7. Parallel lines never meet.Well, these aren't quite accurate. There's an implicit constraint on these statements that they are true only in euclidean (planar) geometry. In non-euclidean geometry, these statements can take wild turns. For example, on the surface of a sphere like our own planet, we can start at the north pole, walk south 1 mile, east 1 mile and north 1 mile and return exactly to our starting point. Our turns were approximately right angles and our return also consists of a right angle, meaning that the triangle we walked had interior angles summing up to almost 270° (to the nit-picky, this isn't strictly true--in order to get exactly 270°, we'd need to walk all the way down to the equator, but I'm too lazy to walk that far). And while we're talking about the globe, we can observe the long parallel longitudinal lines to see that they can indeed meet twice: once at each pole. In other more intriguing spaces, such as lobechevskian space whose shape is often compared to that of a saddle, we can find parallel lines that intersect exactly once. And if the real-world example of the globe isn't enough to discredit the universality of propositions 7 & 8, we could look at the math supporting Einstein's theory of special relativity which relies on non-euclidean math to derive its results.
8. The sum of the interior angles of a triangle is 180°.
Wednesday, May 23, 2007
making sense of the absurd
If you have time on your hands, then the following piece is recommended for reading; Making Sense of the Absurd. It sort of goes through a list of things that starts to blur the line between absurd, right and wrong. It isn't making the case that religion isn't absurd, but that we probably take too many scientific statement for granted. for instance: