## 2011-09-17

### Upside down world

Here's a screenshot from Google Maps (click to view full-size):

If you look at the bottom (it's also true of the top), when the 90th latitudinal parallel is reached the world just stops. Yet you can see that South America starts repeating: scroll east or west on Google Maps and the program shows you that the world indeed keeps going. But not so much north-south.

Shouldn't the south pole continue again below (this time upside down), with an upside down globe ending with a north pole that continues again right-side up? That's the conceptual way to look at it.

Of course, the thing about the bottom "line" of the world is that its actually deceptively tiny: The 90th parallel isn't even a line, it's a point. You can stand on the top of the world. Walk four feet away from the 90th parallel and you can walk in circles equidistant from the north pole. You are literally walking around the world in a manner of seconds!

Anybody who's driven in northern Alberta has found this map effect come to life. A 3-D world doesn't translate well onto a 2-D sheet of paper (it never can, as Carl Gauss proved mathematically in 1827). Since Alberta is defined by latitudinal lines, and since latitudinal lines are closer together the closer to the north pole you get (our world-walker crosses all 360 latitudinal integers within the span of 60 seconds), any map of Alberta has to choose between showing the BC and Saskatchewan borders as being parallel (which they ain't) or else failing to preserve right angles ("why is my GPS telling me every intersection in Athabasca is a 'slight turn'?"). They always choose the former, as the latter causes brains to explode.

So the next time you're thinking that that drive from Slave Lake to Grande Prairie looked further on the map, or you're wondering why Google Maps shows the northern half of Greenland looking like a hilarious cartoon island that's been attached to a bicycle pump, you're dealing with the same story.