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Algebra Of PointersI have been thinking a little about pointers, and what kind of mathematical structure they form. They seem to be like a onedimensional vector (as opposed to a simple scalar). If we use the terms location for a point in ndimensional space, and distance for a vector, then we get the following properties, adding a distance to a location results in a location, subtracting a distance from a location results in a location, subtracting a location from a location results in a distance. Where is gets more tricky is that adding a location to a location would seem to be invalid (I don't know what type of thing this is), and yet to average two locations, to get the midpoint seems perfectly reasonable. Topologically what is going on here? What is the type of a location added to a location? If we treat all locations as distances with an origin at zero, then everything makes sense again in terms of types, except for zero itself which seems to still be a location and not a distance (or it all gets horribly selfreferential). Any thoughts on how to make sense of this, what the type of the sum of two locations might be, etc? By Keean Schupke at 20160507 10:12  LtU Forum  previous forum topic  next forum topic  other blogs  4934 reads

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