Category Archives: History of Navigation

Around the World in One Thousand and Eighty-three Days 

Growing up in the UK in the 1950s, history lessons in primary school, that’s elementary school for Americans, still consisted to a large extent of a glorification of the rapidly fading British Empire. The classroom globes were still covered in swathes of pink and there, at least, the sun never set on the empire that was. Another popular theme, in this collection of fairy tales and myths, was the great period of European exploration and discovery in the Early Modern Period, in which Columbus, Vasco da Gama and Magellan were presented as larger than life, heroic, visionary adventurers, who respectively discovered America, became the first European to sail to India, and, perhaps the greatest achievement of all, circumnavigated the globe. 

At grammar school history became modern European history–Napoleon, Vienna Conference, Franco-Prussian War, unification of German, First World War, rise of Fascism and Hitler, and Second World War–my generation was after all born in and grew up in the aftermath of WWII. The “heroes” of the so-called age of discovery faded into the background, becoming nothing more than a handful of half-remembered facts–1492 Columbus sailed the ocean blue. Somewhere down the line those early tales of daring do became tarnished by inconvenient facts, such as the information that the Vikings almost certainly got to America before Columbus or that Vasco da Gama only managed to sail from Africa to India because he employed a local navigator, who knew how to get there. On the whole it was not a topic that particularly interested me in the early part of my adult life. As far as history went, it didn’t seem to me at that time to be part of the history of mathematics, boy was I wrong on that, so I largely ignored it. 

However, I was aware of the gradual dethroning of Columbus, who having been appointed governor by the Spanish Crown of the islands he had discovered was later stripped of his title because of incompetence and brutality towards the indigenous population. Also, that de Gama had had to use military force to persuade the Indians to trade with him. These men were not the saints they had been painted as in my youth. However, through it all Magellan remained a heroic role model, the first man to circumnavigate the globe. 

I first became more interested in more detail about the so-called age of discovery about fifteen years ago when I became aware that the Renaissance mathematici, who now occupied a large part of my historical activities, were not mathematicians in anything like the modern sense of the word but were, as the English term has it, mathematical practitioners. That is, that they were actively engage in particle mathematics, not to be confused with the modern term applied mathematics, which included navigation and map making, as well as the design and production of mathematical instruments for navigation, surveying, and cartography. All of these activities have, of course, a direct and important connection to those voyages of discovery. This was brought home to me when I discovered that one of my favourite mathematici, the Nürnberger Johannes Schöner (1477–1547 most well known as a pioneer in the production of printed globes, had probably produced a terrestrial globe in 1523 displaying Magellan’s circumnavigation. As I wrote in a blog post from 2010:

So, what does all of this have to do with Magellan and the first circumnavigation? As Schöner was in Kirchehrenbach in his banishment he tried to curry favour with his Bishop in that he dedicated his newest terrestrial globe to him, produced in 1523 this globe featured the route of Magellan’s circumnavigation only one year after those 18 seamen struggled back to Spain. At least we think he did! The accompanying cosmographia for the globe exists but none of the globes has survived the ravages of time. How did Schöner manage to transfer the knowledge of this epic voyage so quickly into a printed globe? In this day and age where the news of Ms Watson’s achievement is blasted around the globe in all form of media within seconds of her landfall, we tend to forget that such news sometimes took years to permeate through Europe in the 16th century. At the instigation of Cardinal Matthäus Lang a great sponsor of science in this age Maximilianus Transylvanus interviewed the survivors in Spain and published his account of the voyage in 1523 and it was this account, which Schöner, who made sure to always acquire the latest travel reports through a network of contacts, used to make his globe. I said that none of his Magellan globes have survived but there is a set of globe gores in New York that appear to be those of Schöner’s 1523 globe. Globes were printed on gores, these are strips of paper shaped like segments of an orange that were then glued on to a papier mâché sphere and coloured by hand. The set of gores in New York have Schöner’s cartographical style and Magellan’s route printed on them and although there are some dissenting voices, in general the experts think that they are Schöner’s original.

Included in this quote in the information that only a very small number of the 237 seamen, who set out on this much acclaimed voyage actually made it back to Spain, and only one of the original five ships. Moreover, Magellan was not amongst the survivors having been killed in an imperial attack on indigenous natives on the island of Mactan, who refused to accept the authority of the king of Spain. I had personally garnered this information somewhere down the line.

I became increasingly interested in the mathematical aspects of the so-called age of discovery and became embroiled in an Internet debate on the naming of America with a famous, British pop historian, who was erroneously claiming that it was far more likely that America was named after the Welsh merchant, Richard Ap Meric, an investor in John Cabot’s voyages of discovery, than after Amerigo Vespucci. Being well aware of the reasons why Waldseemüller and Ringmann had named America after Vespucci on their 1507 map of the world, I wrote a long blog post challenging this twaddle. 

As part of my study of this piece of history I acquired my first book by historian extraordinary of exploration, Felipe Fernández-Armesto, his excellent biography of Vespucci, AmerigoThe Man who Gave His Name to America.[1] This was quickly followed by his equally good biography of Columbus,[2] and somewhat later by his PathfindersA Global History of Exploration.[3] So, when it was announced that Felipe Fernández-Armesto’s latest book, he’s incredibly prolific, was to be a biography of Magellan, I immediately ordered a copy and this blog post is a review of  his STRAITSBeyond the myth of Magellan.[4]

I will start by saying that Fernández-Armesto does not disappoint, and this biography of the man and his infamous voyage is up to his usual very high standards. If you have a serious interest in the topic, then this is definitely a book you should read. Although this is a trade book rather than an academic tome, Fernández-Armesto has scrupulously researched his topic and all of the book’s statements and claims are backed up by detailed endnotes. While we are by the apparatus the book also has an extensive and very comprehensive index but no general bibliography. This is one of several new books that I have without a general bibliography, meaning that if you become interested in a referenced volume and it’s not the first reference, then you have to plough your way back through the endnotes, desperately searching for that all important first reference, which contains the details that you require to actually find the book. Staying briefly with the general description, each chapter has a frontispiece consisting of a contemporary print with a detailed descriptions that related to the following chapter. There are also five grey tone maps scattered throughout the book showing places referred to in the narrative.

One thing that Fernández-Armesto makes very clear throughout his book is that the sources for actual hard information about Magellan are very thin and those that do exist are often contradictory. Because he very carefully qualifies his statements concerning Magellan, weighing up the sources and explaining why he believes the one version rather than the other, this makes the book, whilst not a hard read, shall we say a very intense read. Put another way, Fernández-Armesto doesn’t present his readers with a smooth novel like narrative, lulling them into thinking that we know more than we do, but shows the reader how the historian is forced to construct their narrative despite inadequate sources. This is a lesson that other trade book authors could learn.

The central myth of the Magellan story that Fernández-Armesto tackles in his book is that of the inspirational figure, who set out to circumnavigate the world. Not only did Magellan personally fail to do so, a fact that is so often swept under the carpet in the simple claim that he was the first man to do so, but that he in fact never had the intention of doing so. 

In the somewhat less than first half of his book Fernández-Armesto takes the reader through the details of what we know about Magellan’s life before that infamous voyage. His origins, his life and education on the Portuguese court, his service for the Portuguese Crown both as a seaman and a soldier. His reasons for leaving Portugal and moving to Spain, where he offered his services to the Spanish Crown instead. All of this leads up to his plans for that voyage and the motivation behind it. His intended aim was not to sail around the world but to find a passage through the Americas from the Atlantic to the Pacific, or Southern Sea, as it was generally known then, and then to sail across the Pacific to the Moluccas (Spice Islands), today known as the Maluka Islands, and hopefully demonstrate that they lay in the Spanish half of the globe, as designated by the Pope’s Tordesillas Treaty. Having done so to then return to Spain by the same route. Nobody actually knew in which half of the globe the Moluccas lay, as the treaty only specified the demarcation line or meridian in the Atlantic and it was not known where the anti-meridian lay in the Pacific, which in general everybody, including Magellan, thought was much smaller than it actually is.

Due to the uncertainties that this plan, was there even a passage through the Americas joining the two oceans, was it possible to cross the Pacific by ship, did the Moluccas actually lay within the Spanish hemisphere, the negotiations to set up the voyage and the persuade the Spanish Crown to finance it were tough and complex and Fernández-Armesto takes the reader through them step by step. Having succeeded, we then set sail with Magellan on a voyage that was an unmitigated disaster every single sea mile of the way.

The somewhat more than second half of Fernández-Armesto’s narrative is a detailed account, as far as it is possible to reconstruct it, of what might be described, with only slight exaggeration, as the voyage to hell and back with long periods in purgatory. Possibly the only thing that is admirable about Magellan and the voyage is his tenacity in the constant face of doom and disaster, although that tenacity takes on more and more maniacal traits as the voyage proceeds.

Fernández-Armesto’s biography of the man and his voyage is a total demolition of the myths that have been created and propagated over the last five centuries, leaving no trace of valour, heroism, or gallant endeavour. The voyage was an unmitigated disaster perpetrated by a ruthless, driven monomaniac. At the end of his excellent tome Fernández-Armesto illustrates how the myth of Magellan and his circumnavigation was put into the world, starting almost as soon as the Victoria, the only one of the five ships to complete the circumnavigations, docked in Spain more than a thousand days after it set sail with only a handful of the crews that started that voyage. Fernández-Armesto also list some of the myriad of organisations, objects, institutes, prizes etc. that proudly bear Magellan’s name, his attitude to all this being summed up perhaps by his comment on the Order of Magellan awarded by the Circumnavigators Club of New York:

Though it seems astonishing that an award for “world understanding should be named for a failed conqueror who burned villages ad coerced and killed people. (p. 277)

As a final comment on this possibly definitive biography, I learnt in reading this book that the early explorers, Columbus, da Gamma, Magellan et al identified both themselves and their endeavours with the heroic knights in the medieval tales of chivalry and romance, riding their ships out on quests of discovery that would bring the fame, fortune, and honour. Magellan’s quest was about as far removed from this image as it was possible to get. 


[1] Felipe Fernández-Armesto, AmerigoThe Man who Gave His Name to America, Weidenfeld & Nicolson, London, 2006.

[2] Felipe Fernández-Armesto, Columbus, OUP, Oxford & London, 1991, ppb Duckworth, London, 1996

[3] Felipe Fernández-Armesto, PathfindersA Global History of Exploration, W W Norton, New York, 2006, ppb 2007

[4] Felipe Fernández-Armesto, STRAITSBeyond the myth of Magellan, Bloomsbury, London, Oxford, New York, New Delhi, Sydney, 2022

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Filed under Book Reviews, History of Navigation, Renaissance Science

Renaissance science – XXVIII

In the last episode of this series, we explored the history of the magnetic compass in Europe and marine cartography from the Portolan chart to the Mercator Projection. We will now turn our attention to the other developments in navigation at sea in the Renaissance. As already stated in the last episode, the need to develop new methods of navigation and the instruments to carry them out was driven by what I prefer to call the Contact Period, commonly called the Age of Discovery or Age of Exploration. The period when the Europeans moved out into the rest of the world and exploited it. 

This movement in turn was motivated by various factors. Curiosity about lands outside of Europe was driven both by travellers’ tales such as The Travels of Marco Polo c. 1300 and The Travels of Sir John Mandeville, which first appeared around 1360, both of which were highly popular throughout Europe, and also by new cartographical representation of the know world, known to the Europeans that is, in particular Ptolemaeus’ Geographia, which first became available in the early fifteenth century. Another development was technological, the development by the Portuguese, who as we shall see led the drive out of Europe into the rest of the world, of a new type of ship, the caravel, which was more manoeuvrable than existing vessels and because of its lateen sails was capable of sailing windward, making it more suitable for long ocean voyages, as opposed to coastal sailing.

The Portuguese invention of the caravel, which was maneuverable and able to undertake ocean voyages, was essential to European maritime exploration. The present image shows the “Caravela Vera Cruz“, navigating the Tagus river, Lisboa. Source: Wikipedia Commons
Depending on the situation, different intervals between tacking can be used. This does not influence the total distance travelled (though may impact the time required). Sailing from point A to point B, path P1 involves more turns but only requires a narrow channel. Path P2 involves fewer turns but a wider channel. Path P3 requires only a single turn but covers comparatively the widest channel. Source: Wikimedia Commons

The final and definitely most important factor was trade or perhaps more accurately greed. The early sailors, who set out to investigate the world outside of Europe, were not the romantic explorers or discoverers, we get taught about in school, but hard-headed businessmen out to make a profit by trade or if necessary, theft. 

The two commodities most desired by these traders, were precious metals, principally gold but also silver and copper, and spices. The metal ore mines of Middle Europe could not fill the demands for precious metals, so other sources must be found. This is perhaps best illustrated by the search in South America, by the Spanish, for the mythical city of gold, El Dorado, during the sixteenth century. Spices had been coming into Europe from the East over the Indian Ocean and then overland, brought by Arab traders, to the port cities of Northern Italy, principally Venice and Genoa, from where there were distributed overland throughout Europe since the eleventh century. The new generation of traders thought they could maximise profits by cutting out the middlemen and going directly to the source by the sea route. This was the motivation of both Vasco da Gama (c. 1460–1524), sailing eastwards, and Christopher Columbus (1451–1506), sailing westward. Their voyages are, however, one end point of a series of voyages, which began with the Portuguese capture of Ceuta, in North Africa, from the Arabs, in 1415.

Having established a bridgehead in North Africa the Portuguese, who were after all situated on the Atlantic coast of the Iberian Peninsula, argued that they could bypass the middleman, their trading partners the Arabs, and sail down the coast to Sub-Saharan West Africa and fetch for themselves, the gold and the third great trading commodity of the Contact Period, slaves, who they had previously bought from Arab traders. It is fair to ask why other countries, further north, with Atlantic coasts did not lead the expansion into unknown territory? The first decades of the Portuguese Atlantic ventures were still very much coastal sailing progressively further down the African coast; other northern European countries, such as Britain did sail north and south along the Atlantic coast, but their journeys remained within Europe. 

Starting in 1520, Portuguese expeditions worked their way down the west coast of Africa until the end of the sixteenth century.

The gradual Portuguese progress down the West Coast of Africa Source: Wikipedia Commons

The Nürnberger Martin Behaim (1459–1507), responsible for the creation of the oldest surviving terrestrial globe and member of the Portuguese Board of Navigation (to which we will return), claimed to have sailed with Diogo Cão, who made two journeys in the 1480s, which is almost certainly a lie. At the time of Cão’s first voyage along the African coast Behaim is known to have been in Antwerp. On his second voyage Cão erected pillars at all of his landing places naming all of the important members of the crew, who were on the voyage, Martin Behaim is not amongst them. 

The two most significant Portuguese expedition were that of Bartolomeu Dias (c. 1450–1500) in 1488, which was the first to round the Cape of Good Hope, actually Diogo Cão’s aim on his two voyages, which he failed to achieve, and, of course, Vasco da Gama’s voyage of 1497, which took him not only up the east African coast but all the way to India with the help of a local navigator. The two voyages also showed that the Indian Ocean was open to the south, whereas Ptolemaeus had shown it to be a closed sea in his Geographia. 

Much earlier in the century the Portuguese had ventured out into the Atlantic and when blown off course by a storm João Gonçalves Zarco (c. 1390 –1471) and Tristão Vaz Teixeira (c. 1395–1480) discovered the archipelago of Madeira in 1420 and one expedition discovered the Azores, 1,200 km from the Portuguese coast in 1427. The Canaries had already been discovered in the early fourteenth century and were colonised by the Spanish in 1402. The Cap Verde archipelago was discovered around 1456. The discovery of the Atlantic islands off the coasts of the Iberian Peninsula and Africa was important in two senses. Firstly, there developed myths about other islands further westward in the Atlantic, which encouraged people to go and look for them. Secondly, by venturing further out into the Atlantic sailors began to discover the major Atlantic winds and currents,, known as gyres essential knowledge for successful expeditions.

The Atlantic Gyres influenced the Portuguese discoveries and trading port routes, here shown in the India Run (“Carreira da Índia“), which would be developed in subsequent years. Source: Wikipedia Commons

Dias could only successfully round the Cape because he followed the prevailing current in a big loop almost all the way to South America and then back past the southern tip of Africa. Sailors crossing the Indian Ocean between Africa and India had long known about the prevailing winds and currents, which change with the seasons, which they had to follow to make successful crossings. The Spanish and the Portuguese would later discover the currents they needed to follow to successfully sail to the American continent and back.

The idea of island hopping to travel westwards in the Atlantic that the discoveries of the Azores and the other Southern Atlantic islands suggested was something already been followed in the North Atlantic by fishing fleets sailing out of Bristol in Southwest England in the fifteenth century. They would sail up the coast of Ireland going North to the Faroe Islands, settled by the Vikings around 800 CE and then onto Iceland, another Viking settlement, preceding to Greenland and onto the fishing grounds off the coast of Newfoundland. This is the route that Sebastian Cabot (c. 1474–c. 1557) would follow on his expedition to North America in the service of Henry VIII. It is also probable that Columbus got his first experience of navigating across the Atlantic on this northern route. 

Columbus famously made his first expedition to what would be erroneously named America in 1492, in an attempt to reach the Spice Islands of Southeast Asia by sailing westward around the globe. This expedition was undertaken on the basis of a series of errors concerning the size of the globe, the extent of the oikumene, the European-Asian landmass known to the Greek cartographers, and the distance of Japan from the Asian mainland. Columbus thought he was undertaking a journey of about 3,700 km from the Canary Islands to Japan instead of the actual 19,600 km! If he hadn’t bumped into America, he and his entire crew would have starved to death on the open sea. Be that as it may, he did bump into America and succeeded in returning safely, if only by the skin of his teeth. With Columbus’ expedition to America and da Gama’s to India, the Europeans were no longer merely coastal sailors but established deep sea and new approaches to navigation had to be found.

The easiest way to locate something on a large open area is to use a geometrical coordinate system with one set of equally spaced lines running from top to bottom and a second set from side to side or in the case of a map from north to south and east to west. We now call such a grid on a map or sea chart, lines of longitude also called meridians, north to south, and lines of latitude also called parallels, east to west. The earliest know presentation of this idea is attributed to the Greek polymath Eratosthenes (c. 276­–c. 195 BCE).

A perspective view of the Earth showing how latitude (𝛟) and longitude (𝛌) are defined on a spherical model. The graticule spacing is 10 degrees.

The concept was reintroduced into Early Modern Europe by the discovery of Ptolemaeus’ Geographia. It’s all very well to have a location grid on your maps and charts but it’s a very different problem to determine where exactly you are on that grid when stuck in the middle of an ocean. However, before we consider this problem and its solutions I want to return to the Portuguese Board of Navigation, which I briefly mentioned above.

Both the Portuguese and the Spanish realised fairly early on as they began to journey out onto the oceans that they needed some way of collecting and collating new geographical and navigation relevant information that their various expeditions brought back with them and also a way of imparting the relevant information and techniques to navigators due to set out on new expeditions. Both countries established official institutions to fulfil these tasks and also appointed official cosmographers to lead these endeavours. Pedro Nunes (1502–1578), who we met in the first episode on navigation, as the discoverer of the loxodrome, was appointed Portugal’s Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547, a post he held until his death.

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The practice of establishing official organisations to teach cartography and navigation, as well as the mathematics they needed to carry them out to seamen was followed in time by France, Holland, and Britain as they too began to send out deep sea marine expeditions. 

To determine latitude and longitude are two very different problems and I will start with the easier of the two, the determination of latitude. For the determination of longitude or latitude you first need a null point, for latitude this is the equator. In the northern hemisphere your latitude is how many degrees you are north of the equator. You can determine your latitude using either the Sun during the day or the North Star at night. At night you need to observe the North Star with some sort of angle measuring device then measure the angle that makes to the horizon and that angle is your latitude in degrees. During the day you need to observe the Sun at exactly noon with an angle measuring device then the angle to makes with a vertical plumb line is your latitude. This is only strictly true for the date of the two equinoxes. For other days of the year, you have to calculate an adjustment using tables. For these observations mariners initially used either a quadrant,

Geometric quadrant with plumb bob. Source: Wikimedia Commons

which had been in use since antiquity or a Jacob’s Staff or Cross Staff, the invention of which is attributed to the French astronomer Levi Ben Gershon (1268–1344).

A sailor uses a ‘Jacob’s Staff’ to calculate the angle between a star and the horizon Source

Contrary to many claims, astrolabes were never used on ships for this purpose. However, around the end of the fifteenth century a much-simplified version of the astrolabe, the mariner’s astrolabe began to be used for this purpose. 

Mariner’s astrolabe Source: Wikimedia Commons

Because looking directly into the Sun is not good for the eyes, the backstaff was developed over time. With a backstaff the mariner stands with his back to the Sun and a shadow is cast onto the angle measuring scale. Thomas Harriot (c. 1560–1621) is credited with being the originator of the concept. The mariner John Davis (c. 1550–1605) introduced the double quadrant or Davis quadrant in his book on practical navigation, The Seaman’s Secrets in 1594, a device that evolved over time.

Davis quadrant, made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons
How a Davis Quadrant is used Source includes a video of how to use one

In 1730, John Hadley invented the reflecting octant, which incorporated a mirror to reflect the image of the Sun, whilst the user observed the horizon.

John Hadley Source: Wikimedia Commons
Hadley Octant Source includes video

This evolved into the sextant the device still used today to “shoot the Sun” as it is called. Here we see an evolution of instruments used to fulfil a specific function.

The determination of longitude at sea is a much more difficult problem. First, there is no natural null point, and any meridian can be and indeed was used until the Greenwich Meridian was chosen as the international null point for the determination of longitude at the International Meridian Conference in Washington in 1884. Because the Earth revolves once in twenty-four hours the determination of the difference in longitude between two locations is equivalent to the difference in local time between them, one degree of longitude equals four minutes of time difference, so the determination of longitude is basically the determination of time differences, which is easy to state but much more difficult to carry out.

The various European sea going nations–Spain, Portugal, France, Holland, Britain–all offered financial awards to anybody who could come up with a practical solution for determining longitude at sea. 

In antiquity, the difference in longitude between two locations was determined by calculating the difference in the observation times of major astronomical events such as lunar or solar eclipses. Then, if one had determined the difference in longitude between two given locations and their respective distances from a third location, it was possible to calculate the difference in longitude for the third location geometrically. Using these methods, astronomers, and cartographers gradually built-up tables of longitude for large numbers of towns and cities such as the one found in Ptolemaeus’ Geographia. This method is, of course, not practical for mariners at sea.

Starting in the early sixteenth century, various methods were suggested for determining time differences in order to determine longitude. The Nürnberger mathematicus Johannes Werner (1468 – 1522) in his In hoc opere haec continentur Nova translatio primi libri geographiae Cl’ Ptolomaei … (Nürnberg 1514) proposed the so-called lunar distance method. In this method an accurate table of the position of the Moon relative to a given set of reference stars for a given location for the entire year needs to be created.

Source: Wikimedia Commons

The mariner then has to observe the position of the Moon relative to the reference stars for his local time and then calculate the time difference to the given location from the tables. Unfortunately, because the Moon is pulled all over the place by the gravitational influence of both the Sun and the Earth, its orbit is highly irregular and the preparation of such tables proved beyond the capabilities of sixteenth century astronomers and indeed of seventeenth century astronomers, when the method was proposed again by Jean-Baptiste Morin (1583–1656). There was also the problem of an instrument accurate enough to measure the position of the Moon on a moving ship. It was Tobias Mayer (1723–1762), who first managed to produce accurate tables and Hadley’s octant or rather the sextant that evolved out of it solved the instrument problem. The calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766.

Portrait of Nevil Maskelyne by Edward Scriven Source: Wikimedia Commons
Source: Library of Congress Washington

The next solution to the problem of determining longitude suggested during the Renaissance by Gemma Frisius (1508–1555) was the clock, published in his De principiis astronomiae et cosmographiae. (Antwerp, 1530).

Gemma Frisius 17th C woodcut by E. de Boulonois Source: Wikimedia Commons

The mariner should take a clock, capable of maintaining accurate time over a long period under the conditions that prevail on a ship on the high seas, set to the time of the point of departure. By comparing local time with the clock time, the longitude difference could then be calculated. The problem was that although mechanical clocks had been around for a couple of centuries when Gemma Frisius made his suggestion, they were incapable of maintaining the required accuracy on land, let alone on a ship at sea. Jean-Baptiste Morin thought it would never be possible, “I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.” A view apparently shared by Isaac Newton, when he sat on the English Board of Longitude.

Only when Christiaan Huygens (1629–1695) had the first pendulum clock constructed by Salomon Coster (c. 1620–1659) accord his design in 1657 that Frisius’ idea began to seem realistic.

Christiaen Huygens II (1629-1695) signed C.Netscher / 1671 Source: Wikimedia Commons
Spring-driven pendulum clock, designed by Huygens and built by Salomon Coster (1657),  with a copy of the Horologium Oscillatorium (1673), at Museum Boerhaave, Leiden. Source: Wikimedia Commons

One of Huygens’ clocks was actually sent on sea trials but failed the test. In what is, thanks to Dava Sobel[1], probably the most well-known story in the history of technology John Harrison (1693–1776)

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

finally succeeded in producing a clock capable of fulfilling the demands with his H4 in 1761, slightly later than the successful fulfilment of the lunar distance method. In one sense the problem was still not really solved because the H4 was too complex and too expensive for it to be mass produced at a reasonable cost for use in sea transport. It was only really in the nineteenth century, after further developments in clock technology, that the marine chronometer became a real solution to the longitude problem.

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

Back tacking, at the beginning of the seventeenth century with the discovery of the four largest moons of Jupiter another method suggested itself. These moons, Io, Europa, Ganymede, and Callisto, have orbital periods of respectively, 1.77, 3.55, 7.15, and 16.6 days.

A montage of Jupiter and its four largest moons (distance and sizes not to scale) Source: Wikimedia Commons

This means that one or other of them is being fairly often eclipsed by Jupiter. Galileo argued that is one could calculate the orbits accurately enough they could be used as a clock to determine longitude. He tried to sell the idea to the governments of both Spain and the Netherlands without success. The principal problem was the difficulty of observing them with a telescope on a moving ship. Galileo worked on an idea of an observing chair with the telescope mounted on a helmet, but the idea never made it off the paper. Later in the seventeenth century Jean-Dominique Cassini (1625–1712) produced tables of the orbits accurate enough for them to be used to determine longitude and he and Jean Picard (1620–1682) used the method on land to accurately determine the borders of France, leading Louis XVI to famously quip that he had lost more territory to the cartographers than he ever lost to his enemies.

Map showing both old and new French coastlines Source: Wikimedia Commons

In the first part of this account of navigation I described the phenomenon of magnetic variations or declination, which is the fact that that a compass does not point to true north but to magnetic north, which is somewhat removed from true north. I also mentioned that magnetic declination is not constant but varies from location to location. This led to the thought that if one were to map the magnetic inclination for the entire Atlantic one could use the data to determine longitude, whilst at sea. Edmond Halley (1556–1742) did in fact create such a map on a voyage from1699 to 1700. However, this method of determining longitude was never really utilised. 

Portrait of Halley (c. 1690) by Thomas Murray Source: Wikimedia Commons
Halley’s 1701 map showing isogonic lines of equal magnetic declination in the Atlantic Ocean. Source: Wikimedia Commons

Although the methods eventually developed to determine longitude on the high seas all came to fruition long after the Renaissance, they all have their roots firmly planted in the practical science of the Renaissance. This brief sketch also displays an important aspect of the history of science and technology. A lot of time can pass, and very often does, between the recognition of a problem, the suggestion of one or more solutions to that problem, and the realisation or fulfilment of those solutions.

Having gone to great lengths to describe the principal methods suggested and eventually realised for determining longitude, there were others ranging from the sublime to the ridiculous that I haven’t described, there remains the question, how did mariners navigate when far away from the coast during the Early Modern Period? There are two answers firstly latitude sailing and secondly dead reckoning. In latitude sailing, instead of, for example, trying to cross the Atlantic by the most direct course from A to B, the navigator first sails due north or south along the coast until he reaches the latitude of his planned destination. They then turn their ship through ninety degrees and maintain a course along that latitude. This, of course, nearly always means a much longer voyage but one with less risk of getting lost. 

In dead reckoning, the navigator, starting from a fixed point, measures the speed and direction of his ship over a given period of time transferring this information mathematically to a sea chat to determine their new position. The direction is determined with the compass, but the determination of the ship’s speed is at best an approximation, which was carried out in the following manner. A log would be thrown overboard at the front of the ship and the mariners would measure how long it took for the ship to pass the log, and the result recorded in a book, which became known as the logbook. The term logbook expanded to include all the information recorded on a voyage on a sip and then later on planes and even lorries. Of note, the word blog is an abbreviation of the term weblog, a record of web or internet activity, but I’m deviating from the topic.

An example of dead reckoning Columbus’ return voyage Source

The process of measuring the ships speed evolved over time. The log was thrown overboard attached to a long line and using an hourglass, the time how long the line needed to pay out was recorded. Later the line was knotted at regular intervals and the number of knots were recorded for a given time period. This is, of course, the origin of the term knots for the speed of ships and aircraft. Overtime the simple log of wood was replaced with a so-called chip-log, which became standardised:

The shape is a quarter circle, or quadrant with a radius of 5 inches (130 mm) or 6 inches (150 mm), and 0.5 inches (13 mm) thick. The logline attaches to the board with a bridle of three lines that connect to the vertex and to the two ends of the quadrant’s arc. To ensure the log submerges and orients correctly in the water, the bottom of the log is weighted with lead. This provides more resistance in the water, and a more accurate and repeatable reading. The bridle attaches in such a way that a strong tug on the logline makes one or two of the bridle’s lines release, enabling a sailor to retrieve the log. (Wikipedia)

Model of chip log and associated kit. The reel of log-line is clearly visible. The first knot, marking the first nautical mile is visible on the reel just below the centre. The timing sandglass is in the upper left and the chip log is in the lower left. The small light-coloured wooden pin and plug form a release mechanism for two lines of the bridle. From the Musée de la Marine, Paris. Source: Wikimedia Commons

The invention of the log method of determining a ship’s speed is attributed to the Portuguese mariner Bartolomeu Crescêncio at the end of the fifteenth century. The earliest known published account of using a log to determine a ship’s speed was by William Bourne (c. 1535–1582) in his A regiment of the Sea in 1574, which went through 11 English editions up to 1631 and at least 3 Dutch edition from 1594. 

Dead reckoning is a process that is prone to error, as it doesn’t take into account directional drift caused by wind and currents. Another problem was that not all mariners processed the necessary mathematical knowledge to transfer the data to a sea chart. Those mariners, who disliked and rejected the mathematical approach used a traverse board, which uses threads and pegs to record direction and speed of a ship. William Bourne writing in 1571 said:

I have known within these 20 years that them that were ancient masters of shippes hathe derided and mocked them that have occupied their cards and plattes and also the observation of the Altitude of the Pole saying; that they care not for their sheepskinne for he could keepe a better account upon a board.

This blog post is already far too long, so I’ll skip a detailed description of the traverse board, but you can read one here.

We have one last Renaissance contribution to the art of navigation from the English mathematical practitioner, Edmund Gunter (1581–1626), who we have already met as the inventor of the standard English surveyor’s chain in the episode on surveying. Gunter invented the Gunter scale or rule, simply known as the “gunter” by mariners, which he published in his Description and Use of the Sector, the Crosse-staffe and other Instrumentsin 1623. Developed shortly after the invention of logarithms, the scale is usually somewhat more than a half metre long and about 40 mm broad. It is engraved on both sides with various scales or lines. Usually, on the one side are natural line, chords, sines, tangents, rhumbs etc., and on the other scales of the logarithms of those functions. Navigational mathematical problems were then worked through using a pair of compasses. 

Gunter scale front
Gunter scale back Source

Despite its drawbacks, uncertainties, and errors dead reckoning was used for centuries by European mariners to crisscross the oceans and circumnavigate the globe. It continued to be used well into the nineteenth century, long after the perfection of the marine chronometer and the lunar distance method. 

This over long blog post is but a sketch of the contributions made by the Renaissance mathematical practitioners to the development of methods of deep-sea navigation required by the European mariners during the Contact Period, when they swarmed out to investigate the world beyond Europe and exploit it. Those contributions were in the form of theories, publications, instruments, charts, and practical instruction (which I haven’t really expanded upon here). For a more detailed version of the story, I heartily recommend Margaret Scotte’s excellent Sailing School: Navigation Science and Skill, 1550–1800 (Johns Hopkins University Press, 2019).


[1] Sobel’s account of the story is somewhat less than historically accurate and as always, I recommend instead Dunne and Higgitt, Finding LongitudeHow ships, clocks and stars helped solve the longitude problem (Collins, 2014)

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

WRONG, WRONG, WRONG…

I think the Internet has finally broken the HISTSCI_HULK; he’s lying in the corner sobbing bitterly and mumbling wrong, wrong, wrong… like a broken record. What could have felled the mighty beast? 

29 January was the anniversary of the birth (1611) and death (1687) of the Danzig astronomer Johannes Hevelius and numerous people, including myself, posted or reposted articles about him on the Internet. One of those articles was the 2018 article, The 17th-Century Astronomer Who Made the First Atlas of the Moon by Elizabeth Landau, with the lede Johannes Hevelius drew some of the first maps of the moon, praised for their detail, from his homemade rooftop observatory in the Kingdom of Poland, in the Smithsonian Magazine.

Johannes Hevelius by Daniel Schultz Source: Wikimedia Commons

I suppose that I’m really to blame because I let him read it. He was chugging along quite happily, nodding his head, and burbling to himself, on the lookout, as always, for history of science errors and howlers, when he let out a piercing scream, NOOOOOO!!!!!! And collapsed in a sobbing heap on the floor. I’ve tried everything but I haven’t been able to console the poor beast.

So, what was it that caused this total breakdown? The first six paragraphs of the article are harmless enough, with only some very minor questionable statements, not really worth bothering about, but then comes this monstrosity:

Mapping the moon was one of Hevelius’s first major undertakings. The seafaring nations at the time were desperately searching for a way to measure longitude at sea, and it was thought that the moon could provide a solution. The idea was that during a lunar eclipse, if sailors observed the shadow of the moon crossing a particular point on the surface at 3:03 p.m., but they knew that in another location, such as Paris, the same crossing would occur at 3:33 p.m., then they could calculate their degrees of longitude away from the known location of the city. More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

One can only assume that it is an attempt to describe the lunar distance method for determining longitude but apart from the word moon, it has absolutely nothing in common with the actual lunar distance method. Put very mildly it is a complete travesty that should never have seen the light of day, let alone been published. 

Lunar eclipses had already been used for many centuries to determine the longitude difference between two locations, but you don’t need either a map of the moon or a telescope to do so. Two observers, in their respective locations, merely record the local time of the beginning and/or the end of the eclipse (initial and final contacts) and the resulting time difference gives the difference in longitude. Lunar eclipses are impractical as a method of determining longitude for navigation, as they occur too infrequently; there will only be a total of 230 lunar eclipses in the whole of the twenty-first century, of which only eighty-five will be total lunar eclipses. For example, if you were sitting in the middle of the Atlantic Ocean on 6 June 2022 and wished to determine your longitude, you would have to wait until 8 November for the next total lunar eclipse. After that you would have to wait until 14 March 2025 for the next total lunar eclipse, although there are a couple of partial and penumbral eclipses in between. 

Early Modern explorers did use solar and lunar eclipses combined with an ephemeris, a book of astronomical tables, to determine longitude on land, to establish their location and to draw maps. Columbus, famously, used his knowledge of the total lunar eclipse on 1 March 1504, taken from an ephemeris, to intimidate the natives on the island of Jamaica into continuing to feed his hungry stranded crew.

The lunar distance method of determining longitude is something completely different. It was first proposed by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524. For reasons that I will explain in a minute, it was found impractical, but was proposed again in 1634 by the French astronomer Jean-Baptiste Morin (1586–1656), but once again rejected as impractical. 

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. 

We now turn our attention to Landau’s closing statement in this horror paragraph:

More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

Historically, tables of the necessary accuracy were produced by Tobias Meyer (1723–1762) in 1755. However, the calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne (1732–1811) produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766. One does not need a telescope to make the necessary observations. A sextant is sufficient to measure the distance between the moon and the reference stars and that had been invented by John Hadley (1682–1744) in 1731. The lunar distance method was in fact ready for practical use before the marine chronometer. 

One question that I have, is did Landau extract this heap of nonsense out of her own posterior or is she paraphrasing somebody else’s description? Throughout her article she gives links to various books with the information she is using, so did she take this abomination from another source? If so, it is still out there somewhere creating confusion for anybody unlucky enough to read it. On the question of sources, Dava Sobel’s Longitude, which, despite her prejudices against it, contains a correct description of the lunar distance method was published in 2005 and the much better Finding Longitude by Rebekah Higgitt and Richard Dunn was published in 2014, so there is no real excuse for Landau’s load of bovine manure in 2018. 

I don’t know how many people have subscriptions to the Smithsonian Magazine, but it has over 300,000 followers on Twitter. If we look at the Wikipedia article on the Smithsonian Institutions it starts thus, “The Smithsonian Institution, or simply, the Smithsonian, is a group of museums and education and research centers, the largest such complex in the world, created by the U.S. government for the increase and diffusion of knowledge (my emphasis), so why is the Smithsonian Magazine diffusing crap?

I’m hoping that with plenty of sweet tea and digestive biscuits, I’ll be able to restore the HISTSCI_HULK to his normal boisterous self. 

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

Renaissance science – XXVII

Early on in this series I mentioned that a lot of the scientific developments that took place during the Renaissance were the result of practical developments entering the excessively theoretical world of the university disciplines. This was very much the case in the mathematical sciences, where the standard English expression for the Renaissance mathematicus is mathematical practitioner. In this practical world, areas that we would now regard as separate disciples were intertwined is a complex that the mathematical practitioners viewed as one discipline with various aspects, this involved astronomy, cartography, navigation, trigonometry, as well as instrument and globe making. I have already dealt with trigonometry, cartography and astronomy and will here turn my attention to navigation, which very much involved the other areas in that list.

The so-called Age of Discovery or Age of Exploration, that is when Europeans started crossing the oceans and discovering other lands and other cultures, coincides roughly with the Renaissance and this was, of course the main driving force behind the developments in navigation during this period. Before we look at those developments, I want to devote a couple of lines to the terms Age of Discovery and Age of Exploration. Both of them imply some sort of European superiority, “you didn’t exist until we discovered you” or “your lands were unknown until we explored them.” The populations of non-European countries and continents were not sitting around waiting for their lands and cultures to be discovered by the Europeans. In fact, that discovery very often turned out to be highly negative for the discovered. The explorers and discoverers were not the fearless, visionary heroes that we tend to get presented with in our schools, but ruthless, often brutal chancers, who were out to make a profit at whatever cost.  This being the case the more modern Contact Period, whilst blandly neutral, is preferred to describe this period of world history.

As far as can be determined, with the notable exception of the Vikings, sailing in the Atlantic was restricted to coastal sailing before the Late Middle Ages. Coastal sailing included things such as crossing the English Channel, which, archaeological evidence suggests, was done on a regular basis since at least the Neolithic if not even earlier. I’m not going to even try to deal with the discussions about how the Vikings possibly navigated. Of course, in other areas of the world, crossing large stretches of open water had become common place, whilst the European seamen still clung to their coast lines. Most notable are the island peoples of the Pacific, who were undertaking long journeys across the ocean already in the first millennium BCE. Arab and Chinese seamen were also sailing direct routes across the Indian Ocean, rather than hugging the coastline, during the medieval period. It should be noted that European exploited the navigation skills developed by these other cultures as they began to take up contact with the other part of the world. Vasco da Gamma (c. 1460–1524) used unidentified local navigators to guide his ships the first time he crossed the Indian Ocean from Africa to India. On his first voyage of exploration of the Pacific Ocean from 1768 to 1771, James Cook (1728–1779) used the services of the of the Polynesian navigator, Tupaia (c. 1725–1770), who even drew a chart, in cooperation with Cook, Joseph Banks, and several of Cooks officer, of his knowledge of the Pacific Ocean. 

Tupaia’s map, c. 1769 Source: Wikimedia Commons

There were two major developments in European navigation during the High Middle Ages, the use of the magnetic compass and the advent of the Portolan chart. The Chinese began to use the magnetic properties of loadstone, the mineral magnetite, for divination sometime in the second century BCE. Out of this they developed the compass needle over several centuries. It should be noted that for the Chinese, the compass points South and not North. The earliest Chinese mention of the use of a compass for navigation on land by the military is before 1044 CE and in maritime navigation in 1117 CE.

Diagram of a Ming Dynasty (1368–1644) mariner’s compass Source: Wikimedia Commons

Alexander Neckam (1157–1219) reported the use of the compass for maritime navigation in the English Channel in his manuscripts De untensilibus and De naturis rerum, written between 1187 and 1202.

The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.

This and other references to the compass suggest that it use was well known in Europe by this time.

A drawing of a compass in a mid 14th-century copy of Epistola de magnete of Peter Peregrinus. Source: Wikimedia Commons

The earliest reference to maritime navigation with a compass in the Muslim world in in the Persian text Jawāmi ul-Hikāyāt wa Lawāmi’ ul-Riwāyāt (Collections of Stories and Illustrations of Histories) written by Sadīd ud-Dīn Muhammad Ibn Muhammad ‘Aufī Bukhārī (1171-1242) in 1232. There is still no certainty as to whether there was a knowledge transfer from China to Europe, either direct or via the Islamic Empire, or independent multiple discovery. Magnetism and the magnetic compass went through a four-hundred-year period of investigation and discovery until William Gilbert (1544–1603) published his De magnete in 1600. 

De Magnete, title page of 1628 edition Source: Wikimedia Commons

The earliest compasses used for navigation were in the form of a magnetic needle floating in a bowl of water. These were later replaced with dry mounted magnetic needles. The first discovery was the fact that the compass needle doesn’t actually point at the North Pole, the difference is called magnetic variation or magnetic declination. The Chinese knew of magnetic declination in the seventh century. In Europe the discovery is attributed to Georg Hartmann (1489–1564), who describes it in an unpublished letter to Duke Albrecht of Prussia. However, Georg von Peuerbach (1423–1461) had already built a portable sundial on which the declination for Vienna is marked on the compass.

NIMA Magnetic Variation Map 2000 Source: Wikimedia Commons

There followed the discovery that magnetic declination varies from place to place. Later in the seventeenth century it was also discovered that declination also varies over time. We now know that the Earth’s magnetic pole wanders, but it was first Gilbert, who suggested that the Earth is a large magnet with poles. The next discovery was magnetic dip or magnetic inclination. This describes the fact that a compass needle does not sit parallel to the ground but points up or down following the lines of magnetic field. The discovery of magnetic inclination is also attributed to Georg Hartmann. The sixteenth century English, seaman Robert Norman rediscovered it and described how to measure it in his The Newe Attractive (1581) His work heavily influenced Gilbert. 

Illustration of magnetic dip from Norman’s book, The Newe Attractive Source: Wikimedia Commons

The Portolan chart, the earliest known sea chart, emerged in the Mediterranean in the late thirteenth century, not long after the compass, with which it is closely associated, appeared in Europe. The oldest surviving Portolan, the Carta Pisana is a map of the Mediterranean, the Black Sea and part of the Atlantic coast.

Source: Wikimedia Commons

The origins of the Portolan chart remain something of a mystery, as they are very sophisticated artifacts that appear to display no historical evolution. A Portolan has a very accurate presentation of the coastlines with the locations of the major harbours and town on the coast. Otherwise, they have no details further inland, indicating that they were designed for use in coastal sailing. A distinctive feature of Portolans is their wind roses or compass roses located at various points on the charts. These are points with lines radiating outwards in the sixteen headings, on later charts thirty-two, of the mariner’s compass.

Central wind rose on the Carta Pisana

Portolan charts have no latitude or longitude lines and are on the so-called plane chart projection, which treats the area being mapped as flat, ignoring the curvature of the Earth. This is alright for comparatively small areas, such as the Mediterranean, but leads to serious distortion, when applied to larger areas.

During the Contact Period, Portolan charts were extended to include the west coast of Africa, as the Portuguese explorers worked their way down it. Later, the first charts of the Americas were also drawn in the same way. Portolan style charts remained popular down to the eighteenth century.

Portolan chart of Central America c. 1585-1595 Source:

A central problem with Portolan charts over larger areas is that on a globe constant compass bearings are not straight lines. The solution to the problem was found by the Portuguese cosmographer Pedro Nunes (1502–1578) and published in his Tratado em defensam da carta de marear (Treatise Defending the Sea Chart), (1537).

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The line is a spiral known as a loxodrome or rhumb lines. Nunes problem was that he didn’t know how to reproduce his loxodromes on a flat map.

Image of a loxodrome, or rhumb line, spiraling towards the North Pole Source: Wikimedia Commons

The solution to the problem was provided by the map maker Gerard Mercator (1512–1594), when he developed the so-called Mercator projection, which he published as a world map, Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata (New and more complete representation of the terrestrial globe properly adapted for use in navigation) in 1569.

Source: Wikimedia Commons
The 1569 Mercator world map Source: Wikimedia Commons.

On the Mercator projection lines of constant compass bearing, loxodromes, are straight lines. This however comes at a price. In order to achieve the required navigational advantage, the lines of latitude on the map get further apart as one moves away from the centre of projection. This leads to an area distortion that increases the further north or south on goes from the equator. This means that Greenland, slightly more than two million square kilometres, appear lager than Africa, over thirty million square kilometres.

Mercator did not publish an explanation of the mathematics used to produce his projection, so initially others could reproduce it. In the late sixteenth century three English mathematicians John Dee (1527–c. 1608), Thomas Harriot (c. 1560–1621), and Edward Wright (1561–1615) all individually worked out the mathematics of the Mercator projection. Although Dee and Harriot both used this knowledge and taught it to others in their respective functions as mathematical advisors to the Muscovy Trading Company and Sir Walter Raleigh, only Wright published the solution in his Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected. (The Voyage of the Right Ho. George Earle of Cumberl. to the Azores, &c.) published in London in 1599. A second edition with a different, even longer, title was published in the same year. Further editions were published in 1610 and 1657. 

Source: Wikimedia Commons
Wright explained the Mercator projection with the analogy of a sphere being inflated like a bladder inside a hollow cylinder. The sphere is expanded uniformly, so that the meridians lengthen in the same proportion as the parallels, until each point of the expanding spherical surface comes into contact with the inside of the cylinder. This process preserves the local shape and angles of features on the surface of the original globe, at the expense of parts of the globe with different latitudes becoming expanded by different amounts. The cylinder is then opened out into a two-dimensional rectangle. The projection is a boon to navigators as rhumb lines are depicted as straight lines. Source: Wikimedia Commons

His mathematical solution for the Mercator projection had been published previously with his permission and acknowledgement by Thomas Blundeville (c. 1522–c. 1606) in his Exercises (1594) and by William Barlow (died 1625) in his The Navigator’s Supply (1597). However, Jodocus Hondius (1563–1612) published maps using Wright’s work without acknowledgement in Amsterdam in 1597, which provoked Wright to publish his Certaine Errors. Despite its availability, the uptake on the Mercator projection was actually very slow and it didn’t really come into widespread use until the eighteenth century.

Wright’s “Chart of the World on Mercator’s Projection” (c. 1599), otherwise known as the Wright–Molyneux map because it was based on the globe of Emery Molyneux (died 1598) Source: Wikimedia Commons

Following the cartographical trail, we have over sprung a lot of developments in navigation to which we will return in the next episode. 

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

The black sheep of the Provence-Paris group

I continue my sketches of the seventeenth century group pf mathematicians and astronomers associated with Nicolas-Claude Fabri de Peiresc (1580-1637) in Provence and Marin Mersenne (1588–1648) in Paris with Jean-Baptiste Morin (1583–1656), who was born in Villefranche-sur-Saône in the east of France.

Jean-Baptiste Morin Source: Wikimedia Commons

He seems to have come from an affluent family and at the age of sixteen he began his studies at the University of Aix-en-Provence. Here he resided in the house of the Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix and Peiresc’s observing partner. For the last two years of his time in Aix, the young Pierre Gassendi, also lived in Gaultier de la Valette’s house and the two became good friends and observing partners.

In 1611, Morin moved to the University of Avignon, where he studied medicine graduating MD in 1613. For the next eight years, until 1621, he was in the service of Claude Dormy (c.1562–1626) the Bishop of Boulogne, in Paris, who paid for him to travel extensively in Germany, Hungary and Transylvania to study the metal mining industry. As well as serving Dormy as physician, he almost certainly acted as his astrologer, this was still in the period when astro-medicine or iatromathematics was the mainstream medical theory.

The tomb of Claude Dormy Source

From 1621 to 1629 he served Philip IV, King of Spain, and Duke of Luxembourg, also probably as astrologer. 

In 1630, he was indirectly asked by Marie de’ Medici, the Queen Mother, to cast a horoscope for her son, Louis XIII, who was seriously ill and whose doctor had predicted, on his own astrological reading, that he would die. Morin’s astrological analysis said that Louis would be severely ill but would survive. Luckily for Morin, his prediction proved accurate, and Marie de’ Medici used her influence to have him appointed professor for mathematics at the Collège Royal in Paris, a position he held until his death in 1656.

Marie de Médici portrait by Frans Pourbus, the Younger Source: Wikimedia Commons

In Paris, Morin he took up his friendship with Gassendi from their mutual student days and even continued to make astronomical observations with him in the 1630s, at the same time becoming a member of the group around Mersenne. However, in my title I have labelled Morin the black sheep of the Provence-Paris group and if we turn to his scholarly activities, it is very clear why. Whereas Peiresc, Mersenne, Boulliau, and Gassendi were all to one degree or another supporters of the new scientific developments in the early seventeenth century, coming to reject Aristotelean philosophy and geocentric astronomy in favour of a heliocentric world view, Morin stayed staunchly conservative in his philosophy and his cosmology.

Already in 1624, Morin wrote and published a defence of Aristotle, and he remained an Aristotelian all of his life. He rejected heliocentricity and insisted that the Earth lies at the centre of the cosmos and does not move. Whereas the others in the group supported the ideas of Galileo and also tried to defend Galileo against the Catholic Church, Morin launched an open attack on Galileo and his ideas in 1630, continuing to attack him even after his trial and house arrest. In 1638, he also publicly attacked René Descartes and his philosophy, not critically like Gassendi, but across-the-board, without real justification. He famously wrote that he knew that Descartes philosophy was no good just by looking at him when they first met. This claim is typical of Morin’s character, he could, without prejudice, be best described as a belligerent malcontent. Over the years he managed to alienate himself from almost the entire Parisian scholarly community. 

It would seem legitimate to ask, if Morin was so pig-headed and completely out of step with the developments and advances in science that were going on around him, and in which his friends were actively engaged, why bother with him at all? Morin distinguished himself in two areas, one scientific the other pseudo-scientific and it is to these that we now turn.

The scientific area in which made a mark was the determination of longitude. With European seamen venturing out into the deep sea for the first time, beginning at the end of the fifteenth century, navigation took on a new importance. If you are out in the middle of one of the Earth’s oceans, then being able to determine your exact position is an important necessity. Determining one’s latitude is a comparatively easy task. You need to determine local time, the position of the Sun, during the day, or the Pole Star, during the night and then make a comparatively easy trigonometrical calculation. Longitude is a much more difficult problem that relies on some method of determining time differences between one’s given position and some other fixed position. If one is one hour time difference west of Greenwich, say, then one is fifteen degrees of longitude west of Greenwich. 

Finding a solution to this problem became an urgent task for all of the European sea going nations, including France, and several of them were offering substantial financial rewards for a usable solution. In 1634, Morin suggested a solution using the Moon as a clock. The method, called the lunar distance method or simply lunars, was not new and had already suggested by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524.

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. Another method that was under discussion was taking time with you in the form of an accurate clock, as first proposed by Gemma Frisius (1508–1555), Morin did not think much of this idea:

“I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.”

Morin was well aware of the difficulties involved and suggested a comprehensive plan to overcome them. Eager to win the offered reward money, Morin put his proposal to Cardinal Richelieu (1585–1642), Chief Minister and most powerful man in France. Morin suggested improved astronomical instruments fitted out with vernier scales, a recent invention, and telescopic sights, also comparatively new, along with improvements in spherical trigonometry. He also suggested the construction of a national observatory, with the specific assignment of collected more accurate lunar data. Richelieu put Morin’s proposition to an expert commission consisting of Étienne Pascal (1588–1651), the father of Blaise, Pierre Hérigone (1580–1643), a Parisian mathematics teacher, and Claude Mydorge (1585–1647), optical physicist and geometer. This commission rejected Morin’s proposal as still not practical, resulting in a five year long dispute between Morin and the commission. It would be another century before Tobias Mayer (1723–1762) made the lunar distance method viable, basically following Morin’s plan.

Although his proposal was rejected, Morin did receive 2000 livre for his suggestion from Richelieu’s successor, Cardinal Mazarin (1602–1661) in 1645. Mazarin’s successor Jean-Baptiste Colbert (1619–1683) set up both the Académie des sciences in 1666 and the Paris Observatory in 1667, to work on the problem. This led, eventually to Charles II setting up the Royal Observatory in Greenwich, in 1675 for the same purpose.

Today, Morin is actually best known as an astrologer. The practice of astrology was still acceptable for mathematicians and astronomers during Morin’s lifetime, although it went into steep decline in the decades following his death. Although an avid astronomer, Peiresc appears to have had no interest in astrology. This is most obvious in his observation notes on the great comet of 1618. Comets were a central theme for astrologers, but Peiresc offers no astrological interpretation of the comet at all. Both Mersenne and Gassendi accepted the scientific status of astrology and make brief references to it in their published works, but neither of them appears to have practiced astrology. Boulliau also appear to have accepted astrology, as amongst his published translations of scientific texts from antiquity we can find Marcus Manilius’ Astronomicom (1655), an astrological poem written about 30 CE, and Ptolemaeus’ De judicandi jacultate (1667). Like Mersenne and Gassendi he appears not to have practiced astrology.

According to Morin’s own account, he initially thought little of astrology, but around the age of thirty he changed his mind and then spent ten years studying it in depth.

Jean-Baptiste Morin’s with chart as cast by himself

He then spent thirty years writing a total of twenty-six volumes on astrology that were published posthumously as one volume of 850 pages in Den Hague in 1661, as Astrologia Galllica (French Astrology). Like Regiomontanus, Tycho Brahe, and Kepler before him, he saw astrology as in need of reformation and himself as its anointed reformer. 

Source: Wikimedia Commons

The first eight volumes of Astrologia Galllica hardly deal with astrology at all but lay down Morin’s philosophical and religious views on which he bases his astrology. The remaining eighteen volumes then deal with the various topics of astrology one by one. Central to his work is the concept of directio in interpreting horoscopes. This is a method of determining the times of major events in a subject’s life that are indicated in their birth horoscope. Originally, to be found in Ptolemaeus’ Tetrabiblos, it became very popular during the Renaissance. The standard text was Regiomontanus’ Tabulae Directionum, originally written in 1467, and large numbers of manuscripts can still be found in libraries and archives. It was published in print by Erhard Ratdolt in Augsburg in 1490 and went through eleven editions, the last being published in 1626. Aware of Kepler’s rejection of both the signs of the zodiac and the system of houses, Morin defends both of them.

Coming, as it did at a time when astrology was in decline as an accepted academic discipline, Morin’s Astrologia Galllica had very little impact in the seventeenth century, but surprisingly, in English translation, it enjoys a lot of popularity amongst modern astrologers.

Morin was cantankerous and belligerent, which cost him most of his contacts with the contemporary scholars in Paris and his adherence to Aristotelian philosophy and a geocentric world view put him out of step with the rest of the Provence-Paris group, but he certainly didn’t suffer from a lack of belief in his own abilities as he tells us in this autobiographical quote:

“… I am excessively inclined to consider myself superior to others on account of my intellectual endowments and scientific attainments, and it is very difficult for me to struggle against this tendency, except when the realization of my sins troubles me, and I see myself a vile man and worthy of contempt. Because of all this my name has become famous throughout the world.”

 

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Filed under History of Astrology, History of Astronomy, History of medicine, History of Navigation

OHMS or everything you wanted to know about the history of trigonometry and didn’t know who to ask

When I was a kid, letters from government departments came in buff, manila envelopes with OHMS printed on the front is large, black, capital letters. This acronym stood for, On Her Majesty’s Service and earlier during Liz’s father’s reign (and no I’m not that old, although I was just born in his reign), On His Majesty’s Service, implying that civil servants worked directly for the monarch.  This was, of course, the origin of the title of Ian Fleming’s eleventh James Bond novel, On Her Majesty’s Secret Service

When I started learning trigonometry at school this acronym took on a whole new meaning as a mnemonic for the sine relation in right angle triangles, Opposite over Hypotenuse Means Sine. Recently it occurred to me that we had no mnemonic for the other trigonometric relations. Now in those days or even later when the trigonometry I was taught got more complex, I wasn’t aware of the fact that this mathematical discipline had a history. Now, a long year historian of mathematics, I am very much aware of the fact that trigonometry has a very complex, more than two-thousand-year history, winding its way from ancient Greece over India, the Islamic Empire and Early Modern Europe down to the present day. 

The Canadian historian of mathematics, Glen van Brummelen has dedicated a large part of his life to researching, writing up and publishing that history of trigonometry. The results of his labours have appeared in three volumes, over the years, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, Princeton and Oxford, 2013 and most recently The Doctrine of TrianglesA History of Modern Trigonometry, Princeton University Press, Princeton and Oxford, 2021. He describes himself as the “best trigonometry historian, and the worst trigonometry historian”, as he is the only one[1]

A review of these three volumes could be written in one sentence, if you are interested in the history of trigonometry, then these three masterful volumes are essential. One really doesn’t need to say more, but in what follows I will give a brief sketch of each of the books. 

The Mathematics of the Heavens and the Earth: The Early History of Trigonometry delivers exactly what it says on the cover. The book opens with a brief but detailed introduction to the basics of spherical astronomy, because for a large part of the period covered, what we have is not the history of plane trigonometry, that’s the stuff we all learnt at school, but spherical trigonometry, that is the geometry of triangles on the surface of a sphere, which was developed precisely to do spherical astronomy. 

A friendly warning for potential readers this is not popular history but real, hardcore history of mathematics with lots of real mathematical examples worked through in detail. However, given the way Van Brummelen structures his narrative, it is possible to skip the worked examples and still get a strong impression of the historical evolution of the discipline. This is possible because Van Brummelen gives a threefold description of every topic that he elucidates. First comes a narrative, fairly non-technical, description of the topic he is discussing. This is followed by an English translation of a worked example from the historical text under discussion, followed in turn by a technical explication of the text in question in modern terminology. Van Brummelen’s narrative style is clear and straightforward meaning that the non-expert reader can get good understanding of the points being made, without necessarily wading through the intricacies of the piece of mathematics under discussion. 

The book precedes chronologically. The first chapter, Precursors, starts by defining what trigonometry is and also what it isn’t. Having dealt with the definitions, Van Brummelen moves onto the history proper dealing with things that preceded the invention of trigonometry, which are closely related but are not trigonometry. 

Moving on to Alexandrian Greece, Van Brummelen takes the reader through the beginnings of trigonometry starting with Hipparchus, who produced the first chord table linking angles to chords and arcs of circles, Moving on through Theodosius of Bithynia and Menelaus of Alexandria and the emergence of spherical trigonometry. He then arrives at Ptolemy his astronomy and geography. Ptolemy gets the longest section of the book, which given that everything that follows in some way flows from his work in logical. Here we also get two defining features of the book. The problem of calculating trigonometrical tables and what each astronomer or mathematician contributed to this problem and the trigonometrical formulas that each of them developed to facilitate calculations. 

From Greece we move to India and the halving of Hipparchus’ and Ptolemy’s chords to produce the sine function and later the cosine that we still use today. Van Brummelen takes his reader step for step and mathematician for mathematician through the developments of trigonometry in India. 

The Islamic astronomers took over the baton from the Indians and continued the developments both in astronomy and geography. It was Islamic mathematicians, who developed the plane trigonometry that we know today rather than the spherical trigonometry. As with much other mathematics and science, trigonometry came into medieval Europe through the translation movement out of Arabic into Latin. Van Brummelen traces the development in medieval Europe down to the first Viennese School of mathematics, John of Gmunden, Peuerbach, and Regiomontanus. This volume closes with Johannes Werner and Copernicus, with a promise of a second volume. 

In the book itself, the brief sketch above is filled out in incredible detail covering all aspects of the evolution of the discipline, the problems, the advances, the stumbling stones and the mathematicians and astronomers, who discovered each problem, solved, or failed to solve them. To call Van Brummelen comprehensive would almost be an understatement. Having finished this first volume, I eagerly awaited the promised second volume, but something else came along instead.

Having made clear in his first book that the emphasis is very much on spherical trigonometry rather than plane trigonometry, in his second book Van Brummelen sets out to explain to the modern reader what exactly spherical trigonometry is, as it ceased to be part of the curriculum sometime in the modern period. What we have in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry is a spherical trigonometry textbook written from a historical perspective. The whole volume is written in a much lighter and more accessible tone than The Mathematics of the Heavens and the Earth. After a preface elucidating the purpose of the book there follow two chapters, Heavenly Mathematics and Exploring the Sphere, which lay out and explain the basics in clear and easy to follow steps.

Next up, we have the historical part of the book with one chapter each on The Ancient Approach and The Medieval Approach. These chapters could be used as an aid to help understand the relevant sections of the authors first book. But fear not the reader must not don his medieval personality to find their way around the complexities of spherical trigonometry because following this historical guide we are led into the modern textbook.

The bulk of the book consists of five chapters, each of which deals in a modern style with an aspect of spherical trigonometry: Right Angle Triangles, Oblique Triangles, Areas, Angles and Polyhedra, Stereographic Projection, and finally Navigation by the Stars. The chapter on stereographic projection is particularly interesting for those involved with astrolabes and/or cartography. 

The book closes with three useful appendices. The first is on Ptolemy’s determination of the position of sun. The second is a bibliography of textbooks on or including spherical trigonometry with the very helpful indication, which of them are available on Google Books. The final appendix is a chapter by chapter annotated list of further reading on each topic. 

If you wish to up your Renaissance astrology game and use the method of directions to determine your date of death, which require spherical trigonometry to convert from one celestial coordinate system to another, then this is definitely the book for you. It is of course also a brilliant introduction for anybody, who wishes to learn the ins and outs of spherical trigonometry. 

I bought Van Brummelen’s first book when it was published, in 2009, and read it with great enthusiasm, but experienced a sort of coitus interruptus, when in stopped in the middle of the Renaissance, the period that interested me most. I was consoled by the author’s declaration that a second volume would follow, which I looked forward to with great expectations. Over the years those expectations dimmed, and I began to fear that the promised second volume would never appear, so I was overjoyed when the publication of The Doctrine of Triangles was announced this year and immediately placed an advanced order. I was not disappointed. 

The modern history of trigonometry continues where the early history left off, tracing the developments of trigonometry in Europe from Regiomontanus down to Clavius and Gunter in the early seventeenth century. There then follows a major change of tack, as Van Brummelen delves into the origins of logarithms.

Today in the age of the computer and the pocket calculator, logarithmic tables are virtually unknown, a forgotten relic of times past. I, however, grew up using my trusty four figure log tables to facilitate calculations in maths, physics, and chemistry. Now, school kids only know logarithms as functions in analysis. One thing that many, who had the pleasure of using log tables, don’t know is that Napier’s first tables were of the logarithms of trigonometrical factions in order to turn the difficult multiplications and divisions of sines, cosines et al in spherical trigonometry into much simpler additions and subtractions and therefore Van Brummelen’s detailed presentation of the topic.

Moving on, in his third chapter, Van Brummelen now turns to the transition of trigonometry as a calculation aid in spherical and plane triangles to trigonometrical functions in calculus. There where they exist in school mathematics today. Starting in the period before Leibniz and Newton, he takes us all the way through to Leonard Euler in the middle of the eighteenth century. 

The book now undergoes a truly major change of tack, as Van Brummelen introduces a comparative study of the history of trigonometry in Chinese mathematics. In this section he deals with the Indian and Islamic introduction of trigonometry into China and its impact. How the Chinese dealt with triangles before they came into contact with trigonometry and then the Jesuit introductions of both trigonometry and logarithms into China and to what extent this influenced Chinese geometry of the triangle. A fascinating study and an enrichment of his already excellent book.

The final section of the book deals with a potpourri of developments in trigonometry in Europe post Euler. To quote Van Brummelen, “A collection of short stories is thus more appropriate here than a continuous narrative.” The second volume of Van Brummelen’s history is just as detailed and comprehensive as the first. 

All three of the books display the same high level of academic rigour and excellence. The two history volumes have copious footnotes, very extensive bibliographies, and equally extensive indexes. The books are all richly illustrated with many first-class explanatory diagrams and greyscale prints of historical title pages and other elements of the books that Van Brummelen describes. All in all, in his three volumes Van Brummelen delivers a pinnacle in the history of mathematics that sets standards for all other historians of the discipline. He really does live up to his claim to be “the best historian of trigonometry” and not just because he’s the only one.

Coda: If the potential reader feels intimidated by the prospect of the eight hundred and sixty plus pages of the three volumes described here, they could find a gentle entry to the topic in Trigonometry: A Very Short Introduction (OUP, 2020), which is also authored by Van Brummelen, a sort of Van Brummelen light or Van Brummelen’s greatest hits.

In this he covers a wide range of trigonometrical topics putting them into their historical context. But beware, reading the Very Short Introduction could well lead to further consumption of Van Brummelen’s excellent work. 


[1] This is not strictly true as Van Brummelen has at least two predecessors both of who he quotes in his works. The German historian Anton von Braunmühl, who wrote several articles and a two volume Vorlesung über Geschichte der Trigonometrie (Leipzig, 1900/1903) and the American Sister Mary Claudia Zeller, The Development of Trigonometry from Regiomontanus to Pitiscus (Ann Arbor 1944)

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Filed under History of Astronomy, History of Cartography, History of Islamic Science, History of Mathematics, History of Navigation

The amateur, astronomical, antiquarian aristocrat from Aix

In a recent blog post about the Minim friar, Marin Mersenne (1588–1648), I mentioned that when Mersenne arrived in Paris in 1619 he was introduced to the intellectual elite of the city by Nicolas-Claude Fabri de Peiresc (1580-1637). In another recent post on the Republic of Letters I also mentioned that Peiresc was probably, the periods most prolific correspondent, with more than ten thousand surviving letters. So, who was this champion letter writer and what role did he play in the European scientific community in the first third of the seventeenth century?

Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

Nicolas-Claude Fabri was born, into a family of lawyers and politicians, in the town Belgentier near Toulon on 1 December in 1580, where his parents had fled to from their hometown of Aix-en-Provence to escape the plagues. He was educated at Aix-en-Provence, Avignon, and the Jesuit College at Tournon. Having completed his schooling, he set off to Padua in Italy, nominally to study law, but he devoted the three years, 1600–1602, to a wide-ranging, encyclopaedic study of the history of the world and everything in it. 

In this he was aided in that he became a protégé of Gian Vincenzo Pinelli (1535–1601) a humanist scholar and book collector, his library numbered about 8,500 printed works, with all-embracing intellectual interests, whose main areas were botany, optics, and mathematical instruments.

Gian Vincènzo Pinelli Source: Rijksmuseum via Wikimedia Commons

Pinelli introduced Fabri to many leading scholars including Marcus Welser (1558–1614), Paolo Sarpi (1552–1623) and indirectly Joseph Scaliger (1540–1609). Pinelli also introduced him to another of his protégés, Galileo Galilei (1564–1642). One should always remember that although he was thirty-eight years old in 1602, Galileo was a virtually unknown professor of mathematics in Padua. When Pinelli died, Fabri was living in his house and became involved in sorting his papers.

In 1602, Fabri returned to Aix-en-Provence and completed his law degree, graduating in 1604. In the same year he assumed the name Peiresc, it came from a domain in the Alpes-de-Haute-Provence, which he had inherited from his father. He never actually visited Peiresc, now spelt Peyresq.

Village of Peyresq Source: Wikimedia Commons

Following graduation Peiresc travelled to the Netherlands and England via Paris, where he made the acquaintance of other notable scholars, including actually meeting Scaliger and also meeting the English antiquarian and historian William Camden (1551–1623).

Returning to Provence, in 1607, he took over his uncle’s position as conseiller to the Parliament of Provence under his patron Guillaume du Vair (1556–1621), cleric, lawyer, humanist scholar and president of the parliament.

Guillaume-du-Vair Source: Wikimedia Commons

In 1615 he returned to Paris with du Vair as his secretary, as du Vair was appointed keeper of the seals during the regency of Marie de’ Medici (1575–1642). Peiresc continued to make new contacts with leading figures from the world of scholarship, and the arts, including Peter Paul Rubens (1577–1640).

Peter Paul Rubens self-portrait 1623

Peiresc acted as a go between in the negotiations between Reubens and the French court in the commissioning of his Marie de’ Medici Cycle. Just one of Peiresc’s many acts of patronage in the fine arts.

Marie de’ Medici Cycle in the Richelieu wing of the Louvre Source: Wikimedia Commons

In 1621 de Vair died and in 1623 Peiresc returned to Provence, where he continued to serve in the parliament until his death in 1637.

Peiresc was an active scholar and patron over a wide range of intellectual activities, corresponding with a vast spectrum of Europe’s intellectual elite, but we are interested here in his activities as an astronomer. Having developed an interest for astronomical instruments during his time as Pinelli’s protégé, Peiresc’s astronomical activities were sparked by news of Galileo’s telescopic discoveries, which reached him before he got a chance to read the Sidereus Nuncius. He rectified this lack of direct knowledge by ordering a copy from Venice and borrowing one from a friend until his own copy arrived.

Source: Wikimedia Commons

He immediately began trying to construct a telescope to confirm or refute Galileo’s claims, in particular the discovery of the first four moons of Jupiter. At this point in his life Peiresc was still a geocentrist, later he became a convinced heliocentrist. We know very little about where and how he acquired his lenses, but we do know that he had various failures before he finally succeeded in observing the moons of Jupiter for himself, in November 1610. In this he was beaten to the punch by his fellow Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix. At this point it is not clear whether the two were competing or cooperating, as they would then later do with Gaultier de la Valette becoming a member of Peiresc’s Provencal astronomical observation group. Shortly thereafter, Peiresc became the first astronomer to make telescopic observations of the Orion Nebular and Gaultier de la Valette the second. This is rather strange as the Orion Nebular is visible to the naked eye. However, apparently none of the telescopic astronomy pioneers had turned their telescopes to it before Peiresc.

In one of the most detailed astronomical images ever produced, NASA/ESA’s Hubble Space Telescope captured an unprecedented look at the Orion Nebula. … This extensive study took 105 Hubble orbits to complete. All imaging instruments aboard the telescope were used simultaneously to study Orion. Source: Wikimedia Commons

Peiresc, like Galileo, realised that the moons of Jupiter could be used as a clock to determine longitude and began an observation programme of the moons, viewing them every single day that the weather conditions permitted, well into 1612. Having compiled tables of his observations he sent one of his own protégés Jean Lombard, about whom little is known, equipped with suitable instruments on a tour of the Mediterranean. Lombard observed the satellites at Marseille in November 1611 and then proceeded to Malta, Cyprus and to Tripoli observing as he went, until May 1612. Meanwhile, Peiresc made parallel observation in Aix and Paris, he hoped by comparing the time differences in the two sets of observations to be able to accurately determine the longitude differences. Unfortunately, the observations proved to be not accurate enough for the purpose and the world would have to wait for Giovanni Domenico Cassini (1625–1712) to become the first to successfully utilise this method of determining longitude. Peiresc’s own observation were, however, the longest continuous series of observations of the Jupiter moons made in the seventeenth century and displayed a high level of accuracy even when compared with this of Galileo.

I mentioned, above, Peiresc’s Provencal astronomical observing group. Peiresc employed/sponsored young astronomers to help him with his observation programmes, supplying them with instruments and instructions on how to use them. This group included such notable, future astronomers, as Jean-Baptiste Morin (1583–1556),

Jean-Baptiste Morin Source: Wikimedia Commons

Ismaël Boulliau (1605–1694),

Ismaël Boulliau Source: Wikimedia Commons

and Pierre Gassendi (1592–1655). Peiresc’s patronage extended well beyond this. Gassendi had held the chair of philosophy at the University of Aix-en-Provence since 1617 but in 1623 the university was taken over by the Jesuits and Gassendi was replaced by a Jesuit and became unemployed.

Portrait of Pierre Gassendi by Louis-Édouard Rioult Source: Wikimedia Commons

From then until he again found regular employment in 1634, Peiresc provided him with a home base in his own house and financed his travels and research. Similarly, Peiresc, having introduced Mersenne to Parisian intellectual circles in 1619, continued to support him financially, Mersenne as a Minim friar had no income, supplying him with instruments and financing his publications. 

Marin Mersenne Source: Wikimedia Commons

Patronage played a central role in Peiresc’s next venture into astronomy and another attempt to solve the longitude problem. There has been much talk in recent decades about so-called citizen science, in which members of the public are invited to participate in widespread scientific activities. Annual counts of the birds in one’s garden is a simple example of this. Citizen science is mostly presented as a modern phenomenon, but there are examples from the nineteenth century. Peiresc had already launched a variation on citizen science in the seventeenth century.

In order to determine longitude Peiresc further developed a method that had been in use since antiquity. Two astronomers situated in different location would observe a lunar or solar eclipse and then by comparing their observations they could determine the local time difference between their observations and thus the longitude difference between the locations. By the seventeenth century predicting eclipses had become a fairly accurate science and Peiresc thought that if he could organise and coordinated a world spanning network of observers to accurately observe and record an eclipse, he could then calculate a world spanning network of longitude measurements. The idea was good in theory but failed in practice.

Most of Peiresc’s team of observers were amateurs–missionaries, diplomats, traders, travellers–whom he supplied with astronomical instruments and written instructions on how to use them, even paying travelling expenses, where necessary. Peiresc organised mass observations for lunar eclipses in 1628, 1634, and 1635 and a solar eclipse in 1633. Unfortunately, many of his observers proved to be incompetent and the results of their observations were too inaccurate to be usable. One positive result was that Peiresc was able to correct the value for the length of the Mediterranean. Before one is too hard on Peiresc’s amateur observers, one should remember that in the middle of the eighteenth century the world’s professional astronomical community basically failed in their attempt to use the transits of Venus to determine the astronomical unit, despite being equipped with much better instruments and telescopes.

Although, Peiresc’s various astronomical activities and their results were known throughout Europe by word of mouth through his various colleagues and his correspondence, he never published any of his work. Quite why, is not really known although there are speculations.

Peiresc was a high ranking and highly influential Catholic and he applied that influence in attempts to change the Church’s treatment of astronomers he saw as being persecuted. He interceded on behalf Tommaso Campanella (1568–1639), actively supporting him when he fled to France in 1634.

Tommaso Campanella portrait by Francesco Cozza Source: Wikimedia Commons

More famously he personally interceded with the Church on behalf of Galileo, without any great success.

Nicolas-Claude Fabri de Peiresc’s career is, like that of his friend Mersenne, a good illustration that the evolution of science is a product of widespread cooperation of a community of practitioners and not the result of the genial discoveries of a handful of big names, as it is unfortunately too often presented. Morin, Boulliau, Gassendi and Mersenne, who all made serious contributions to the evolution of science in the seventeenth century, did so with the encouragement, guidance, and very active support of Peiresc.

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Filed under History of Astronomy, History of Navigation, History of science, Renaissance Science, The Paris Provencal Connection

The alchemist, who became a cosmographer

As an Englishman brought up on tales, myths and legends of Francis Drake, Walter Raleigh, Admiral Lord Nelson, the invincible Royal Navy and Britannia rules the waves, I tend not to think about the fact that Britain was not always a great seafaring nation. As an island there were, of course, always fisher boats going about their business in the coastal waters and archaeology has shown us that people have been crossing the strip of water between Britain and the continent, as long as the island has been populated. However, British sailors only really began to set out onto the oceans for distant lands in competition to their Iberian brethren during the Early Modern Period. Before the start of these maritime endeavours there was a political movement in England to get those in power to take up the challenge and compete with the Spanish and the Portuguese in acquiring foreign colonies, gold, silver and exotic spices. One, today virtually unknown, man, whose writings played a not insignificant role in this political movement was the alchemist Ricard Eden[1] (c. 1520–1576).

Richard Eden[2] was born into an East Anglian family of cloth merchants and clerics, the son of George Eden a cloth merchant. He studied at Christ’s College Cambridge (1534–1537) and then Queen’s College, where he graduated BA in 1538 and MA in 1544. He studied under Sir Thomas Smith (1533–1577) a leading classicist of the period, who was also politically active and a major supporter of colonialism, which possibly influenced Eden’s own later involvement in the topic.

Sir_Thomas_Smith,_ob._1577_(c._early_19th_century)

A c. 19th-century line engraving of Sir Thomas Smith. Source: Wikimedia Commons

Through Smith, Eden was introduced to John Cheke (1514–1557), Roger Ascham (c. 1515–1568) and William Cecil (1520–1598), all of whom were excellent classicists and statesmen. Cecil would go on under Elizabeth I to become the most powerful man in England. From the beginning Eden moved in the highest intellectual and political circles.

After leaving Cambridge Eden was appointed first to a position in the Treasury and then distiller of waters to the royal household, already indicating an interest in and a level of skill in alchemy. Eden probably acquired his interest in alchemy from his influential Cambridge friends, who were all eager advocates of the art. However, he lost the post, probably given to someone else by Somerset following Henry VIII’s death in 1547 and so was searching for a new employer or patron.

Through a chance meeting he became acquainted with the rich landowner Richard Whalley, who shared his interest in alchemy. Whalley provided him with a house for his family and an income, so that he could devote himself to both medicinal and transmutational alchemy. His activities as an alchemist are not of interest here but one aspect of his work for Whalley is relevant, as it marked the beginning of his career as a translator.

Whalley was obviously also interested in mining for metal ores, because he commissioned Eden to translate the whole of Biringuccio’s Pirotechnia into English. Although he denied processing any knowledge of metal ores, Eden accepted the commission and by 1552 he had completed twenty-two chapters, that is to the end of Book 2. Unfortunately, he lent the manuscript to somebody, who failed to return it and so the project was never finished. In fact, there was no English translation of the Pirotechnia before the twentieth century. Later he produced a new faithful translation of the first three chapters dealing with gold, silver and copper ores, only omitting Biringuccio’s attacks on alchemy, for inclusion, as we shall see, in one of his later works.

800px-de_la_pirotechnia_1540_title_page_aq1_1

Title page, De la pirotechnia, 1540, Source: Science History Museum via Wikipedia Commons

In 1552, Eden fell out with Whalley and became a secretary to William Cecil. It is probable the Cecil employed him, as part of his scheme to launch a British challenge to the Iberian dominance in global trade. In his new position Eden now produced a translation of part of Book 5 of Sebastian Münster’s Cosmographia under the title A Treatyse of the New India in 1553. As I explained in an earlier blog post Münster’s Cosmographia was highly influential and one of the biggest selling books of the sixteenth century.

treatyseofnewein00mnst

This first cosmographical publication was followed in 1555 by his The Decades of the newe worlde or west India, containing the nauigations and conquests of the Spanyardes… This was a compendium of various translations including those three chapters of Biringuccio, probably figuring that most explorers of the Americas were there to find precious metals. The main parts of this compendium were taken from Pietro Martire d’Anghiera’s De orbe novo decades and Gonzalo Fernández de Oviedo y Valdés’ Natural hystoria de las Indias.

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Source: The British Library

Pietro Martire d’Anghiera (1457–1526) was an Italian historian in the service of Spain, who wrote the first accounts of the explorations of Central and South America in a series of letters and reports, which were published together in Latin. His De orbe novo (1530) describes the first contacts between Europeans and Native Americans.

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Source: Wikimedia Commons

Gonzalo Fernández de Oviedo y Valdés (1478–1557) was a Spanish colonist, who arrived in the West Indies a few years after Columbus. His Natural hystoria de las Indias (1526) was the first text to introduce Europeans to the hammock, the pineapple and tobacco.

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MS page from Oviedo’s La Natural hystoria de las Indias. Written before 1535, this MS page is the earliest known representation of a pineapple Source: Wikimedia Commons

Important as these writings were as propaganda to further an English involvement in the new exploration movement in competition to the Iberian explorers, it was probably Eden’s next translation that was the most important.

As Margaret Schotte has excellently documented in her Sailing School (Johns Hopkins University Press, 2019) this new age of deep-sea exploration and discovery led the authorities in Spain and Portugal to the realisation that an active education and training of navigators was necessary. In 1552 the Spanish Casa de la Contratación established a formal school of navigation with a cátedra de cosmografia (chair of cosmography). This move to a formal instruction in navigation, of course, needed textbooks, which had not existed before. Martín Cortés de Albacar (1510–1582), who had been teaching navigation in Cádiz since 1530, published his Breve compendio de la sphere y de la arte de navegar in Seville in 1551.

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Retrato de Martín Cortés, ilustración del Breve compendio de la sphera y de la arte de navegar, Sevilla, 1556. Biblioteca Nacional de España via Wikimedia Commons

In 1558, an English sea captain from Dover, Stephen Borough (1525–1584), who was an early Artic explorer, visited Seville and was admitted to the Casa de la Contratación as an honoured guest, where he learnt all about the latest instruments and the instruction for on going navigators. On his return to England, he took with him a copy of Cortés’ Breve compendio, which he had translated into English by Richard Eden, as The Arte of Navigation in 1561. This was the first English manual of navigation and was immensely popular going through at least six editions in the sixteenth century.

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In 1562, Eden became a companion to Jean de Ferrières, Vidame of Chartres, a Huguenot aristocrat, who raised a Protestant army in England to fight in the French religious wars. Eden, who was acknowledged as an excellent linguist, stayed with de Ferrières until 1573 travelling extensively throughout France and Germany. Following the St. Batholomew’s Day massacre, which began in the night of 23–24 August 1572, Eden together with de Ferrières party fled from France arriving in England on 7 September 1573. At de Ferrières request, Elizabeth I admitted Eden to the Poor Knights of Windsor, a charitable organisation for retired soldiers, where he remained until his death in 1576.

After his return to England Eden translated the Dutch musician and astrologer, Jean Taisnier’s Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuio, which was a plagiarism of Petrus Peregrinus de Maricourt’s (fl. 1269) Epistola de magnete and a treatise on the fall of bodies by Giambattista Benedetti (1530–1590) into English.

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This was published posthumously together with his Arte of Navigation in 1579. His final translation was of Ludovico de Varthema’s (c. 1470–1517) Intinerario a semi-fictional account of his travels in the east. This was published by Richard Willes in The History of Travayle an enlarged version of his Decades of the newe worlde in 1577.

Eden’s translations and publications played a significant role in the intellectual life of England in the sixteenth century and were republished by Richard Hakluyt (1553–1616) in his The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation (1589, 1598, 1600), another publication intended as propaganda to promote English colonies in America.

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Unlike Sebastian Münster or Richard Hakluyt, Eden has been largely forgotten but he made important and significant contributions to the history of cosmography and deserves to be better known.

[1] I want to thank Jenny Rampling, whose book The Experimental Fire, which I reviewed here, made me aware of Richard Eden, although, I have to admit, he turns up, managing to slip by unnoticed in other books that I own and have read.

[2] The biographical details on Eden are mostly taken from the ODNB article. I would like to thank the three wonderful people, who provided me with a pdf of this article literally within seconds of me asking on Twitter

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Filed under Early Scientific Publishing, History of Cartography, History of Navigation

Renaissance Science – V

According to the title, this series is supposed to be about Renaissance science but as we saw in the last episode the Renaissance started off as anything but scientific, so what exactly is Renaissance science, does it even exist, and does it actually have anything to do with the language and linguistics movement that kicked of the period that is now known as the Renaissance? I will start with the second of these questions and return later to the other two.

The history of science in its present form is actually a very young discipline, which really only came to fruition in the twentieth century. There are of course early elements of the discipline scattered around the past but the structured academic discipline as we know it only really began in the decades between the two world wars and came to maturity following the second world war. The early discipline was of course very euro-centric, and a major element was the so-called scientific revolution, which was initially seen as a single historical block. Maria Boas Hall (1919–2009) was, as far as I know, the first to divide that block into two parts, a sort of proto scientific revolution, her The Scientific Renaissance 1450–1630 (published, 1962), followed by the full scientific revolution. She was followed in this bifurcation by Peter Dear in his book Revolutionizing the Sciences: European Knowledge in Transition 1500–1700 (originally 2001, 3rd ed. 2019), who sees two phases, 1500-1600 and 1600-1700. These two books established, I think correctly, the idea of a separate Scientific Renaissance, which preceded the Scientific Revolution.

So, what is the nature of this Renaissance science, how did it differ from the existing medieval science and what changed and when going forward into the so-called scientific revolution? There is quite a lot to unpack here and the first thing we need to do is to stop talking about science and instead talk about knowledge, the more correct translation of the Latin term, scientia used in this period. Also, within the scope of scientia, what we might regard as the areas of hard science, which Aristotle called physics, meaning the study of nature, should more appropriately be referred to as natural philosophy. However, medieval natural philosophy was a very restricted area, it included cosmology but did not for example include astronomy, which was a mathematical discipline. Aristotle rejected mathematics as scientia, because its objects were not real. The mathematical disciplines, such as astronomy and optics, were not regarded as belonging to natural philosophy but were given a sort of halfway status. Natural philosophy also didn’t include any of what we would now call the life sciences.

Knowledge in the European medieval context was divided into two completely distinct areas, which didn’t intersect in anyway. On the one side there was the knowledge propagated by the medieval universities, which, as I explained in an earlier post, was almost totally theoretical book knowledge, with almost no practical aspects to it at all. This knowledge was not static, as it is often falsely presented, but evolved over time. However, this evolution was also a theoretical process. The knowledge progressed through debate and the application of argumentation and logic, not through the acquisition of new empirical facts.

The other area of knowledge was artisanal knowledge, that is the knowledge of the maker, the craftsman. This knowledge was empirical and practical, consisting of directions or instruction on how to complete a given task, how to achieve a given aim or fulfil a given assignment. It might, for example, be how to make bricks out of clay, or how to build a stone arch that would be stable and not collapse under load. This knowledge covered a vast range of activities and had been accumulated from a very wide range of sources over virtually the whole of human existence. This knowledge was, traditional, rarely written down but was usually passed on by word of mouth and direct training from master to apprentice, often from father to son over many generations. This knowledge was in general not viewed as knowledge by scholars within the university system.

Starting around fourteen hundred a process of what we would today call crossover began between these two previously distinct and separate areas of knowledge. Scholars began to write learned works about specific areas of artisanal knowledge, a classic example being Georgius Agricola’s De re metallica, published posthumously in 1556, and craftsmen began to write books explaining and elucidating their forms of knowledge, for example the goldsmith Lorenzo Ghiberti’s I commentarii, which remained unfinished in manuscript and unpublished at the time of his death in 1455. It should be noted that before the Renaissance the people we now call artists were regarded as craftsmen. Crossover is here perhaps the wrong term, as people didn’t just cross the boundary in both directions but the boundary itself began to dissolve producing a meld between the two types of knowledge that would over the next two and a half centuries lead to the modern concept of knowledge or science.

What provoked this move towards practical, empirical knowledge during the Renaissance? There are two major areas of development driving this shift in emphasis, as to what constitutes knowledge. The first is general social, political, economical and cultural developments. The rapid increase in long distant trade produced a demand for new methods of navigation and cartography. Changes in concepts of land ownership also drove developments in cartography and the closely associated surveying. Developments in warfare again drove developments in cartography but also in gunnery, a new discipline, and military tactics in general. The invention of gunpowder and with-it military gunnery drove developments in metallurgy, as did other areas where the use of metals increased, for example in the wider use of metal coinage. The greater demand for metals in turn drove the development of mining. Greater wealth in society in general and the perceived need for rulers to display their power through ostentatious display increased the demand for architecture and fine art. The introduction of gunpowder and gunnery also drove the development of architecture because of the need for better defences. These are just some examples of the growing demand for artisanal knowledge within an increasingly urban culture financed by long distance trade.

But what of the movement that gave the Renaissance its name, which we saw was initially language and linguistic based movement, how did this play a role in this move towards the elevation of the status of empirical and practical knowledge if at all? This is in fact our second area of development. Those early Renaissance scholars, who searched for Latin literature texts and orations in the monastic libraries also unearthed Greek and Latin texts on science, technology, mathematics and medicine and in the general renewal of the culture of antiquity also translated and made these texts available, often arguing for their purity in comparison to the texts from the same authors that had come into Europe through the filter of translation into Arabic and then back into Latin. Example of texts that became available for the first time are Vitruvius’ work on architecture De architectura and Ptolemaeus’ Geographia. The latter had been known to the Islamic cartographers but had not been translated into Latin from Arabic during the twelfth century translation movement. As well as bringing new original Greek and Latin manuscripts into circulation the Renaissance scholars introduced a strong empirical element through their philological work. This work was based on an empirical analysis of various copies of a given work as well as an investigation of the plausibility of a given word, phrase or sentence, which didn’t appear to make sense. Beyond this in some areas the Renaissance scholars, as we shall see in more detail later, began to try and understand what the scholars were referring to in specific instances. For example, which plants was Dioscorides referring to in his De meteria medica? The answer to such questions required real empirical research.

The Renaissance opened up a whole new world of practical, empirical knowledge alongside the theoretical book knowledge of the medieval university. The last question is how did this differ from the knowledge of the following period and when did this transition take place?

The emphasis on this Renaissance empirical knowledge was very much on the practical. How can we use it, where and how can it be applied? During the seventeenth century the emphasis changed to one of devising theoretical explanations for all of the freshly won empirical knowledge from the previous two hundred years. The transition is from how do we use or apply it, to how do we explain it. It is impossible to set a firm date for this transition as it was by its very nature a gradual one, so both Boas Hall and Dear are in a certain sense correct with their respective 1630 and 1600. The transition had definitely already begun by 1600 and probably wasn’t finished, yet by 1630. In my case I follow Francis Yates in choosing the end of the Thirty Year’s War in 1648, as I think the transition had been completed by then at the latest.

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

Illuminating medieval science

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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