7 ms·

It's not a bias for 2d projection. If someone tells me to "go east in a straight line", I think about how practically I'd go about it. In this case, I'd take a

• w-j-w 2y ago
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• happytoexplain 2y ago
  Nobody familiar with navigation would say "go east in a straight line" because it's a paradox. That's why they say "maintain an easterly heading", or, for shorter distances (e.g. car directions), "head straight east", as in "exactly east", and not "east in a perfectly straight line", which would be less relevant for shorter distances. It's also why the question is (paraphrased) "start facing east and go in a straight line", and not "go east in a straight line".
  • davidw 2y ago
    Of course it's not a perfectly straight line, because the earth is a curved object. Perfectly straight puts you in outer space.
    • mynameisvlad 2y ago
      The article quite clearly says “in a straight line along the Earth’s surface.” Emphasis mine.
    • happytoexplain 2y ago
      Now that is, in fact, a silly gotcha. It's a third abstraction, irrelevant to the topic of two dimensional navigation. It is abstracted away for both cartesian and global concepts, and nobody is realistically confused by its absence.
• mc10 2y ago
  Perhaps the HN headline doesn't match the article, but the instructions say: > Imagine you begin a journey in Seattle WA, facing exactly due east. Then start traveling forward, in a straight line along the Earth’s surface. where there isn't any wording saying "go east in a straight line".
  • tacitusarc 2y ago
    The most reasonable interpretation of this is to follow the latitudenal geodesic along its eastern path. You cannot claim that one geodesic is more “straight” than another in 3d Euclidean geometry, that is nonsense. But that is what the author does. Edit: Ok, the latitudinal geodesic only exists at the equator, so the question is fundamentally impossible, with how the author defines a straight line.
    • pdonis 2y ago
      > the latitudenal geodesic There is no such thing. A curve of constant latitude on Earth, except for the equator, is not a geodesic. > You cannot claim that one geodesic is more “straight” than another in 3d Euclidean geometry In terms of 3D Euclidean geometry, neither a curve of constant latitude on Earth's surface nor a great circle on Earth's surface is a straight line/geodesic. Both are curved. If you restrict to the 2D surface of the Earth, a great circle is a geodesic but a curve of constant latitude, except for the equator, is not.
      • lxgr 2y ago
        Except that the original instruction was "straight line", not "geodesic", so does it matter all that much which kind of non-straight-line one follows?
        • pdonis 2y ago
          > the original instruction was "straight line", not "geodesic" If you're working within a 2-sphere, such as the Earth's surface, or indeed any non-Euclidean geometry, they mean the same thing. More precisely, there are no "straight lines" in the exact sense you mean in a non-Euclidean geometry, but there are geodesics that satisfy all of the geometric properties of "straight lines" within that non-Euclidean geometry.
• lxgr 2y ago
  Surely you mean Paris, Ontario, Canada? :)