Author's blog

On this page, observations of various kinds will appear that are related to big history teaching as well as to big history in general.
Earlier blogs
- Big history and web site design
- Did Galileo overstate the magnification of his telescope? 
- Did Columbus falsify his latitude measurements?
- Reflections on observations in big history
- What about questions in learning goals?
- What to think about machines that think?
- Was the Juan de la Cosa map (1500 CE) an instrument to stake claims?
- How can we examine chance and necessity in big history?
- How did Europeans acquire the first accurate nautical charts and Arabic numerals?
- What about experimental history?
The European nautical expansion into the wider world starting in the 1450s CE led to an unprecedented effort of mapping it, first of all its coastlines. Yet while a great deal is known about the early global map makers and their products, such as Martin Waldseemüller, Abraham Ortelius, Gerardus Mercator, and many others, very little seems to be known about how the data were obtained on which these maps were based.
How did those adventurous sailors take such measurements, most notably: how did they chart the unknown coastlines that they encountered? Who were these mariners, and what did their data looked like? And how did these data arrive at the map makers workshops?
So far I have been unable to find any scholarly studies about these matters, while my enquiries among specialists have not yielded anything substantial either. For instance, in his otherwise most interesting book Coast Lines: How Mapmakers Frame the World and Chart Environmental Change (2009), Canadian scholar Mark Monmonier did not even devote one single sentence to these aspects.
Yet it seems to me that the question of how these data were obtained and what they looked like is essential for understanding mapmaking during this period in time.
So how did these salty dogs do all of that? For lack of scholarly studies we can only speculate. Yet some of my speculations seem to be in line with evidence that can be found in contemporary images, which strengthens the impression that this may be a reasonable track to explore.
Earlier I argued that the Mediterranean coastlines may have been partially mapped carefully by Muslims seeking to accurately establish the qibla, the direction to Mecca that is required for their daily prayers. But this was, of course, not a motivation for European sailors seeking to familiarize themselves with unknown coastlines all around the world. They wanted to know what the world looked like for their own purposes, first of all navigation aimed at domination and trade.
Determining reasonably accurate latitudes was not the biggest problem. Taking celestial observations with quadrants on shore yielded a precision of a degree or less already at the time of Columbus, while mariner’s astrolabes could yield a precision of about one degree at sea. But measuring longitudes accurately did remain a big problem, especially onboard a sailing ship.
Already in the sixteenth century the Spanish made valiant efforts to determine longitude in their new colonies using lunar eclipses, as described in the excellent book Secret Science: Spanish Cosmography and the New World by Dr. María Portuondo (2009), pp. 229-236.
In combination with sailed distances and mapped coastlines this yielded the information on which the first reasonably accurate maps of the Americas were based. Yet it seems to be unknown how exactly those coastlines were mapped and what the resulting data looked like.
Measuring longitudes on land became more reliable after Galileo's method of using the moons of Jupiter as a celestial clock had come into use in the seventeenth century. All of that required a great deal of skillful work, which was not always available.
On board, however, none of these methods worked very well, because it was hard to keep an eye on Jupiter and its satellites through a telescope on the deck of a moving ship, if visible at all (Jupiter does not always appear in the sky at night), while suitable lunar eclipses happen only very sporadically.
As a result, measuring longitude on the high seas remained a problem until reliable chronometers were invented in the middle of the nineteenth century, even though a century earlier the method of measuring lunar distances had already solved this problem to some extent. Yet also the moon is not always visible in the sky. In consequence, much like the tracking of Jupiter's moons, the method of measuring lunar distances was similarly limited.
While it remained unclear for a long time where exactly the unknown coastlines were situated on the globe, for obvious reasons it was important to map them. Ashore, it is relatively easy to do so using the method of triangulation proposed in 1533 CE by Dutch scholar Gemma Frisius (1508-1555 CE), while teaching at Louvain University, now in Belgium.
Surely, the Spanish and Portuguese may have started doing so on land whenever feasible and judged necessary. That may have yielded excellent coastlines, yet no data of such efforts seem to be available. This description shows how the British sea captain and explorer James Cook did it, much later, in the 1760s.

More likely than not, in the sixteenth and seventeenth centuries the opportunities for doing so on land by the seafaring predecessors of captain Cook were often not sufficiently available, simply because there were often no good places to go ashore or no pressing reasons or sufficient time to do so. So how did these mariners map such coastlines?
In those days, the practical way of charting coastlines consisted of using triangulation from the deck of a ship while sailing along the coast, by measuring a great number of horizontal angles between clearly recognizable points such as mountain tops, islands, inlets, etc. This method is known as the running traverse, of which remarkable little information appears to be available on the Internet.
If one knows the baseline, such as the distance covered by one's ship sailing along the coast, and also its positions during the measurements, this can yield a reliable coastline chart. Coastlines charted in the sixteenth century with the aid of the running traverse  can sometimes be recognized on old maps, since they show inlets as semi-circles (because these were not yet well known), while markers used on the coastlines may also show up.
On land, triangulation works well, because it is possible to position one’s instruments in stable ways on fixed points for longer periods of time. As a result, a high degree of accuracy can be obtained with the aid of instruments that could measure precise angles. But how could such angles reliably be measured on a moving and shaking ship, while the sailed distances could also be determined much less accurately?
By using a directional compass with a movable visor with sights attached to it, it is, in principle, possible to do this also onboard. This was the method recommended by Gemma Frisius, and later also in navigational handbooks.
Yet the ship’s movements make such observations a little difficult to do in practice, because they may contain relatively large errors as a result of the ship's movements, and also because compass angles cannot be read very precisely. The variation and deviation of the compass readings introduced further complications.
Yet such compasses may well have been used during early attempts at charting unknown coastlines, including by Columbus and those who followed him, to obtain basic coordinates.
Quadrants and mariner’s astrolabes can also be used for this purpose to some extent, and may have been used to do so as well. But they are far less handy, while also in such cases the precision must have left a lot to be desired because of the ship’s movements as well as because of the problems of reading the instrument scales accurately.
So how may these unknown seafaring explorers have performed their triangulation measurements, if that is what they did?
In 2014 CE, as part of my experiments with replicas of ancient navigational instruments, I built a so-called cross-staff. Such an instrument consists of a wooden stick with markers on it, over which a perpendicularly mounted stick, called a vane, can slide.
Observing both ends of the vane and lining it up with the objects to be measured by sliding the vane into the required position allows one to measure the angle between those two objects, such as the altitude of the sun or of certain stars above the horizon.

Although the design was (at least) centuries older, from about 1515 CE the cross-staff was introduced on board Portuguese ships, and soon also on Spanish vessels, for navigational purposes, where it began to replace quadrants and mariner’s astrolabes (The Cross-Staff: History and Development of a Navigational Instrument by W.F.J. Mörzer Bruyns, 1994, Walburg Pers,  p.14). The cross-staff was a relatively cheap instrument, while it yielded more accurate readings than its predecessors, which helps to explain its rapid introduction.

From the 1730s CE onward, the cross-staff was, in its turn, replaced by octants, followed by sextants, because those instruments yielded even more precise angle measurements. Sextants remained in general use among seafarers until the 1980s CE when satellite navigation replaced them. But they are still in use as a back-up option in case the electronic technology fails.
While I was calibrating my cross-staff replica in the spring of 2015 CE by measuring horizontal angles across the Amsterdam horizon as seen from my window and comparing those values with the same angles taken with a Davis Mark 15 sextant, I realized that, in contrast to my quadrant and astrolabe replicas, the cross-staff was well suited for measuring horizontal angles, even on a moving ship.
So was the cross-staff perhaps used for charting coastlines, I wondered, and was that perhaps another reason for its relatively rapid introduction among the European mariners, simply because it yielded a quick, efficient, and relatively precise way of doing so?
How would I find out? My searches on the Internet did not yield any analyses or references that could throw any light on this question. I then consulted one of the world’s foremost experts on the cross-staff, the Dutch scholar Dr. W.F.J. Mörzer Bruyns, former curator of the Maritime Museum Amsterdam, and author of the aforementioned excellent book Cross-Staff: History and Development of A Navigational Instrument.
Interestingly, Dr. Mörzer Bruyns did not know either how such measurements had been obtained or whether the cross-staff had been used for such purposes. His book did not yield any further data other than that the earliest reported use of the cross-staff had been for measuring angles between stars, and between stars and the moon, so for measuring non-vertical angles, for which quadrants and astrolabes were less suitable.
I then started looking at contemporary pictures. Already in 2003 I had taken a picture of a gable stone on a house on the Prins Hendrikkade in Amsterdam, probably dating from eighteenth century, which prominently shows a cross-staff, apparently as a tool of navigation.
Furthermore, in 2014 CE, while being shown around in the Supreme Court in the Hague, to my great surprise I saw a ceiling painting that even more prominently displays the cross-staff. This piece of art called ‘Allegory of Seafaring,’ as I later found out, probably dates from around 1680 CE and was made by Philip Tideman from Hamburg (1657–1705 CE). Also Mörzer Bruyns’s book Cross-staff contains such pictures, most notably on the front cover.
All of that confirms the importance of the cross-staff for contemporary seafaring. But it does not offer any conclusive evidence for its possible use while charting coastlines.
In the spring of 2015 CE I was working on a presentation about the first wave of globalization, for which I had been using a picture of the illustrious map makers Gerardus Mercator and Jodocus Hondius seated at a table in their office. I decided to give that picture a closer look.
And what could be seen in this picture, to my great surprise? On top of the cabinet two cross-staffs are prominently displayed, each of them sitting next to a globe: a celestial globe on the left and a world globe on the right. Next to each of these instruments a roll of paper can be seen, which appears to suggest that on those rolls the data had been recorded that were important for mapping the heavens and the earth by using those instruments.
Of course this does not yet provide conclusive evidence. But it does provide another hint that the hypothesis advanced here could be realistic. Much more research is needed to provide more clarity, most notably in archives by perusing ancient mariner’s journals and logbooks.
Right now, this idea is no more than a hypothesis about how such geographical observations may have been made, at least partially, always supplemented by compass readings from time to time, one would assume.
Whatever the case may turn out to be, these coastal observations must have been made in one way or the other. The question remains how this was done. One would expect that some traces of such measurements must still exist in the archives.
If these ideas turn out to be correct, making replicas of those instruments and attempting to perform ancient measurements may have helped to throw some fresh light onto what the mariners and map makers of old achieved while making their careful measurements and engaging in equally careful scholarly interpretations.

Postscript: chart dividers
In November of 2015 CE, I bought two Portland chart dividers in the Datema nautical store in Amsterdam: a straight chart divider and a curved one, both of which are still used for plotting distances on sea charts. Very similar chart dividers can be seen on that 17th century picture: Mercator holding a straight chart divider, and Hondius a curved one. So this technology is at least 500 years old and still virtually unchanged.
In the Datema store I was told that both the US and British navies as well as Asian maritime businesses still use the curved chart dividers, while the British merchant fleet and mariners from the entire European continent use the straight ones.
Like everything else in the universe, both types of dividers have their pros and cons. The curved chart dividers can be handled more comfortably with one hand, which is why they are designed like that, while the straight chart dividers can cover more distance. It is unknown to me how this division among seafarers originated and has persisted, if this is indeed a correct view. In addition I was told that navigational instructors in the Netherlands still tend to be very firm in their opinions about what the preferred dividers are.
The fact that on the Mercator-Hondius picture both types of dividers are shown indicates that also at that time these two instruments already existed. Perhaps the idea of the depiction was to convey that whatever chart dividers were preferred for whatever reasons, the resulting maps were reliable. In other words, this may have represented an attempt to capture the entire market. It would be interesting to look at other contemporary pictures and see what types of dividers were depicted.
There may well be many further details on that picture that had specific meanings to those who drew it, that have now been lost.
I do not know whether this intriguing little detail has already been noticed by scholars. I have not yet found any references to it, and only noticed it after I started experimenting with chart dividers myself and was further informed about them by experienced sailors. Nothing surpasses experiencing and trying out things oneself, or so it seems to me, or learning from the practical experiences of competent others.
International Big History Association
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Cosmic Evolution
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Bill Bryson: Short History of Nearly Everything
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