monday on the Guardian’s website. This preview is unfortunately a mixture of exaggerations, half-truths and fantasies that is a blot on the Guardian’s reputation for good journalism. Now it could be argued in her defence that several of the false claims made in her article are also made in the video interview with the director of the piece Rufus Norris and the Public Astronomer at the Royal Observatory Marek Kukula at the head of the article and that they are also to blame for this piece of shoddy journalism. However there is a thing in writing in general and in journalism in particular that seems to be going out of fashion called fact checking, something that Ms Jahme apparently can’t be bothered to waste her time on. I did consider letting the big green monster loose on her but didn’t fancy the job of cleaning up the carnage so I’ve decided to expose some of Ms Jahme’s worst history of science sins myself.

Before I deal with any detail from the article I would like to address the premise given by Norris for the opera itself. He, and Albarn in previous interviews, create the impression that Dee is somehow a neglected figure, particularly as a mathematicus (which is what he was), I beg to differ. There are at least eight monographs that deal with large parts or the whole of Dee’s biography as well as several monographs that deal with wider contexts of Elizabethan culture that have Dee as a central figure. A couple of these works deal explicitly with Dee as a Renaissance scientific figure. There is also a volume of academic papers on Dee as well as academic annotated editions of his principle works. Already in the 1930s, as modern history of science was beginning to emerge, historians of astronomy, geography and navigation devoted quite a considerable amount of attention to Dee. There are articles on Dee in the Encyclopaedia Britannica, the Dictionary of Scientific Biography, the New Oxford dictionary of Biography and in the Internet at MacTutor and on Wikipedia, some of them quite substantial. I do not think Dee has been neglected, in fact I can’t think of another scientific figure of his stature who has been covered in anything approaching the expansive extant to which Dee has been. This brings us to the next problem, what is Dee’s scientific stature. Just as it is easy to underestimate Dee’s importance and influence in the development of the mathematical sciences in late sixteenth century England it is also possible to overestimate them and in my opinion both in the video and the article this is done. Dee played a role as a teacher and facilitator along with Robert Recorde, Leonard Digges, Thomas Digges, Thomas Harriot, Edward Wright and others in introducing the mathematical sciences into Britain but he made no original contributions to the mathematical sciences himself. He is not a Kepler, Galileo, Descartes or Huygens and he is certainly not one of the giants on whom shoulders Newton stood as claimed by Norris in the interview. Dee is an important figure but he is no more important than at least a dozen of his contemporaries who have received not even ten per cent of the scholarly attention that Dee has.

John Dee

Now to Ms Jahme who tells us that:

Dee was a larger-than-life magus figure. He was probably the inspiration for Christopher Marlowe’s character Doctor Faustus, Ben Jonson’s The Alchemist and Shakespeare’s Prospero.

We’ve been here before as the opera was premiered in Manchester but it is worth re-examining these claims. Marlow’s Faustus is of course based on the real life German magus Dr Johann Georg Faust whose fictionalised life story was a sixteenth century best seller. Ben Johnson’s The Alchemist is a satire on alchemy and alchemists in general, of which Dee was only one of many, and whilst Dee is not name-checked in the piece his medium Edward Kelly is. The claim that Dee is Prospero is old and there is no evidence to support it. Frances Yates one of the real experts for sixteenth century alchemy and magic thinks that Prospero is Giordano Bruno but addresses the claim for Dee pointing out that Dee and Bruno share many key characteristics. I think Prospero is probably a composite figure with elements of Bruno, Dee, Faust, Kelly, Robert Fludd, Cornelius Agrippa, Oswald Croll and a dozen other less well-known contemporary hermetic figures. Instantly identifying Prospero with Dee is in my opinion an act of hagiography and a failure to recognise just how widespread hermeticism was at the end of the sixteenth and beginning of the seventeenth centuries.

Ms Jahme informs us that:

Dee taught Raleigh and Drake “the perfect art of navigation” for calculating longitude from lunar distance observation, which helped facilitate the establishment of the British Empire.

Dee was certainly one of the mathematical practitioners teaching navigation and cartography to English sea captains in the sixteenth century along with Thomas Digges, Harriot, Wright and others but he did not teach Drake or Raleigh. I don’t actually know who, if anyone, taught Drake but if it had been Dee I’m sure I would have read about it in my studies and I haven’t. Raleigh and his ship’s captains were of course instructed not by Dee but by his friend Thomas Harriot who even accompanied the ill fated expedition to establish a colony on Roanoke Island in Virginia, as a sort of scientific officer. Dee instructed Martin Frobisher and other captains of the Muscovy Company in their attempts to discovery either a North-West or a North-East passage to China.

There is more to come Ms Jahme continues with the following:

Infamous in his lifetime, Dee was a risk-taker and exceptional scholar. With his eye on the court he rejected the comfort of university tenure at Cambridge, preferring to collate and categorise his data independently. A serious bibliophile, his private library became the largest in Britain. Dee charted the movement of the planets and in his early career toured Europe giving talks on astronomy – a form of science outreach that was entirely new.

We have here four claims of which two are true, one shows a complete lack of understanding of sixteenth century intellectual culture and one is complete rubbish. The first sentence and the statement about Dee’s love of books are both correct. The statement about university tenure is quite frankly bizarre. It seems to assume that Mediaeval Cambridge was like a modern university. Dee had a fellowship at Trinity but after graduating MA he left the university, as he apparently did not wish to study for a doctorate. Accepting a life as fellow and under-reader in Greek would have been tantamount to giving up before he started, not the comfort of university tenure but a dead end in badly paid futility. However it is the final sentence that this time takes the prize for wrongness. Jahme has exaggerated and misinterpreted a moderately false statement of Norris’ and made a real mess out of it.

In the period of his life that he dedicated to the study of the mathematical sciences Dee made three trips to the European continent; these were not lecture but study tours. Such tours were common practice in the High Middle Ages and the Renaissance with young scholars travelling from university to university to study manuscripts not available in their home university libraries and to meet, study under and discuss or dispute with other scholars. Norris says that this was unique for an English mathematical practitioner at this time and although rare it was not unique. Henry Savile, who would later use his fortune to found the chairs for geometry and astronomy in Oxford, is a contemporary of Dee’s who also undertook such a study tour of the continent. Norris also claims that this was a lecture tour and it is this that Jahme falsely makes unique. On his first trip of only a few months in 1547 Dee studied in Louvain under Gemma Frisius and Gerald Mercator. He returned to Louvain for further studies in 1548 and staid until 1550. Here I would like to correct another of Norris’ false statements. He claims in the video interview that Dee’s range of subjects mathematics, astronomy, astrology, geography, cartography, navigation and history was unusually wide and unique. This is simply not true. This is the normal range of study of the Renaissance mathematicus and is exactly what Dee would have studied with Frisius and Mercator in Louvain. When he left Louvain Dee went to Paris were he did indeed lecture, not on astronomy, but Euclidian geometry. Again this is not out of the ordinary, the visiting scholar demonstrating his own learning to his hosts, nothing new or unusual here. His third trip abroad in 1562 to 1564 was to visit other scholars such as Gesner in Switzerland or the Italian mathematician Commandino with whom he published the translation of a Greek mathematical text.

He was opposed to a tiered system of education where those without classical scholarship were held back, so when his translation of Euclid’s mathematics was complete he made the arcane information accessible to non-university-taught artisans and craftsmen. In his General and Rare Memorials Pertaining to the Perfect Arte of Navigation, he advocated the usefulness of mathematics as a “Publick Commodity”.

In the above quote Jahme has got something right for a change. Dee, following Robert Recorde, is one of the founders of the so-called English School of Mathematics; a group of mathematical practitioners who made their knowledge available in the vernacular. However Dee, unlike Digges for example, also wrote extensively in Latin for an educated public. The paragraph does however contain one serious error. Although Dee wrote his very famous preface for the first English translation of Euclid’s Elements, the translation itself was not by Dee but by Henry Billingsley.

We now come to what I regard as the weirdest claim made by Jahme:

His students include Francis Bacon, promoter of the “scientific method”, and the astronomer Thomas Diggs, who believed the universe to be infinite.

Thomas Digges was not only Dee’s student but also his foster son and he was indeed the first modern astronomer to propose an infinite universe. Although Dee was instrumental in spreading knowledge of Copernican heliocentricity in England he does not appear to have been a totally convinced Copernican. Digges, however, was a totally convinced Copernican who also published the first ever partial translation into the vernacular of De revolutionibus. Now I wouldn’t claim to be an expert on either Dee or Bacon but I have read an awful lot about and by both of them and I have never ever come across the claim that Bacon was a student of Dee’s. If we look at this rationally it also seems highly unlikely. Dee was absolutely convinced that mathematics was the most important discipline of all and was the number one propagator of the works of Copernicus in Britain. Bacon rejected both mathematics and heliocentricity so it does no appear very likely that he was Dee’s student. I will happily admit that I haven’t really researched this properly but a quick search revealed that Dee mentions Bacon just once in his diary. The then 21 year old accompanied somebody else who was visiting Dee in Mortlake in 1583. Bacon never mentions Dee at all in his voluminous writings! I did stumble across one website that actually claimed the fact of Dee’s absence from Bacon’s writings as proof that Bacon was Dee’s disciple! On that basis I could prove literally anything!

It is to the enigmatic Dr John Dee that we must look for the origins of Britain’s contribution to modern Western science, yet Dee has been largely left out of the history books – why?

Both of the claims made in the quote above are simply false and two wrongs definitively do not make a right. This post is already over long but there are two short claims made by Ms Jahme that I wish to include before I close my demolition of her pitifully bad piece of history of science journalism. She writes:

In 1600, astronomer Giordano Bruno was burnt at the stake for daring to say the sun was a star.

And a few lines further on:

Within Dee’s lifetime Copernicus’s sun-centric theories would be strengthened by Galileo’s discoveries.

Giordano Bruno was not an astronomer and he was burnt for his religious opinions and not for his cosmological ones. The reports are not totally in agreement but Dee died in either 1608 or 1609. Galileo first published his telescopic discoveries in 1610 so not in Dee’s lifetime.

It would appear that one qualifies as a history of science writer these days when one is good at making things up so I’ve decided to stop being a pedant and to go with the flow. My next work will be the sensational discovery that Elizabeth the Virgin Queen was in reality Renaissance magus John Dee in drag! Remember you read it here first.


Filed under History of Astrology, History of Astronomy, History of Mathematics, History of Navigation, Myths of Science, Renaissance Science