>Il giorno 18/ago/2013, alle ore 17:54, "Christian Müller" <cmu...@gmx.de> ha >scritto: >> The term boundary does not make any implication on it's width. > it has no width at all, it is a line
-1. It may be _represented_ by a line, as declared by an entity. Even though the boundaries of territories may be declared using lines, you have to keep in mind that this is an abstraction. Often these lines just represent the center of a _buffer_ around a core area. A line of zero width is an abstraction for a boundary. Again, the term boundary does not make any implication on it's width. It may be represented by a line with zero width, but may just as well be by an area with constant or variing width as you walk around the core area to be defined. Of course, if you use an (buffer) area for definition, you may very well start to realize the recursive nature in trying to define a boundary - as you wonder about how to represent the boundary of the buffer area. Should it be a line of zero width or, again, be a buffer area? [..] This especially holds true for natural regions that originally might just have been "declared" by a mere description in a natural language. However you will find examples of this in other fields - take Bohr's model of the atom. The probability for an electron to reside in one shell won't change abruptly on the shells boundary abstracted by a sphere's surface of zero width. These shells are zones. Back to our matter of _topographic areas_ you will find a note about the abstract nature of boundaries elsewhere, e.g. in the article http://en.wikipedia.org/wiki/Boundaries_in_landscape_history If you focus on the last part of the second sentence, quote "the boundary can often be seen by differences in land use on either side." you may find that the concept of natural boundaries is about finding similar features on one of two adjacent sides, separating them from similar-found features on the other. So a boundary separates one side from the other, or connects one side to the other, depending on the glass being half empty or half full. The criteria taken into account when grouping similar features to form undivided areas and the precision of measurement together determine how sharp or fuzzy this boundary between areas will be. To simplify the fact that in practice you will never find a zero width boundary you could also substitute: A boundary is an area between areas. When institutions define natural regions you will sometimes see this reflected in coined terms such as "boundary zone". These are crippling a sharp, mathematically used, zero width expressed boundary into what effectively is an area boundary, since it's not feasible to narrow down a natural area, i.e. zone to a point where a zero-width line abstraction comes to mind naturally. >> Even political boundaries are in reality many meters wide, e.g. to defend >> them. Think of the historical inner german border for example. > The Berlin Wall (the 2 walls and the space in between) was entirely on > eastern German territory and > wasn't the actual boundary (which was a few meters before the actual wall) It all depends on what exactly you refer to. In day-to-day life you should not find too many people that think of a zero width line abstraction when talking about this histo-political boundary. It may have been at the time it was declared, but there are other people having more insight on this. And it may have been a bad example, yes. Greetings _______________________________________________ Tagging mailing list Tagging@openstreetmap.org http://lists.openstreetmap.org/listinfo/tagging
