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The projection chosen IS the model, and we chose a useful one - and that projection is flat. Is paper maps not models of the real world?

• pdonis 10y ago
  > The projection chosen IS the model Not if you're going to say the projection is flat. If the projection is flat, and the projection is the model, then I should be able to lay a flat ruler, appropriately scaled, between any two points on the flat map and read off the actual distance between those two points. But I can't do that; and the model knows I can't do that. The model tells me to take the coordinates on the map of two points and plug them into a complicated mathematical formula if I want to get the actual distance between them. So the model is not flat in the sense that matters--in the predictions it makes for distances between points.
  • zardo 10y ago
    >Not if you're going to say the projection is flat. If the projection is flat, and the projection is the model, then I should be able to lay a flat ruler, appropriately scaled, between any two points on the flat map and read off the actual distance between those two points. Is a constant distance metric part of the definition of flat? Why don't the grid lines on the map count as an appropriately scaled ruler?
    • pdonis 10y ago
      > Is a constant distance metric part of the definition of flat? Yes. Otherwise "flat" would have no meaning; we can always make a flat map of any surface, if we are willing to allow the distance metric to be distorted to any extent we like, so every possible surface would be "flat".