On Mon, 2009-02-09 at 11:47 -0800, Martin Davis wrote: > I see Adrian's point, but in actual fact I still say my statement was > well-posed. I was talking about a linear geometric representation of > the coastline. Obviously this is only an approximation to the "true" > coastline.
No! There is *no* "true" length of any coastline! This is not a question of approximation to a difficultly knowable reality but an issue that our intuitive concept of reality does not make actual sense. Since the "true" coastline length is essentially[1] infinity (the conclusion made in the paper), then what exactly does the metric we would be giving our users represent? I maintain the example is talking about a non-existent concept: "the length of a coastline". This is much like the notion of suction --- something we all share which, physically, is non-sense. This is a great danger of GIS---we can give very precise (double precision) nonsense. So the example *application* of metric distances on an ellipsoid was unfortunate: calculating on the ellipsoid does not add any precision to the metric since the metric is non-sensical. Maybe, use airline flight paths instead---they are inherently restricted to a particular scale and often closely approximate piecewise great circle paths. --adrian [1] This is a conceptual coastline. In a real coastline, we quickly get down to the error level of High/Low tide lines so the coastline is undefinable. Even if it were, we would get down to the plank length before hitting infinity. Of course, at that scale it would take longer than rate of erosion to measure the coastline... [2] Left as an exercise to the reader is the question of why, if the length of a coastline is non-sensical, we can in all practicality speak of the mileage of a road. _______________________________________________ jts-devel mailing list [email protected] http://lists.refractions.net/mailman/listinfo/jts-devel
