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<   No. 2430   2009-09-21   >

Comic #2430

1 Serron: So how does this hyperspace thing work, Spanners?
2 Spanners: The local coordinate system is a conformal map of our own dimensions on to a logarithmic polar space.
3 Spanners: Angles are preserved so navigation is straightforward. But distances are wildly distorted, allowing us to cover parsecs in just a few days.
4 Serron: What's that enormous shape in the distance?
4 Spanners: Greenland.

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A conformal map is essentially a deformation of a multidimensional space (for example, a flat surface, or 3-dimensional space) in such a way that any angle in the original space is the same in the deformed space.

An example of such a map is the familiar Mercator projection of the Earth's surface on to a flat page. In this projection, the lines of latitude are all horizontal and lines of longitude are all vertical, so that they all intersect at right angles - which is exactly how they intersect on the Earth. Also, a straight line drawn on the map at any angle to the lines of latitude and longitude corresponds to a rhumb line around the Earth, which intersects the latitude and longitude lines at a constant angle, making it very convenient for keeping on course if you're steering a ship or other vessel with compass bearings.

So it's all cool and very useful for navigation. This is the big advantage of the Mercator map projection, because this property is not true of most other map projections.

A rhumb line is not the same as a great circle however, which is the shortest distance across the Earth's surface (ignoring the fact that the Earth isn't precisely a sphere) between any two points. For distances less than about a third of the way around the globe, however, the distance difference between a rhumb line route and the great circle route is quite small, and more than compensated for by the ease of navigation if you're in something like a 17th century ship. In these days of computer aided navigation and intercontinental air travel, however, great circle routes are more common.

The bad thing about the Mercator projection is that - while it preserves angles - it distorts the shapes and sizes of objects, such as countries and continents. If you've ever thought that Greenland was roughly the same size as Africa, it's because you're familiar with the Mercator projection. Greenland's size is so wildly distorted that it looks much bigger than it is in reality - approximately 14 times bigger.

One would assume that, given the distortions necessary to compress parsecs of distance into something reasonable, that some other bits of the universe are going to be massively enlarged. One guess which bit.


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