“He does smile his face into more lines than is in the new map with the augmentation of the Indies.”
Shakespeare, Twelfth Night, Act III, Scene II (Maria to Toby, referring to Malvolio)
By the end of the 16C maritime references were common. In Twelfth Night, a comedy first performed in 1602, Shakespeare refers, obliquely, to the “new” Mercator maps with their rhumb lines, and assumes his audience will understand. In 1590, after returning from Walter Ralegh’s ill-fated Roanoke colony, Thomas Harriot sought to understand the mathematics of the helical secant lines that Mercator used. (Arianrhod, pp 92-94) How could such an abstruse topic as long distance ocean navigation become a topic that could be used for popular humor as well as mathematical research?
Margaret Schotte’s 2019 book, Sailing School, provides an explanation. Although educated at Harvard and Princeton, Schotte is from Canada. She is a York (Toronto) history professor with an interest in the history of science. Her interest in the history of navigation is personal as well as professional; she has ancestors from the Netherlands and learned to sail on visits to her grandparents home in Halifax. Her book is based on her dissertation thesis, and both the thesis and book received prizes.
One reason navigation became so important is that the only way to profit from the supposed riches of the lands discovered by European explorers in the 15th and 16th centuries was by ship, and those ships had to be able to go and return across oceans. All sea-facing states in the 16C knew how to build ships, but pilot-navigators were scarce. Schotte uses four case studies to show how navigators’ educations evolved between 1550 and 1800. She begins with a brief discussion of the first “sailing school” which was established in Seville in the mid-16C. Her case studies focus on Netherlands (two chapters), France, and England. Another chapter discusses a case involving a British naval ship that hit an iceberg in the South Indian Ocean. Naval training, including navigational training, skill, and luck enabled the captain to bring the ship to port over a two-month journey. An epilogue surveys the arc of navigational education over her time period. Her conclusion is that navigators were made, not born.
In the 16C there was still a debate about how to get more navigators. Some thought the skill was innate, so navigators had to be found; debates focused on the essential qualities, often focused on family status. Others thought navigation was teachable, but there was no agreement on how that was to be accomplished. Schotte’s case studies show how the “navigation is teachable” intuition translated into specific pedagogical and institutional arrangements and how those arrangements changed over time. The major military powers—Spain, France, and England—established state-run schools. Sailing schools in the Netherlands were independent. Unsurprisingly, each country had its own maritime tradition and its own geographical circumstances. For instance, the mercantile interests of the Netherlands had created an extensive trade network throughout the Baltics; knowledge of specific ports, tides, currents, hazards, and coastal landmarks, what was known as “small navigation,” was essential for Dutch navigator-pilots who captained relatively small ships. Navigators on large ships on long ocean voyages needed additional navigational skills; locating a ship in the featureless ocean required specialized instruments and astronomical and mathematical knowledge, i.e., celestial navigation. This developing skill-set, or “large navigation,” was taught at all the sailing schools of the period.
During the roughly 250-year period that is the focus of Schotte’s book, the main problems faced by “large navigation” practitioners were measuring a ship’s speed and its longitude. Latitude could be measured with a crossbar or astrolabe (or an octant or sextant by the late 18C). Direction could be measured with a compass. These tools were well-understood, and their use had long been incorporated into common maritime practice. What was beginning to change was the quality of the instruments, the measurement protocols, and the use of more accurate and easier to use tables to adjust raw observations for the earth’s position in its orbit. Although elements of plane trigonometry had been known since antiquity, practical application to celestial navigation on a sphere, took place primarily in the 17C and required what were considered at the time to be difficult and time-consuming calculations. Logarithms and devices based on them greatly simplified calculation by transforming multiplication and division operations into simpler addition and subtraction, or physical manipulation. By increasing the quality of the tools, procedures, and mathematical techniques, navigators could improve the accuracy of their estimates of latitude. But few tools or techniques were available for estimating speed and longitude; experience, careful observation, and the techniques of dead reckoning remained the primary method used to complete the determination of ship’s position for most of the period.
Over time the curriculum of the sailing schools changed. Initially, the schools’ students were mostly experienced sailors who had multiple years of practical experience; they only needed to be instructed in state-of-the-art navigation techniques and examined for competency. Few early students were literate or numerate, so instruction typically consisted of recitation, demonstration, and discussion. Gradually students became more literate and numerate, and this allowed the schools to incorporate textbooks into their curriculum. This was especially true in the Netherlands (and, to some degree, England) where there was a widespread network of commercial mathematics instructors for students interested in commercial mathematics (basic arithmetic, accounting, weights and measures). Amsterdam was also a major printing location, so navigational textbooks flourished there. As basic literacy and numeracy spread more students of the sailing schools came prepared for more advanced topics and the schools’ instructors obliged. The royal schools in France and England were more centralized, and this led to documentation of the debate over curriculum which Schotte has used to good effect to show change in curricular emphasis over time.
By the end of the 18C, knowledge of celestial navigation had become an essential skill for sailors who wished to be navigators or captains. The baseline level of knowledge and mathematical knowledge was much higher than it had been even in 1700. The instruments were easier to use and more accurate. Speed calculations had been made easier. Marine chronometers were beginning to be used so longitude could be calculated with good accuracy. Navigational expertise was no longer scarce; the sailing schools now had to emphasize judgment and basic maritime skills that had been common among 16C students.
By 1800 thousands of men from many parts of Europe were involved in the maritime effort as sailors, stevedores, and merchants. Schotte estimates that for some large cities one in six men were involved in marine activities. Knowledge of marine activities appears to have been commonplace. Celestial navigation posed interesting and novel problems that drew the attention of mathematicians, physicists, and other natural philosophers. Both playgoers and mathematicians became more familiar with abstract symbols, such as those used in maps (e.g., the rhumb lines that Shakespeare compared to the lines on Malvolio’s face), numbers, and letters. All of this knowledge indicates a growing use of the tools needed for thinking about the natural world in the new “mechanical” way.
