On Tue, 2009-02-10 at 14:01 +0000, Paul Uszak wrote: > Err, this sounds like an interesting but somewhat frivolous debate. Whilst > it > may be mathematically correct to look towards fractal theory in discussing > the > length of a coastline, I'm fairly certain they have an accepted length.
Not that I know of, indeed I challenge you (for yourself) to find 3 independent resources which show the same value for the length of any, non trivial, seacoast. The reported length of the borders of countries depends entirely on the scale at which they were digitized, same for river length, same for... Those "length" measures are completely unstable metrics and therefore useless for science. > > I have a picture of one on my wall. The paper it's on isn't of infinite size > though. I also walked along one once. The fact that I'm now back writing > this > suggests that the walk didn't take an infinite length of time. These two examples are broken from a theoretical standpoint. The image of a coastline is obviously not a coastline; your infinity debate takes us all the way back to Greek philosophy. > > It doesn't always advance the position of science in our world to rigorously > adhere to the theoretical, whilst ignoring the perceptual. After all, quantum > theory states also states that I simultaneously both did and didn't write > this > post... > Here you are mixing metaphors for no gain in understanding. It seems that the interesting response, when confronted with theory that says one thing and 'experience' another, is not ignoring the theory but reaching a deeper understanding of nature. That drove my comment about road lengths at the end of my last mail. Since coastline length is scale dependent then we can only meaningfully discuss it if we *share* the same length. That hidden dependency is what trips us up. At our scale it seems that coastlines have length. But if you know better, then you will know that any representation of a coast at other scales will reach very different results as a function of the scale and the coastal characteristic. That's how you can have your cake and eat it too---but it does make you aware, in a deeper sense, of how the world works. But like everyone else must, I have had enough of this thread. Take from it what you will. cheers, --adrian _______________________________________________ jts-devel mailing list [email protected] http://lists.refractions.net/mailman/listinfo/jts-devel
