In the year 1707, the British navy suffered a major disaster. A sizable fleet had been engaged in naval action in the Mediterranean, and they were now headed for home. They sailed from Gibraltar in October. and encountered extremely bad weather on the way up the coast of Europe. The bad weather prevented them from getting noon sights much of the time, so they were navigating by dead reckoning. Three weeks later they were approaching England, and the admiral in charge thought they were here, based on his dead reckoning, and so he instructed the fleet to alter course to this course, which would take them into their home base in Portsmouth. Unfortunately they weren't here, they were there. And that same course, as you can see, took them straight onto the rocks of the Scilly Isles. Four ships were wrecked. Fifteen hundred or more naval men, including the admiral, were drowned. It was a major disaster. The British government was seriously pissed. They had to build a whole lot of new ships. They had to hire a whole new navy. And the British government offered a prize: 20,000 English pounds — in today's money that would be several millions of dollars — to anybody who would come up with a reliable method of measuring longitude at sea. There's a little book called "Longitude", — very simple — which details all of the intrigue and everything else associated with this. It's an interesting story all of its own. But the way you solve this is with an understanding of time, and the person who eventually got the prize was a clockmaker. Enter John Harrison . . . Again, clocks in those days used a pendulum, and the swing of the pendulum, always taking the same time to make its swing, is what marked the passage of time. Take a pendulum clock out on a boat rocking around on the ocean — what happens? Either it stops working altogether, or it gets way off as the waves buffet the pendulum and change the length of its swing. England's best clockmaker, an incredibly inventive genius, figured out how to solve that and we actually use the same — use his — solution still today. In essence, what he came up with was the idea: instead of having a pendulum that is hinged at one end let's hinge it in the middle, so it goes backwards and forwards like this. Because a wave that pushes this end off balance in that direction will simultaneously push the other end off balance in the exact opposite direction, and so the effect of the waves is self-cancelling, and the thing goes on keeping perfect time. There was more to it than that: he had to make it of materials that would stand up to corrosion in the marine environment. He had to make it so that it adjusted for temperature, because metals expand in warm temperatures and shrink in cold temperatures. He had to do all kinds of stuff. But eventually he built a machine — it was pretty big — and he said it would do what was required, so it was loaded onto a naval ship — sailing ship, of course — and tested. Basically the government requirement was: you had to be able to cross the ocean and, arriving at your destination, you had to be within like a few miles of where you thought you were, in other words, close enough that you would be able to see rocks before you ran onto them. So his device was loaded onto a ship. They crossed the Atlantic to North America and the device gave them longitude to well within the required specifications. Then the British government refused to pay him the money. There's a long and dirty story here. Long story short: over the rest of his life he invented one after another after another devices. They got smaller, they got simpler, they got neater, and they all worked perfectly; and eventually he got his money. By the way, wristwatches — until a few years ago we started to use the vibration of a quartz crystal to do our timing — they used little pendulums exactly like the ones invented by Mr. Harrison all those centuries ago; basically anchored in the middle, spinning backwards and forwards, and therefore you can bang your wrist around and they still keep time. So exactly how does this work? You have, on your ship, a clock set to the time at Greenwich — zero degrees of longitude. It has to keep accurate time — in fact, there's a technical term for a clock that keeps that kind of time — it's called a chronometer. A chronometer is a clock that will stand up to those exacting requirements of not getting . . . getting off from the correct time. You have your sextant: you take the noon sight — the angle of the sun. The angle of the sun at noon gives you your latitude. How do you know it's noon? — Because the sun has reached its highest point. At that moment, when it is noon where you are, you look at your chronometer, and you determine the time at Greenwich. Let us say that you have 12 noon, and the time at Greenwich is 11:00 a.m. You are one hour away from Greenwich. How many degrees of longitude is one hour? — Width of a time zone — 15 degrees. 360 divided by 24 — 15 degrees. You are 15 degrees away from Greenwich. Now are you east of Greenwich or west of Greenwich? Well, the sun is overhead where you are, and the sun crosses the sky from east to west. the sun has reached you, but it hasn't reached Greenwich yet, so where are you? You're ahead of Greenwich — you're east of Greenwich. You are therefore at a longitude of 15 degrees — that's the one hour. East because your time is ahead of the time in Greenwich. OK? Another example: noon site — 12 noon where you are, the time on the chronometer is 3:00 p.m. What's your longitude? Three hours is 3 times 15 — 45 degrees, and where are you in relation to Greenwich? The sun is overhead where you are; it has passed on into the afternoon at Greenwich. OK? The sun went past Greenwich a while ago, and has now reached you. The sun travels westwards: you are at a longitude of 45 degrees west. That's how it's done. Today of course, you don't really need a chronometer; you can get the time, worldwide, through radio signals. And actually, today we have a technology that makes all of this — the sextant, the chronometer, all of this — obsolete. What is the modern technology that tells you precisely where you are on the surface of the Earth? Any place, any time? — GPS. We'll talk about that a little bit later on. It's important to understand this process — using the sextant, using the chronometer — because that gives you an understanding of the significance of latitude and longitude, and how one is related to some angle, and the other is related to the passage of time. Now something else important about time. I want you to imagine that you're independently wealthy; you don't have to work, and you decide to take a world cruise. We'll set off from the Port of Long Beach and travel around the world. Here's the map. We'll start off, as I say, from Long Beach. First of all we'll travel southwest across the Pacific Ocean to Australia. OK? As we go, we'll cross time zone boundaries. We'll have to set our watches back an hour, 2, 3, 4, 5, 6 hours back. When we get to Australia, let's get off the boat at Sydney, here; spend a year exploring Australia, but heading west: 7, 8 hours. At Perth here, on the west coast, we'll take a ship and continue: 9 hours, 10 hours, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, through the Panama Canal, 22, 23, 24 hours — we're back home. So what happened there? We set our watches back an hour, 24 times. That's a total of 24 hours. Doesn't matter whether we zoomed around the trip as fast as we could, or whether we took years over it. We have set our watches back a total of 24 hours. That means the time back in Long Beach is correct, but if you have one of the fancier watches that keeps track of the date, the date is now wrong! Your watch is showing yesterday's date, on arrival. And this is not a fluke. That is a fact. If you travel around the world in a westerly direction, you'll come in a day late at the end of your trip. Conversely, if you travel around the world in an easterly direction, your watch will be showing a day ahead of what it is really, once you get back. The first time this paradox was identified was back in the 1500s by the famous mariner Magellan. Magellan set off with a small fleet of ships, planning to sail around the world. He set off from Spain in the year 1519. Magellan never made it all the way home: he died on the route; some of the ships were lost; but the remnants of the expedition got back to Spain in 1521 — two years later. Now time zones hadn't been invented in those days, but they knew all about solar noon — time measured by the sun — and they kept setting their clocks back, and back, and back, and back, and back, as they traveled westwards around the world. So finally they arrived back in Spain. The crew say, "Well, thank heaven we're home, it's Wednesday", and ashore they said, "No, it's not, it's Thursday." Obviously the first thing that sprang to mind was, "Well, we missed a day somewhere," but think ship's log. Their survival depended on an accurate record being kept. They had faithfully kept that log hour by hour — two-year journey — no, they hadn't just missed a day somewhere. Truly, having gone around the world, they were off by a day. So, if you travel around the world eastwards, on arrival back at your destination, you're a day ahead. And if you travel around the world westwards, arriving back at your destination, you're a day behind.