WEBVTT 00:00:15.531 --> 00:00:19.163 As you can imagine, 400 years ago, 00:00:19.163 --> 00:00:21.997 navigating the open ocean was difficult. 00:00:21.997 --> 00:00:25.713 The winds and currents pushed and pulled ships off course, 00:00:25.713 --> 00:00:29.514 and so sailors based their directions on the port they left, 00:00:29.514 --> 00:00:35.080 attempting to maintain an accurate record of the ship's direction and the distance sailed. 00:00:35.080 --> 00:00:38.380 This process was known as dead reckoning, 00:00:38.380 --> 00:00:46.665 because being just half a degree off could result in sailing right past the island that lay several miles just over the horizon. 00:00:46.665 --> 00:00:49.780 This was an easy mistake to make. 00:00:49.780 --> 00:00:53.497 Thankfully, three inventions made modern navigation possible: 00:00:53.497 --> 00:01:00.863 sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily. 00:01:00.863 --> 00:01:08.414 All are important. Without the right tools, many sailors would be reluctant to sail too far from the sight of land. 00:01:08.414 --> 00:01:11.365 John Bird, an instrument maker in London, 00:01:11.365 --> 00:01:16.830 made the first device that could measure the angle between the sun and the horizon during the day, 00:01:16.830 --> 00:01:19.230 called a sextant. 00:01:19.230 --> 00:01:26.230 Knowing this angle was important, because it could be compared to the angle back in England at the exact same time. 00:01:26.230 --> 00:01:31.947 Comparing these two angles was necessary to determine the longitude of the ship. 00:01:31.947 --> 00:01:33.515 Clocks came next. 00:01:33.515 --> 00:01:38.497 In 1761, John Harrison, an English clockmaker and carpenter, 00:01:38.497 --> 00:01:41.980 built a clock that could keep accurate time at sea. 00:01:41.980 --> 00:01:48.480 The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions 00:01:48.480 --> 00:01:52.796 was necessary in order to know the time back in England. 00:01:52.796 --> 00:01:54.880 There was one catch though: 00:01:54.880 --> 00:01:58.714 since such a timepiece was handmade, it was very expensive. 00:01:58.714 --> 00:02:05.380 So an alternate method using lunar measurements and intense calculations was often used to cut costs. 00:02:05.380 --> 00:02:10.848 The calculations to determine a ship's location for each measurement could take hours. 00:02:10.848 --> 00:02:17.713 But sextants and clocks weren't useful unless sailors could use these tools to determine their position. 00:02:17.713 --> 00:02:24.163 Fortunately, in the 1600s, an amateur mathematician had invented the missing piece. 00:02:24.163 --> 00:02:32.947 John Napier toiled for more than 20 years in his castle in Scotland to develop logarithms, a calculation device. 00:02:32.947 --> 00:02:41.430 Napier's ideas on logarithms involved the form of one over E and the constant 10 to the seventh power. 00:02:41.430 --> 00:02:45.432 Algebra in the early 1600s was not fully developed, 00:02:45.432 --> 00:02:49.130 and Napier's logarithm of one did not equal zero. 00:02:49.130 --> 00:02:55.080 This made the calculations much less convenient than logarithms with a base of 10. 00:02:55.080 --> 00:02:59.547 Henry Briggs, a famous mathematician at Gresham College in London, 00:02:59.547 --> 00:03:07.614 read Napier's work in 1614, and the following year made the long journey to Edinburgh to meet Napier. 00:03:07.614 --> 00:03:11.065 Briggs showed up unannounced at Napier's castle door 00:03:11.065 --> 00:03:18.413 and suggested that John switch the base and form of his logarithms into something much simpler. 00:03:18.413 --> 00:03:23.231 They both agreed that a base of 10 with the log of one equal to zero 00:03:23.231 --> 00:03:26.431 would greatly simplify everyday calculations. 00:03:26.431 --> 00:03:30.797 Today we remember these as Briggs Common Logarithms. 00:03:30.797 --> 00:03:35.098 Until the development of electric calculating machines in the 20th century, 00:03:35.098 --> 00:03:44.017 any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers 00:03:44.017 --> 00:03:46.730 were done using logarithms. 00:03:46.730 --> 00:03:50.181 The history of logarithms isn't just a lesson in math. 00:03:50.181 --> 00:03:54.380 There were many players responsible for successful navigation. 00:03:54.380 --> 00:03:57.913 Instrument makers, astronomers, mathematicians, 00:03:57.913 --> 00:03:59.981 and of course sailors. 00:03:59.981 --> 00:04:04.098 Creativity isn't only about going deep into one's field of work, 00:04:04.098 --> 00:04:08.563 it's about cross-pollination between disciplines too.