Friday, 11 December 2020

Thomas Harriot and the Roanoke Colony (Revised Notes)

Fittingly near the first expedition to Roanoke area, I just saw in the news recently that there are new leads in a 400+ year old missing persons case, and it involves a famous mathematician.  It was on August 17, 1585 that the Colony of  Roanoke Island was established by the landing of Sir Walter Raleigh's agents led by Ralph Lane(Raleigh actually never visited North America).  Along on the first exploratory mission was John White, who among other things, could draw a pretty good map, one of which is located in the British Museum.    Two year later White returned with more than 100 settlers to Roanoke Island, along the barrier islands that today are called the Outer Banks.

It was the second attempt by Sir Walter Raleigh to settle a colony in the new world, but the first to include civilians and families. Virginia Dare, the first child born in the New World to English parents, was White's grandchild. This Colony would become known as the "Lost Colony". But before it got  lost, it was part of the little known story of one of the better English  Mathematicians of the period. Thomas Harriot's name was once synonymous  with a common method of solving quadratics taught in nearly every high  school. Once commonly called Harriot's Method, today it is simply referred to as factoring.

White returned to England and for a quick supply run, but the war with Spain raised its ugly head and he didn't make it back until 1590, and poof, they were all gone.  The only sign was the word Croatoan on a post, suggesting that some or all had moved south to the island now called Hatteras Island..  White stated that he knew the majority might have planned to move fifty miles inland but no evidence of them was ever found.

One of White's maps was in the British Museum, and  around 2012, someone thought to ask what was under the two patches on the map. It turns out there was a symbol for a fort. and so an abandoned rural area of North Carolina, spared from development by its poverty, may offer hope of finding some of the missing early colonists.   

Before I go on I  want to add some notes about Harriot, the mathematician...
From my article on "Twenty Ways to Solve a Quadratic."

"For  most students the first method of solving quadratic equations that they  learn is by factoring. I have written (too often say some) that I think  this is a pedagogical mistake, and that probably a graphic solution  should be first. Vera Sanford points out in her Short History of  Mathematics, 1930 that “In view of the present emphasis given to the  solution of quadratic equations by factoring, it is interesting to note  that this method was not used until Harriot’s work of 1631. Even in this  case, however, the author ignores the factors that give rise to  negative roots.” Harriot died in 1621, and like all his books, this one,  Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas , was  published after his death. An article on Harriot at the Univ of Saint  Andrews math history web site says that in his personal writing on  solving equations Harriot did use both positive and negative solutions,  but his editor, Walter Warner, did not present this in his book."

Harriot was one of the early users of symbolic algebra and modified Viete's use of capital vowels for his unknowns and consonants for his knowns only by making them lower case.  His printed books used the equality of Recorde, but his written manuscripts included little vertical cross strokes to distinguish them from Viete's use of Recorde's equality as a subtraction symbol (actually Viete seemed to  use it more for the absolute difference between two numbers in either order).  He also introduced the less than and greater than symbols we now use, but in manuscript, they also had  vertical cross marks, but these too disappeared in the printed version.  He was one of the first to adopt both letters for variables and symbols for operations (Viete had used verbal language for operations such as "multiplied by" .  Jacqueline Stedall in her "Mathematics Emerging" commented that Harriot's writing would be the "earliest notation that appears to a modern reader both familar and easy to read."  

And how did he come to be in the exploration of Virginia?? Here is the story from Encyclopedia Virginia, 2010:

Thomas  Hariot (often spelled Harriot) was an English mathematician,  astronomer, linguist, and experimental scientist. During the 1580s, he  served as Sir Walter Raleigh's primary assistant in planning and  attempting to establish the English colonies on Roanoke Island off the  coast of present-day North Carolina. He taught Raleigh's sea captains to  sail the Atlantic Ocean using sophisticated navigational methods not  well understood in England at the time. He also learned the Algonquian  language from two Virginia Indians, Wanchese and Manteo. In 1585, Hariot  joined the expedition to Roanoke, which failed and returned to England  the next year. During his stay in America, Hariot helped to explore the  present-day Outer Banks region and, farther north, the Chesapeake Bay.  He also collaborated with the artist John White in producing several  maps notable at the time for their accuracy. Although Hariot left  extensive papers, the only work published during his lifetime was "A  Briefe and True Report of the New Found Land of Virginia", which  evaluated the economic potential of Virginia. The report appeared most  impressively in Theodor de Bry's 1590 edition that included etchings  based on the White-Hariot maps and White's watercolors of Indian life.  After a brief imprisonment in connection to the Gunpowder Plot (1605),  Hariot calculated the orbit of Halley's Comet, sketched and mapped the  moon, and observed sunspots. He died in 1621.

Harriot was not actually involved with the gunpowder plot, and was only held  and questioned briefly because one of his financial sponsors, Henry  Percy, the Ninth Earl of Northumberland, was a second cousin to Thomas  Percy, one of the conspirators. 

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