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SilasBarta comments on Cultivating our own gardens - Less Wrong
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I also am confused by the metaphor; however it's worth noting is that the problem is not to embed a graph in the plane without crossings, but rather to embed a weighted graph in the plane (possibly with crossings) such that the distances given are equal to the Euclidean distances from the embedding. And adding nodes would be changing the problem, no?
It depends on whether the US cities bit was just an illustrative example, or a typical constraint on the problem.
Does the problem take for granted, e.g., that roads can be winding so that the weight necessarily does not equal the Euclidean distance (Riemannian distance, really, on a curved paper, but whatever), and you have to make a planar map that locates the nodes so that the weight is (proportional to) the Euclidean distance?
I don't see how this is relevant to the statement that adding nodes would be changing the problem. You're given a specific graph of distances, the challenge is to realize it in the plane. You can't just add nodes and decide to realize a different graph in the plane instead; where would the distances even come from, anyway, if you haven't yet computed an embedding?
SarahC cleared it up, so I understand what you do and don't know in the problem, and why I assumed certain things were given that aren't.
Though I agree with Roko's comment that this doesn't seem to provide insight on resolving ethical differences.