Okay, let's look at some key features of the real world and then we'll see what happens when we try to transfer those to maps. Okay, feature number one. Latitude lines, called parallels, are always... parallel latitude lines are also equally spaced both statements true everywhere on the planet What can we say about longitude lines?
Well they aren't parallel and they aren't equally spaced. What do they do do? They meet at both the north and the south poles. Remember they start at the north pole Widen out to the equator, come back together again at the South Pole.
Okay, and what happens when they meet? Latitude, I'm going to abbreviate because I'm running out of space. Longitude lines always cross at 90 degrees. Okay, four key rules.
Latitude lines are always parallel. Latitude lines are equally spaced. Longitude lines meet at the poles.
And latitude and longitude lines, when they cross, it is perpendicular, 90 degrees to one another, everywhere on the planet. So now, what happens to these during map projection? First though, quick question. Do we have an issue translating from the globe to a flat map in, say, Long Beach? No problem at all.
On the scale of the city, the difference between the truly curved surface and the idealized flat surface, the difference is minimal. So a flat map can perfectly represent a small area like a city. It's the bigger the area that you're trying to map gets, the bigger the problem becomes.
So mapping the whole nation, something of a problem. Mapping a whole continent, a bigger problem. Mapping the whole world, a huge problem. The key thing to realize is the idea that maps are made for specific purposes. So what are some of the purposes for which we might make a map?
One key idea would be shape. We want a map to correctly portray the shapes of different countries, islands, oceans, regions of the world. We call a map that correctly represents the shapes.
of different places as a conformal projection. That's a term you're going to need to know. Okay, an example of a conformal projection. This particular conformal projection is called the Mercator projection.
Because it was invented by a gentleman called Mr Mercator some 500 years ago. So, look at your Mercator projection and look at these criteria. Are the latitude lines always parallel on the Mercator projection?
Yes, they are. Are they equally spaced? Absolutely not.
They're close together near the equator and get rapidly further apart as you move towards the poles. Do the longitude lines meet at the poles? Well, they go straight up and down, they show no sign of trying to come together at all, so absolutely not. Do the longitude lines cross at 90 degrees?
Yes, they do. And actually that's the critical one you have to have in order to honour shape. Unfortunately, when you honour shape, size gets all messed up. Check out Greenland and South America. Greenland looks bigger, right?
Now let's see what these two look like on a globe. It's hard to position the Google Maps globe so that you can see both, but here's my best shot. Now look at Greenland, small and white up at the top.
You could fit it into a corner of South America down at the bottom. That's the real size comparison. So why? Does Greenland look so huge? On the Mercator projection, notice again how the latitude lines get further and further apart as you move towards the North or the South Pole.
The size of Greenland expands along with the expanding distance between the latitude lines. Another thing you could want a map to provide you with Area. What are the relative sizes of different countries, regions in the world?
Oftentimes that's rather important, trying to compare different land areas. Which of these areas is bigger? A projection that honors area is often, according to a textbook, called an equivalent projection.
Let's go for something easier. It's also called an equal area projection. So here are some equal area projections. There's more than one way of doing it. Here's one that gets the earth onto a rectangular map, sort of resembling the Mercator map.
Now look at Greenland up at the top and South America at the bottom. Greenland is short and wide. South America, tall and narrow.
The shapes are terrible, but the relative areas are accurate. Here's another way of preparing an equal area projection. The shapes of North and South America aren't so bad, but look over to the left and the right of the map. Asia is slanted towards the right and Europe is slanted towards the left.
And the shapes overall are nothing like they were on the other equal area map that we were just looking at. Notice that however we make the equal area projection, however we manage to make areas the same, shape is always messed up pretty badly. Okay, so basically you can have shape or you can have area, you can't have both.
Clearly there is no single right answer. And the key point is maps are made for a specific purpose and should only be used for that purpose. Here's a real world example of using a map for the wrong purpose. This is the general purpose world map from a school atlas vintage 1950. As you can see it's a Mercator projection, Greenland larger than South America.
The Mercator projection was commonly used in those days for general purpose maps, no particular purpose in view, something that is just intended to give us a general idea of sort of how the world looks. Now in 1950, the Cold War was well underway. The United States was having a major political disagreement. with the Soviet Union and people looked at this map. Here is the United States looking pretty small.
There is the Soviet Union. My goodness, it is huge. It could swallow us up easily. We're the little underdog. So what did we do?
We built several thousands of nuclear weapons, enough to basically annihilate every city on earth about 10 times over. And we pointed them all at the Soviet Union. What did the Soviets do in response? They built a similar number of nuclear weapons and they pointed them all at the United States. After another 20 or 30 years, we actually started talking to the Soviets and we agreed that this was pretty ridiculous.
We agreed mutually to cut back on the number of nuclear weapons and now we and I believe the Russians, Soviet Union is no more but this is Russia, And now I believe we only have enough beach to destroy all the cities in the world about one time only. So now we're supposed to feel a whole lot safer. But do you notice, we are this far from the equator, and the Soviet Union is much closer to the North Pole. So this territory is showing at about four times larger than the United States. Okay, Mercator projection.
Nearer the equator is smaller, nearer the pole is way larger. So the Soviet Union isn't five times the size of the United States or larger. It's approaching two times the size, but about half of it is uninhabited Siberia. So it's actually pretty comparable.
Now I'm not saying that the use of a Mercator projection caused the Cold War, but it sure helped to make us feel extremely nervous about this giant evil empire and feel that we needed more bigger weapons to point at them, when in reality we had a comparable population and better technology. So in any conflict we would most likely have been the winning side, not the other way about. So here is a major misconception perpetuated by the use of the wrong projection.
Third thing that we might want from a map is distance. Measure off from the map how far is it from point A to point B. Bad news.
Any map showing a huge area, a continent, the world, it is impossible to accurately represent distance. In order to project a map, you are inevitably going to distort distances. All right then, the fourth thing that you would want from a map is direction. You're going to set off, sail in a particular direction across the ocean, it would be nice to have a map that will get you to your destination.
Back to one we talked about at the very beginning. There is one excellent projection for that purpose and it is the Mercator projection. In fact, Mr Mercator invented this projection back in the year 1569 for the one purpose of allowing sailors to pick a compass bearing, sail along that compass bearing, and successfully reach their destination.
That's what the Mercator projection is for.