Right, the travel-time metric is not compatible with a Euclidean R² metric. You can imagine three subway stations in a triangle loop, such that it's a shorter t

Right, the travel-time metric is not compatible with a Euclidean R² metric. You can imagine three subway stations in a triangle loop, such that it's a shorter trip to do a full loop on the subway then to walk to a point in the interior. There's no way to continuously deform a map so that it represents travel times as distance in a plane.