1 00:00:15,531 --> 00:00:19,163 As you can imagine, 400 years ago, 2 00:00:19,163 --> 00:00:21,997 navigating the open ocean was difficult. 3 00:00:21,997 --> 00:00:25,713 The winds and currents pushed and pulled ships off course, 4 00:00:25,713 --> 00:00:29,514 and so sailors based their directions on the port they left, 5 00:00:29,514 --> 00:00:35,080 attempting to maintain an accurate record of the ship's direction and the distance sailed. 6 00:00:35,080 --> 00:00:38,380 This process was known as dead reckoning, 7 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. 8 00:00:46,665 --> 00:00:49,780 This was an easy mistake to make. 9 00:00:49,780 --> 00:00:53,497 Thankfully, three inventions made modern navigation possible: 10 00:00:53,497 --> 00:01:00,863 sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily. 11 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. 12 00:01:08,414 --> 00:01:11,365 John Bird, an instrument maker in London, 13 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, 14 00:01:16,830 --> 00:01:19,230 called a sextant. 15 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. 16 00:01:26,230 --> 00:01:31,947 Comparing these two angles was necessary to determine the longitude of the ship. 17 00:01:31,947 --> 00:01:33,515 Clocks came next. 18 00:01:33,515 --> 00:01:38,497 In 1761, John Harrison, an English clockmaker and carpenter, 19 00:01:38,497 --> 00:01:41,980 built a clock that could keep accurate time at sea. 20 00:01:41,980 --> 00:01:48,480 The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions 21 00:01:48,480 --> 00:01:52,796 was necessary in order to know the time back in England. 22 00:01:52,796 --> 00:01:54,880 There was one catch though: 23 00:01:54,880 --> 00:01:58,714 since such a timepiece was handmade, it was very expensive. 24 00:01:58,714 --> 00:02:05,380 So an alternate method using lunar measurements and intense calculations was often used to cut costs. 25 00:02:05,380 --> 00:02:10,848 The calculations to determine a ship's location for each measurement could take hours. 26 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. 27 00:02:17,713 --> 00:02:24,163 Fortunately, in the 1600s, an amateur mathematician had invented the missing piece. 28 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. 29 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. 30 00:02:41,430 --> 00:02:45,432 Algebra in the early 1600s was not fully developed, 31 00:02:45,432 --> 00:02:49,130 and Napier's logarithm of one did not equal zero. 32 00:02:49,130 --> 00:02:55,080 This made the calculations much less convenient than logarithms with a base of 10. 33 00:02:55,080 --> 00:02:59,547 Henry Briggs, a famous mathematician at Gresham College in London, 34 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. 35 00:03:07,614 --> 00:03:11,065 Briggs showed up unannounced at Napier's castle door 36 00:03:11,065 --> 00:03:18,413 and suggested that John switch the base and form of his logarithms into something much simpler. 37 00:03:18,413 --> 00:03:23,231 They both agreed that a base of 10 with the log of one equal to zero 38 00:03:23,231 --> 00:03:26,431 would greatly simplify everyday calculations. 39 00:03:26,431 --> 00:03:30,797 Today we remember these as Briggs Common Logarithms. 40 00:03:30,797 --> 00:03:35,098 Until the development of electric calculating machines in the 20th century, 41 00:03:35,098 --> 00:03:44,017 any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers 42 00:03:44,017 --> 00:03:46,730 were done using logarithms. 43 00:03:46,730 --> 00:03:50,181 The history of logarithms isn't just a lesson in math. 44 00:03:50,181 --> 00:03:54,380 There were many players responsible for successful navigation. 45 00:03:54,380 --> 00:03:57,913 Instrument makers, astronomers, mathematicians, 46 00:03:57,913 --> 00:03:59,981 and of course sailors. 47 00:03:59,981 --> 00:04:04,098 Creativity isn't only about going deep into one's field of work, 48 00:04:04,098 --> 00:04:08,563 it's about cross-pollination between disciplines too.