Category Archives: History of Navigation

Getting names right is rather important in the history of science

“Have you seen my new Rolls Royce?”

“But that’s not a Rolls Royce; it’s a Fiat Bambino!”

“It’s got four wheels, an internal combustion engine and it gets you from a to b so it’s a Rolls Royce, isn’t it?”

“Well, no it isn’t.”

The little dialogue above would probably seem pretty ridiculous to any of my readers but today BBC News achieved something similar concerning scientific instruments. On the BBC website they posted a story with the following title, Astrolabe: Shipwreck find ‘earliest navigation tool’

The story is about the find of a scientific instrument found by marine archaeologists in 2014, in the wreck of a Portuguese ship that sank in 1503. Not just in the title, but also throughout the article the discovered instrument is simply referred to as an astrolabe. The article went on to say that astrolabes are relatively rare, and this is the only the 108th to be confirmed catalogued. It is also the earliest known example by several decades.

As it stood this was patent rubbish. There are more than 900 hundred known astrolabes between the earliest known dated instrument from 927 CE and 1900 CE. However the problem is not in the historical accuracy but in the name. The instrument that had been discovered is not an astrolabe but a mariner’s astrolabe a more than somewhat different instrument.

Astrolabe Renners Arsenius 1569
Source: Wikimedia Commons

Mariner’s Astrolabe Francisco de Goes 1608 Source: Istituto e Museo di Storia della Scienza, Firenze

As I explained to someone on Twitter, as I had just corrected the tweet linking to the article for about the zillionth time, a mariner’s astrolabe is a very simplified form of the astrolabe specifically made for use on ships with just one function, the measuring of the altitude of a star or the sun in order to determine latitude. The astrolabe, however, is a very complex instrument with hundreds of different function in astronomy, chronology and surveying.

Following my protests, and those of others, the article has been changed very slightly for the majority of the article it still refers to the instrument as an astrolabe but about three quarters of the way through, the sentence that I have quoted above now starts “Mariners’ astrolabes” instead of simply astrolabes. So everything is now OK? Well, actually no.

All of the references to astrolabe should have been changed to mariner’s astrolabe and above all the click bait title should have been changed, as it also has a second major problem. It states, shipwreck find ‘earliest navigation tool’. This is complete rubbish. Mariner’s astrolabes are quite late developments in the history of navigation and there are many navigation tools that predate it, such as the quadrant, the sea chart, the compass etc. etc. This blatant hyperbolic error is corrected in the subtitle, which reads: An artefact excavated from a shipwreck off the coast of Oman has been found to be the oldest know example of a type of navigation tool [my emphasis]. But of course by now the damage has been done for the casual reader who just glances at the title.

This article is a mess and a lousy piece of history of science communication for which there is absolutely no excuse whatsoever.

Advertisements

4 Comments

Filed under History of Navigation

The House of Blaeu vs.The House of Hondius – The Battle of the Globes and Atlases

There is a South to North trajectory in the evolution of the modern mathematical cartography in Europe over the two hundred years between fourteen hundred and sixteen hundred. Ptolemaic mathematical cartography re-entered Europe in Northern Italy with the first translation into Latin of his Geographia by Jacobus Angulus in 1406. Following this the first modern first modern cartographers, including Paolo dal Pozzo Toscanelli, were also situated in Northern Italy. By the middle of the fifteenth century the main centre of cartographical activity had moved north to Vienna and was centred around Kloster-Neuburg and the University with its First Viennese School of Mathematics, Georg von Peuerbach and Johannes Regiomontanus. Towards the end of the century printed editions of Ptolemaeus’ work began to appear both north and south of the Alps. The beginning of the sixteenth century saw the main centres of cartographic development in the Southern German sphere. Two principle schools are identifiable, the Nürnberg-Vienna school, whose main figures are Johannes Stabius, Peter Apian and Johannes Schöner, and the South-Western school with Waldseemüller and Ringmann in Saint-Dié-des-Vosges and Sebastian Münster in Basel. Again by the middle of the century the centre had once again moved northwards to Leuven and the Flemish school founded by Gemma Frisius and including the two great atlas makers Abraham Ortelius and Gerard Mercator. At the start of the seventeenth century the final step northwards had been taken and the new state of The United Provinces (The Netherlands) had taken the lead in modern cartography. This final step is the subject of this post.

Willem Janszoon Blaeu was born into a prosperous herring trading family in Alkmaar or Uitgeest in 1471. As would have been expected he was sent at an early age to Amsterdam to learn the family trade but it did not appeal to him and he worked instead as a carpenter and clerk in the office of his cousin. In late 1595 his life took a radical turn when he travelled to Hven to study astronomy under Tycho Brahe. It is not known what level of foreknowledge Blaeu took to Hven with him but he spent six months there studiously learning astronomy, instrument making, geodesy and cartography with Tycho and his staff. When he started his observing marathon Tycho had had a large brass globe constructed on which he, over the years, engraved the positions of all the stars that he had measured. Blaeu was given permission to transfer this data to a globe of his own. In 1596 he returned to Alkmaar and his wife Maertgen Cornilisdochter who bore his eldest son Joan on 21 September. On 21 February 1598 Blaeu in Alkmaar and Tycho in Hamburg both observed a lunar eclipse to determine the relative longitude of the two cities.

Portrait of Willem Janszoon Blaeu Artist unknown

Sometime in 1598/9 Blaeu took his family to Amsterdam and set up shop as a printer, instrument maker, globe maker and cartographer; making his first celestial globe, 34 cm diameter, for Adriaan Anthoniszoon, using Tycho’s data; this was the first publication of that data. However Blaeu’s new career was not going to be simple as he had an established competitor, Jocodus Hondius.

Jocodus Hondius was born Joost de Hondt in Wakken and grew up in Ghent, both now in Belgium, on 14 October 1563. He received an education in mathematics and learnt engraving, drawing and calligraphy. He had already established himself as a successful engraver when he was forced by the Spanish, as a Calvinist, to flee to London in 1584. In London he worked for and with Richard Hakluyt and Edward Wright and expanded his knowledge of geography and cartography through contact with the English explorers Francis Drake, Thomas Cavendish and Walter Raleigh. Around 1589 he published a wall map in London showing Drake’s voyage around the world. In 1593 he moved back to The Netherlands, establishing himself in Amsterdam.

Self-portrait of Jodocus Hondas taken from one of his maps

Portrait of Francis Drake by Jodocus Hondas from his Drake world map

He formed an alliance with the Plantin printing house in Leiden for who he made several globes. In 1602 he matriculated at the University of Leiden to study mathematics. In 1604 he made the most important decision of his career in that he bought the copper printing plates of the of both Mercator’s edition of Ptolemaeus’ Geographia and Mercator’s Atlas from his heirs.He published a new edition of Mercator’s Ptolemaeus, Claudïï Ptolemaeï Alexandrini geographicae libri octo graecog latini, in the same year. He set up his own publishing house in Amsterdam in December 1604. In the sixteenth century Mercator’s Atlas had failed to establish itself in a market dominated by Ortelius’ Theatum Orbis Terrarum, however Hondius republished it in 1606 with 36 new maps and it became a best seller.

Atlas sive Cosmographiae Meditationes de Fabrica Mundi et Frabicati Figura
Mercator (left) and Hondius (right) shown working together on tittle page of 1630 Atlas
Slightly ironical as they never met and both were dead by then.

Meanwhile Blaeu had established himself as a globe maker and astronomer. Following the tradition established by Johannes Schöner and continued by Mercator Blaeu issued a pair of 23.5 cm globes, terrestrial and celestial, in 1602. His rival Hondius introduced the southern constellation on a celestial globe produced in cooperation with the astronomer-cartographer Petrus Plancius in 1598. Blaeu followed suite in 1603. Hondius produced a pair of 53.5 cm globes in 1613; Blaeu countered with a pair of 68 cm globes in 1616, which remained the largest globes in production for over 70 years.

Hondas celestial globe 1600
Source: Linda Hall Library

A matching pair of Blaeu globes

As an astronomer Blaeu discovered the star P Cygni, only the third variable star to be discovered. In 1617 Willebrord Snellius published his Eratosthenes Batavus (The Dutch Eratosthenes) in which he described his measurement of a meridian arc between Alkmaar and Bergen op Zoom. This was done in consultation with Blaeu, who had learnt the art of triangulation from Tycho, using a quadrant, with a radius of more than 2 metres, constructed by Blaeu. Blaeu specialised in publishing books on navigation beginning in 1605 with his Nieuw graetbouck and established himself as the leading Dutch publisher of such literature.

Source: Wikimedia Commons

Title page
Source: Wikimedia Commons

Quadrant constructed by Blaeu for Snellius now in Museum Boerhaave in Leiden
Source: Wikimedia Commons

Jodocus Hondius died in 1612 and his sons Jodocus II and Henricus took over the publish house later going into partnership with Jan Janszoon their brother in law. They continued to publish new improved version of the Mercator-Hondius Atlas. Blaeu had already established himself as the successful publisher of wall maps when he began planning a major atlas to rival that of the house of Hondius. That rivalry is also reflected in a name change that Blaeu undertook in 1617. Up till then he had signed his work either Guilielmus Janssonius or Willem Janszoon, now he started add the name Blaeu to his signature probably to avoid confusion with Jan Janszoon (Janssonius), his rival.

Jan Janszoon Original copperplate from his Atlas Novus 1647

In 1630 the strangest episode in the battle of the globes and atlases took place when Jodocus II’s widow sold 37 of the copper plates of the Mercator-Hondius Atlas to Willem Blaeu. He published them together with maps of his own in his Atlantic Appendix in 1631. In 1636 Blaeu published the first two volumes of his own planned world atlas as Atlas Novus or Theatrum Orbis Terrarum, thus reviving the old Ortelius name.

In 1633 the States General (the government of the United Provinces) appointed Blaeu mapmaker of the Republic. In the same year he was appointed cartographer and hydrographer of the Vereenighde Oostindische Compagnie (VOC) – The Dutch East India Company. His son Joan inherited the VOC position, as did his grandson Joan II; The Blaeu family held this prestigious position from 1633 till 1712.

Willem Blaeu had great plans to publish several more volumes of his world atlas but he didn’t live to see them realised, dying 21 October 1638. The publishing house passed to his two sons Joan (1596-1673) and Cornelis (c.1610-1644). The last two volumes prepared by Willem appeared in 1640 and 1645. Joan completed his father’s atlas with a sixth volume in 1655.

Along with all his other achievements Willem Janszoon Blaeu made a substantial improvement to the mechanical printing press by adding a counter weight to the pressure bar in order to make the platen rise automatically. This ‘Blaeu’ or ‘Dutch’ press became standard throughout the low countries and was also introduced into England. The first printing press introduced into America in 1639 was a Blaeu press.

Although he held a doctorate in law, Joan devoted his life to the family cartographic publishing business. In 1662 he set the high point of the atlas battle with the House of Hondius with the publication of the Atlas Maior; containing 600 double page maps and 3,000 pages of text it was the most spectacular atlas of all time. Along with its lavish maps the Atlas Maior contained a map of Hven and pictures of the house and stellar observatory on the island where Willem Janszoon Blaeu first learnt his trade. Whereas Willem was careful not to take sides in the dispute between the different systems for the cosmos – geocentric, heliocentric, geo-heliocentric – in the Atlas Maior, Joan committed to heliocentricity.

Joan Blaeu. By J.van Rossum
Source: Wikimedia Commons

Blaeu Atlas Maior 1662-5, Volume 1
Nova Et Accvratissima Totius Terrarvm Orbis Tabvla
Source: National Library of Scotland

The rivalry between the Houses of Hondius and Blaeu, pushing each other to new heights of quality and accuracy in their maps and globes led to them totally dominating the European market in the first half of the sixteenth century, particularly in the production of globes where they almost had a monopoly. Globes in the period, which weren’t from one of the Amsterdam producers, were almost always pirated copies of their products.

As an interesting footnote, as with all things mathematical England lagged behind the continent in cartography and globe making. Although there had been earlier single globes made in on the island, England’s first commercial producer of terrestrial and celestial globes, Joseph Moxon, learnt his trade from Willem Janszoon Blaeu in Amsterdam. In 1634 Blaeu had published a manual on how to use globes, Tweevoudigh onderwijs van de Hemelsche en Aerdsche globen (Twofold instruction in the use of the celestial and terrestrial globes). In the 1660s, Moxon published his highly successful A Tutor to Astronomie and Geographie. Or an Easie and speedy way to know the Use of both the Globes, Cœlestial and Terrestrial : in six Books, which went through many editions, however the first edition was just an English translation of Blaeu’s earlier manual.

The Dutch painter Jan Vermeer often featured globes and maps in his paintings and it has been shown that these are all reproductions of products from the Blaeu publishing house.

Vermeer’s Art of Painting or The Allegory of Painting (c. 1666–68)
With Blaeu Wall Map
Google Art Project Source: Wikimedia Commons

Jan Vermeer The Astronomer with Blaeu celestial globe and right on the wall a Blaeu wall map
Source: Wikimedia Commons

Jan Vermeer The Geographer with Blaeu terrestrial globe and again right a Blaeu wall map
Source: Wikimedia Commons

The Blaeu wall map used in Vermeers’ The Astronomer and The Geographer

We tend to emphasise politicians, artists and big name scientists, as the people who shape culture in any given age but the cartographic publishing houses of Hondius and Blaeu made significant contributions to shaping the culture of The United Provinces in the so-called Dutch Golden Age and deserve to be much better known than they are.

 

 

 

 

2 Comments

Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Navigation, History of science, Renaissance Science

All at sea

As I’ve said more than once in the past, mathematics as a discipline as we know it today didn’t exist in the Early Modern Period. Mathematics, astronomy, astrology, geography, cartography, navigation, hydrography, surveying, instrument design and construction, and horology were all facets or sub-disciplines of a sort of mega-discipline that was the stomping ground of the working mathematicus, whether inside or outside the university. The making of sea charts – or to give it its technical name, hydrography – combines mathematics, geography, cartography, astronomy, surveying, and the use of instruments so I am always happy to add a new volume on the history of sea charts to my collection of books on cartography and hydrography.

I recently acquired the “revised and updated” reissue of Peter Whitfield’s Charting the Oceans, a British Library publication.

The original edition from 1996 carried the subtitle Ten Centuries of Maritime Maps (missing from the new edition) and this is what Whitfield delivers in his superb tome. The book has four sections: Navigation before Charts, The Sea-Chart and the Age of Exploration, Sea-Charts in Europe’s Maritime Age and War, Empire and Technology: The Last 200 years. As can be seen from these section titles Whitfield not only deals with the details of the hydrography and the charts produced but defines the driving forces behind the cartographic developments: explorations, trade, war and colonisation. This makes the book to a valuable all round introduction of the subject highly recommended to anybody looking for a general overview of the topic.

However, what really makes this book very special is the illustrations.

The Nile Delta, c. 1540, from Piri Re’is Kitab-i Bahriye
Charting the Oceans page 90

A large format volume, more than fifty per cent of the pages are adorned with amazing reproductions of the historical charts that Whitfield describes in his text.

Willem van de Velde II, Dutch Ships in a Calm, c. 1665
Charting the Oceans page 132

Beautifully photographed and expertly printed the illustrations make this a book to treasure. Although not an academic text, in the strict sense, there is a short bibliography for those, whose appetites wetted, wish to delve deeper into the subject and an excellent index. Given the quality of the presentation the official British Library shop price of £14.99 is ridiculously low and a real bargain. If you love maps all I can say is buy this book.

Title page to the English edition of Lucas Janszoon Waghenaer’s Spiegheel der Zeevaert, 1588
Charting the Oceans page 109

The A Very Short Introduction series of books published by the Oxford University Press is a really excellent undertaking. Very small format 11×17 and a bit cm, they are somewhere between 100 and 150 pages long and provide a concise introduction to a single topic. One thing that distinguishes them is the quality of the authors that OUP commissions to write them; they really are experts in their field. The Galileo volume, for example, is authored by Stillman Drake, one of the great Galileo experts, and The Periodic Table: A Very Short Introduction was written by Mr Periodic Table himself, Eric Scerri. So when Navigation: A Very Short Introduction appeared recently I couldn’t resist. Especially, as it is authored by Jim Bennett a man who probably knows more about the topic then almost anybody else on the surface of the planet.

Mr Bennett does not disappoint, in a scant 135-small-format-pages he delivers a very comprehensive introduction to the history of navigation. He carefully explains all of the principal developments down the centuries and does not shy away from explaining the intricate mathematical and astronomical details of various forms of navigation.

Navigation: A Very Short Introduction page 50

The book contains a very useful seven page Glossary of Terms, a short but very useful annotated bibliography, which includes the first edition of Whitfield’s excellent tome, and a comprehensive index. One aspect of the annotated bibliography that particularly appealed to me was his comments on Dava Sobel’s Longitude; he writes:

“[It] …has the disadvantage of being very one-sided despite the more scrupulous work found in in earlier books such as Rupert T. Gould, The Marine Chronometer: Its History and Development (London, Holland Press, 1960); and Humphrey Quill, John Harrison: The Man Who Found Longitude (London, John Baker, 1966)”

I have read both of these books earlier and can warmly recommend them. He then recommends Derek Howse, Greenwich Time and the Discovery of Longitude (Oxford, Oxford University Press, 1980), which sits on my bookshelf, and Derek Howse, Nevil Maskelyne: The Seaman’s Astronomer, (Cambridge, Cambridge University Press, 1989), which I haven’t read. However it was his closing comment that I found most interesting:

“A welcome recent corrective is Richard Dunn and Rebekah Higgitt, Ships, Clocks, and Stars: The Quest for Longitude (Collins: Glasgow, 2014)”. A judgement with which, regular readers of this blog will already know, I heartily concur.

The flyleaf of the Navigation volume contains the following quote:

‘a thoroughly good idea. Snappy, small-format…stylish design…perfect to pop into your pocket for spare moments’ – Lisa Jardine, The Times

Another judgement with which I heartily concur. Although square centimetre for square centimetre considerably more expensive than Whitfield’s book the Bennett navigation volume is still cheap enough (official OUP price £7.99) not to break the household budget. For those wishing to learn more about the history of navigation and the closely related mapping of the seas I can only recommend that they acquire both of these excellent publications.

 

 

4 Comments

Filed under History of Cartography, History of Mathematics, History of Navigation

The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

The title of this post is the subtitle of Dava Sobel’s Longitude, her mega bestselling account of the life and work of the eighteenth-century clock maker John Harrison; probably the biggest selling popular #histSTM book of all time.

I’m quite happy to admit that when I first read it I was very impressed by her account of a man I didn’t know from a period of history with which I was not particularly well acquainted. However, because I was very impressed, I went looking for more information about the history of John Harrison and the marine chronometer. I found and read quite a lot of academic literature on both topics and came to the realisation that Sobel’s account was not really the true story and that she had twisted the facts to make for a more exciting story but quite far removed from the true narrative.

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, London
Source: Wikimedia Commons

The next segment of the subtitle is also not true. Harrison was supported and encouraged in his endeavours by George Graham, possibly the greatest eighteenth-century English clockmaker, and James Short, almost certainly the greatest telescope maker in the world in the eighteenth century. Both men were important and highly influential figures in the scientific and technological communities of the period. Their support of Harrison rather gives the lie to the claim that Harrison was a lone genius.

George Graham
Source: Wikimedia Commons

The final segment of the subtitle is also highly inaccurate. The problem that Harrison and others were working on in the eighteenth century was a reliable method of determining longitude at sea. They were trying to solve a technological problem not a scientific one. The scientific problem had already been solved in antiquity. Scholars in ancient Greece already knew that to determine the difference in longitude between two locations, one ‘merely’ had to determine the local time difference between them; knowing this the problem was how to determine that time difference, as I said a technological problem.

In antiquity and up to the early modern period cartographers and astronomers (usually the same person) used astronomical phenomena such as solar or lunar eclipses. Observers determined the local time of the occurrence of a given astronomical phenomenon at two different locations and it was then possible to determine their longitudinal difference. Unfortunately eclipses are not very frequent occurrences and so this method has rather limited usefulness. Something else had to be developed.

In the early seventeenth century both Galileo Galilei and Simon Marius discovered the four largest moons of Jupiter and Galileo realised that the orbits of these moons and their appearances and disappearances as the circled Jupiter could, if tabulated accurately enough, be used as a clock to determine longitude. Towards the end of the seventeenth century Giovanni Domenico Cassini and Ole Rømer succeeded in producing the necessary tables and Galileo’s idea could be put into practice. Whilst this method was very successful for cartographers on land, on a rolling ship it was not possible to observe the Jupiter moons accurately enough with a telescope to be able to apply this method; something else had to be used.

The two solutions that came to be developed in the eighteenth century and form the backbone of Sobel’s book, the lunar distance method (lunars) and the marine chronometer, were both first suggested in the sixteenth century, the former by Johannes Werner and the latter by Gemma Frisius. Other methods were suggested but proved either impractical or downright impossible. For lunars you need accurate lunar orbit tables and an accurate instrument to determine the position of the moon. Tobias Mayer provided the necessary tables and John Hadley the instrument with his sextant. For the clock method you require a clock that has a high level of accuracy over a long period of time and which retains that accuracy under the often very adverse conditions of a sea voyage; this is the technological problem that Harrison solved. Sobel presents the two methods as in competition but for navigators they are in fact complimentary and they were both used. As my #histsci soul sister Rebekah ‘Becky’ Higgitt constantly repeats, with the marine chronometer you can carry longitude with you, but if you chronometer breaks down you can’t find it, whereas with lunars you can find longitude, as James Cook did in fact do on one of his voyages.

As I said above, I began to seriously doubt the veracity of Sobel’s account through my own study of the academic accounts of the story, these doubts were then confirmed as I began to follow the blog of the Longitude Board research project set up by Cambridge University and the Maritime Museum in Greenwich, of which Becky Higgitt was one of the lead researchers. For a more balanced and accurate account of the story I recommend Finding Longitude the book written by Becky and Richard Dunn to accompany the longitude exhibition at the Maritime Museum, one of the products of the research project.

Recently I have become fully aware of another aspect of the Harrison story that Sobel does not cover. I say fully aware because I already knew something of it before reading David S. Landes’ excellent Revolution in Time: Clocks and the making of the Modern World (Harvard University Press, 1983). Landes covers the whole history of the mechanical clock from the Middle Ages through to the quartz wristwatch. One of his central themes is the increasing accuracy of clocks down the ages in which the invention of the marine chronometer played a central role, so he devotes a whole chapter to Harrison’s endeavours.

Landes quite correctly points out that after a lifetime of experimentation and ingenious invention John Harrison did indeed produce a solution to the technological problem of determining longitude with a clock. An astute reader with a feel for language might have noticed that in the previous sentence I wrote ‘a solution’ and not ‘the solution’ and therein lies the rub. Over the years that he worked on the problem Harrison produced many ingenious innovations in clock making in order to achieve his aim, an accurate, reliable, highly durable timepiece, however the timepiece that he finally produced was too complex and too expensive to be practicable for widespread everyday service at sea. Harrison had, so to speak, priced himself out of the market.

Harrison’s “Sea Watch” No.1 (H4), with winding crank
Source: Wikimedia Commons

Harrison was by no means the only clock maker working on a viable marine chronometer in the eighteenth century and it is actually his competitors who in the end carried away the laurels and not Harrison. Two clockmakers who made important contributions to the eventual development of a mechanically and financially viable marine chronometer were the Frenchman Pierre Le Roy and Swiss Ferdinand Berthoud, who were bitter rivals.

Pierre Le Roy (1717–1785)
Source: Wikimedia Commons

Plans of Le Roy chronometer
Source: Wikimedia Commons

Ferdinand Berthoud (1727–1807)
Source: Wikimedia Commons

Berthoud marine clock no.2, with motor spring and double pendulum wheel, 1763
Source: Wikimedia Commons

Neither of them can be said to have solved the problem but the work of both of them in different ways led in the right direction. Another contributor was George Graham’s one time apprentice, Thomas Mudge, his highly praised marine chronometer suffered from the same problem as Harrison’s too complex and thus too expensive to manufacture.

The two English clock makers, who actually first solved the problem of a viable marine chronometer were John Arnold and Thomas Earnshaw, who also became bitter rivals. This rivalry involved accusations of theft of innovations and disputes over patents. In the end it was John Arnold and Thomas Earnshaw, who became the most successful of the early clock makers, who worked on the development of the marine chronometer.


Chronometer-maker John Arnold (1736–1799) (attributed to Mason Chamberlin, ca. 1767)
Source: Wikimedia Commons

Thomas Earnshaw (!749–1829)
Source: Wikimedia Commons

Earnshaw chronometer No. 506
Source: Wikimedia Commons

I don’t intend to go into the details of which innovations in clock manufacture each of the man listed above contributed to the development of the marine chronometer that would go on to become an essential navigation tool in the nineteenth century. What I wish to make clear is exactly the same point as my essay on the history of the reflecting telescope for AEON made. From its first conception by Gemma Frisius in the sixteenth century, through the failure of Christiaan Huygens to realise it with his pendulum clock in the late seventeenth century (not discussed here), over its first successful realisation by John Harrison and on to the creation of a viable model by a succession of eighteenth-century clock makers, the marine chronometer was not the product of a single man’s (John Harrison’s) genius but a tool that evolved through the endeavours of a succession of dedicated inventors and innovators. Scientific and technological progress is teamwork.

4 Comments

Filed under History of Navigation, History of Technology, Myths of Science

One line to rule them all

A standard concept in the modern politico-military terminology is that of mission creep. This describes the, in the last sixty or seventy years often observed, phenomenon of a military intervention by a dominant power that starts with a so-called police action with a couple of hundred combatants and then within a couple of years grows to a full scale military operation involving thousands of troops and the expenditure of sums of money with an eye watering large number of zeros at the end. Famous examples of mission creep were the Americans in Viet Nam and the Russians in Afghanistan. In fact since the Second World War the American have become world champions in mission creep.

As a historian I, and I strongly suspect virtually all of my historian colleagues, experience a form of mission creep in every field of study to which I turn my attention. In fact the progress of my entire career as a historian of science has been one massive example of mission creep. It all started, at the age of sixteen, when I first learned that Isaac Newton was the (co)discoverer/inventor[1] of the calculus that I so loved at school. (Yes, I know that makes me sound a little bit strange but there’s no accounting for taste). This of course set me off on the trail of the whole history of mathematics, but that is not what I want to talk about here; let us stick with Newton. At some point I started to wonder why Newton, whom I saw as very much the theoretical mathematician and physicist, should have invented a telescope. This set me on the trail of the entire history of the telescope and because the telescope is an optical instrument, with time, the history of optics, not just in the early modern period but backwards through time into the European Middle Ages, the Islamic Empire and Antiquity. Of course Newton is most well known as physicist and astronomer and at some point I started investigating the pre-history of his work in astronomy. This eventually led me back to the Renaissance astronomers, not just Copernicus but all those whose work provided the foundations for Copernicus’s own work.

At some point it became very clear to me that to talk of Renaissance astronomers was in some sense a misnomer because those who pursued the study of astronomy in this time did so within a discipline that encompassed not just astronomy but also astrology, cartography (with a large chunk of geography and history in the mix), navigation, surveying, geodesy as well as the mathematical knowledge necessary to do all of these things. These were not separate disciplines as we see them now but different facets of one discipline. Over the years my studies have expanded to cover all of these facets and one into which I have delved very deeply is the history of cartography with the associated history of surveying. All of this is a rather longwinded explanation of why I have been reading Charles Withers’ new book Zero Degrees[2]

 

This book describes the history of how the Greenwich Meridian became the Prime Meridian.

A brief explanation for those who are not really clear what a meridian is; a meridian (or line of longitude) is any ‘straight’ line on the globe of the of the earth connecting the North Pole with the South Pole, where here straight means taking the shortest path between the two poles, as a meridian is by nature curved because it lies on the surface of the globe. Meridians are by their very nature arbitrary, abstract and non-real. We can chose to put a meridian wherever we like, they are an artificial construct and not naturally given. The Prime Meridian is a singular, unique, universally accepted meridian from which all other meridians (lines of longitude) are measured. The recognition of the necessity for a Prime Meridian is a fairly recent one in human history and Withers’ book deals with the history of the period between that recognition in the Early Modern Period to the realisation of a Prime Meridian at the beginning of the twentieth century.

The first thing that Withers made me aware of is that a meridian is not a singular object but one that has at least four separate functions and at least two different realisations. Meridians are used for navigation, for time determination, for cartography and for astronomy. The latter is because astronomers project our latitude and longitude coordinate system out into space in order to map the heavens. Nothing says that one has to use the same meridians for each of these activities and for much of the period of history covered by Withers people didn’t.

On the realisation of meridians Withers distinguishes two geographical and observed. The majority of meridians in use before the late seventeenth century were geographical. What does this mean? It meant that somebody simply said that they make their measurements or calculations from an imaginary line, the meridian, through some given geographical point on the surface of the earth. Ptolemaeus to whom we own our longitude and latitude coordinate system, although he had predecessors in antiquity, used the Azores as his zero meridian although he didn’t know with any real accuracy where exactly the Azores lay. Also the Azores is a scattered island group and he doesn’t specify exactly where within this island group his zero meridian ran. We have a lovely example of the confusion caused by this inaccuracy. On 4 May 1493 Pope Alexander VI issued the papal bull Inter caetera, which granted the Crowns of Castile and Aragon all the lands to the west and south of a meridian 100 leagues and south of the Azores or the Cape Verde islands.

This led to a whole series of treaties and papal bulls carving up the globe between Spain (Castile and Aragon) and Portugal. The 1494 Treaty of Tordesillas moved the line to a meridian 370 leagues west of the Portuguese Cape Verde islands now explicitly giving Portugal all new discoveries east of this meridian. I’m not going to go into all the gory details but this led to all sorts of problems because nobody actually knew where exactly this meridian or its anti-meridian on the other side of the globe lay. Ownership disputes in the Pacific between Spain and Portugal were pre-programmed. These are classical examples of geographical meridians.

The Cantino planisphere of 1502 shows the line of the Treaty of Tordesillas.
Source: Wikimedia Commons

The first observed meridian in the Early Modern Period was the Paris Meridian surveyed by Jean-Félix Picard in the 1660s. Such meridians are called observed because their exact position on the globe is determined astronomically using a transit telescope.

In the Early Modern Period there was no consensus as to which meridian should be used for which purpose and on the whole each country used its own zero meridian. I fact it was not unusual for several different zero meridians to be used for different purposes or even the same purpose, with one country. For geographers, cartographers and navigators crossing borders chaos ruled. The awareness that a single Prime Meridian would be beneficial for all already existed in the seventeenth century but it wasn’t until the nineteenth century that serious moves were made to solve the problem.

The discussion were long and very complicated and involved scientific, political and pragmatic considerations, which often clashed with each other. On the political level nationalism, of course, raised its ugly head. Surprisingly, at least for me, there was also a very heated discussion as to whether the Prime Meridian should be a geographical or an observed meridian. I personally can discern no reasons in favour of a geographical Prime Meridian but various participants in the discussions could. Another problem was one or more Prime Meridians? Separate ones for cartography, navigation, astronomy and time determination.

Withers deals with all of these topics in great detail and very lucidly in his excellent summery of all of the discussions leading up to the International Meridian Conference in Washington in 1884, which forms the climax of his book.

The delegates to the International Meridian Conference in Washington in 1884
Source: Wikimedia Commons

This is a truly fascinating piece of the history of science and in Withers it has found a more than worthy narrator and I recommend his book whole-heartedly for anybody who might be interested in the topic. Very important is his penultimate chapter Washington’s Afterlife. Every year in October people in the Internet announce that on this day in 1884 (I can’t be bothered to look up the exact date) the Greenwich Meridian became the world’s Prime Meridian and every year my #histsci soul sisterTM Rebekah ‘Becky’ Higgitt (who played a significant role in the genesis of Withers’ book, as can be read in the acknowledgements) announces no it didn’t, the resolutions reached in Washington were non-binding. In fact the acceptance of Greenwich as the Prime Meridian took quite some time after the Washington Conference, some even accepting it initial only for some but not all the four functions sketched above. France, whose Paris Meridian was the main contender against Greenwich, only finally accepted Greenwich as the Prime Meridian in 1912.

I do have a couple of minor quibbles about Withers’ book. In the preface he outlines the structure of the book saying what takes place in each section. He repeats this in greater detail in the introduction. Then he starts each chapter with a synopsis of the chapter’s contents, often repeating what he has already said in the introduction, and closes the chapter with a summary of its contents. It was for this reader a little bit too much repetition. My second quibble concerns the illustrations and tables of which there are a fairly large number in the book. These are all basically black and white but are in fact printed black on a sort of pastel grey. I assume that the book designer thinks this makes them somehow artistically more attractive but I personally found that it makes it more difficult to determine the details, particularly on the many maps that are reproduced. Whatever I wouldn’t let these rather personal minor points interfere with my genuine whole-hearted recommendation.

[1] Chose the word that best fits your personal philosophy of mathematics

[2] Charles W. J. Withers, Zero Degrees: Geographies of the Prime Meridian, Harvard University Press, Cambridge Massachusetts, London England, 2017

1 Comment

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

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_Celsius

Anders Celcius Portrait by Olof Arenius Source: Wikimedia Commons

Daniel-Gabriel-Fahrenheit

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.

800px-Wilkins_An_Essay_towards_a_real

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.

lengths001

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

lengths002

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.

1920px-Metre_étalon,_place_Vendôme,_Paris_2008

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.

Britanski_merki_za_dalzhina_Grinuich_2005

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.

18 Comments

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.

4 Comments

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