How can I find/understand the physical explanation or practical meaning of a distance? For example Euclidean distance is the shortest path between two points, how about for other distances?
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Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that. – Buddha Oct 05 '14 at 13:45
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How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice? – user45297 Oct 05 '14 at 18:49
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you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function. – Buddha Oct 05 '14 at 20:19
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Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
Jasser
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A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
shardulc
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