Aphelion

I don't quite know why, but this one just fell flat for me . . .

This may be topic drift, but I just lately learned a new way to think about what constitutes a dimension.

Start with a point, of course -- zero dimensions -- then stretch it out into a line -- one dimension. You only need one piece of information to describe your location on that line.

Bend that line into a curve and join the ends to form a circle. Is it now two-dimensional? No, because you can still describe the location of any point on it with only one piece of information.

Now consider a sphere . . . is that three-dimensional? No, it's two-dimensional, because you can find any point on its surface using only latitude and longitude (we're talking only about surfaces here, not the volumes within them). I like this one especially, because in my sci-fi universe, all starship courses are plotted by altitude and azimuth.

So, the dimensionality of a thing is described by the number of pieces of information you need in order to find a location on or in it. Welcome to topology.

Check it out:

http://www.teach12.com/ttcx/coursedescl ... x?cid=1460