Let's not get mixed up about what the projection did and didn't do. As you point out, the importance of rhumb lines comes not from the fact that the thing they keep constant -- the bearing (with respect to north/south) -- was something that could actually be measured.
Rhumb lines are not, however, the shortest distance between two points on a sphere. Those would be great circles. In particular, note that along a rhumb line one can never reach the north or south pole. Indeed, rhumb lines are dependent on your choice of poles, which the actual shortest course clearly cannot be!
Argh. Misnegation from earlier version. "As you point out, the importance of rhumb lines comes from the fact that..." -- there shouldnt' be a not there.
You are (it seems intentionally) ignoring the point that Mercator's area distortion doesn't dangerously mislead in navigation, quite the contrary. Or, if that isn't true, please name some cases where navigators were messed up because they thought Greenland looked bigger than it was in area.
Unless you use a globe, every projection onto a flat rectangular surface distorts.
Now how does that make more plausible the claim that world map makers are inflating the area of Taiwan on purpose?
Really? Seemed like he was simply pointing out an error on my part. Don't see where Taiwan enters that at all.
More to the point, there's a big difference between distorting scale in a way that's mathematically consistent throughout the projection (i.e. one in which you preserve shape or position at scale's expense), and simply fudging the scale in a particular spot.
Really? I think you meant rhumb lines. :) They're both important, just for different reasons; and it's rhumb lines that are easily visible on a Mercator projection and that were so useful for navigation.
Comments
Let's not get mixed up about what the projection did and didn't do. As you point out, the importance of rhumb lines comes not from the fact that the thing they keep constant -- the bearing (with respect to north/south) -- was something that could actually be measured.
Rhumb lines are not, however, the shortest distance between two points on a sphere. Those would be great circles. In particular, note that along a rhumb line one can never reach the north or south pole. Indeed, rhumb lines are dependent on your choice of poles, which the actual shortest course clearly cannot be!
Argh. Misnegation from earlier version. "As you point out, the importance of rhumb lines comes from the fact that..." -- there shouldnt' be a not there.
You are (it seems intentionally) ignoring the point that Mercator's area distortion doesn't dangerously mislead in navigation, quite the contrary. Or, if that isn't true, please name some cases where navigators were messed up because they thought Greenland looked bigger than it was in area.
Unless you use a globe, every projection onto a flat rectangular surface distorts.
Now how does that make more plausible the claim that world map makers are inflating the area of Taiwan on purpose?
Really? Seemed like he was simply pointing out an error on my part. Don't see where Taiwan enters that at all.
More to the point, there's a big difference between distorting scale in a way that's mathematically consistent throughout the projection (i.e. one in which you preserve shape or position at scale's expense), and simply fudging the scale in a particular spot.
Indeed, Sniffnoy - thanks for sorting out my terminology. Great circles is exactly what I meant.
Really? I think you meant rhumb lines. :) They're both important, just for different reasons; and it's rhumb lines that are easily visible on a Mercator projection and that were so useful for navigation.