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“With the sextant he made obeisance to the sun-god”*…



A practice exam in the navigation workbook of C. J. Boombaar (1727–32)


In 1673, in a North Sea skirmish that killed nearly 150 men, the French privateer Jean-François Doublet took a bullet that tossed him from the forecastle and broke his arm in two places. How did the precocious young second lieutenant choose to spend his convalescence? Doublet repaired to the French port city of Dieppe, where he signed up for three months of navigation lessons…

During the 16th to 18th centuries, Europeans embarked on thousands of long-distance sea voyages around the world. These expeditions in the name of trade and colonisation had irreversible, often deadly, impacts on peoples around the globe. Heedless of those consequences, Europeans focused primarily on devising new techniques to make their voyages safer and faster. They could no longer sail along the coasts, taking their directional cues from prominent landmarks (as had been common in the preceding centuries). Nor did they have sophisticated knowledge of waves and currents, as did their counterparts in the Pacific. They had no choice but to figure out new methods of navigating across the open water. Instead of memorising the shoreline, they looked to the heavens, calculating time and position from the sun and the stars.

Celestial navigation was certainly feasible, but it required real technical skills as well as fairly advanced mathematics. Sailors needed to calculate the angle of a star’s elevation using a cross-staff or quadrant. They needed to track the direction of their ship’s course relative to magnetic north. Trigonometry and logarithms offered the best way to make these essential measurements: for these, a sailor needed to be adept at using dense numerical tables. All of a sudden, a navigator’s main skill wasn’t his memory – it was his mathematical ability.

To help the average sailor with these technical computations, maritime administrators and entrepreneurs opened schools in capital cities and port towns across Europe. Some were less formal arrangements, where small groups of men gathered in the teacher’s home, paying for a series of classes over the course of a winter when they were on shore…

How did the sailors of early modern Europe learn to traverse the world’s seas? By going to school and doing maths problems: “When pirates studied Euclid.”

* “With the sextant he made obeisance to the sun-god, he consulted ancient tomes and tables of magic characters, muttered prayers in a strange tongue that sounded like Indexerrorparallaxrefraction, made cabalistic signs on paper, added and carried one, and then, on a piece of holy script called the Grail – I mean, the Chart – he placed his finger on a certain space conspicuous for its blankness and said, ‘Here we are.’ When we looked at the blank space and asked, “And where is that?” he answered in the cipher-code of the higher priesthood, “31 -15 – 47 north, 133 – 5 – 30 west.” And we said, ‘Oh,’ and felt mighty small.”                           – Jack London, The Cruise of the Snark


As we find our way, we might send carefully-calculated birthday greetings to John Locke; he died on this date in 1856.  A namesake of the famous philosopher, Locke trained as a doctor, but turned to geology– and to the invention of scientific, surveying, and navigational instruments, including a surveyor’s compass, a collimating level (Locke’s Hand Level), and a gravity escapement for regulator clocks.  The electro-chronograph he constructed (1844-48) for the United States Coast Survey was installed in the Naval Observatory, Washington, in 1848.  It improved determination of longitudes, as it was able to make a printed record on a time scale of an event to within one one-hundredth of a second.  When connected via the nation’s telegraph system, astronomers could record the time of events they observed from elsewhere in the country, by pressing a telegraph key.

Locke,_John source


Written by LW

July 10, 2019 at 1:01 am

The Venn Piagram…

The pie chart one can eat… from Reddit, via the ever-illuminating Flowing Data

As we reach for our forks, we might spare a reasoned thought for the Enlightenment giant John Locke; the physician and philosopher died on this date in 1704. An intellectual descendant of Francis Bacon, Locke was among the first empiricists. He spent over 20 years developing the ideas he published in his most significant work, Essay Concerning Human Understanding (1690), an analysis of the nature of human reason which promoted experimentation as the basis of knowledge. Locke established “primary qualities” (e.g., solidity, extension, number) as distinct from “secondary qualities” (sensuous attributes like color or sound). He recognized that science is made possible when the primary qualities, as apprehended, create ideas that faithfully represent reality.

Locke is, of course, also well-remembered as a key developer (with Hobbes, and later Rousseau) of the concept of the Social Contract. Locke’s theory of “natural rights” influenced Voltaire and Rosseau– and formed the intellectual basis of the U.S. Declaration of Independence.


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