The Mercator projection isn't a good example of a map in which visual distortion and a lack of navigational utility go hand in hand.

Indeed, the hole point of the projection was to make navigation easier by allowing rhumb lines (the shortest distances between two points on a curved surface) to be charted as perfectly straight lines on a two-dimensional map. From these lines of constant bearing, mariners could work out the precise - and constant - angle they should maintain in relation to the pole star in order to get from one point to another.

Without a reliable method for establishing longitude at sea, 17th Century navigators could never be exactly sure how far along their courses they were, but at least they could know that they were heading in the right direction. Given the level of uncertainty involved in these enterprises, this one piece of (relatively) hard and verifiable data was extraordinarily important, making the accuracy of the projection, and the mathematically - if not visually - correct placement of shorelines within it especially important.

Unfortunately, the iconic value of the Mercator projection has vastly outlived its utility - or at least, the common awareness of the once formidable navigational problems it addressed. Far from seeing it as a brilliant technical solution, it is often seen through a purely political filter that views its strengths as weaknesses, while completely missing the map's actual intent.

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.

Mercator distortion has nothing to do with the anecdote in the parent post. There the allegation was of deliberate inaccuracy, which renders a map non-functional for most purposes.

All 2D map projections produce either distortion or discontinuity. Neither of these affects a map's functionality in the way that outright inaccuracy does.

Oh yes, I agree that this is an example of purely the geometry, not a political attempt. But I know people who , upon seeing the distortion, were surprised at how many maps were "wrong". This shows that you can't rely on the market to weed out inaccurate maps. After all, a map that had the south at the top (rather than the bottom) would be viewed as "wrong" and would be penalized with poor sales.

The idea that the market will always produce the best map is not true.

I see what you're saying. I agree.

As an aside, I have often wondered at the way North=up became, and remains, completely universal. An upside-down globe "looks" as wrong to me as an upside-down portrait. Obviously there's no reason this must be so; it's nothing more than familiarity with the shapes of the continents from a particular perspective.

Some day, I'd like to have a globe or a big mercator-type map with South at the top (i.e. with the written labels upside-down from normal), and see how long it would take to become accustomed to it.

In early times, east was up and north to the right. Apparently an Australian group made a south is up map

Isn't that backwards? If east were up, north would be to the left. Unless you're making a celestial map.

Yes, you're right, my mistake. I was thinking of an old map I saw that had west up and north right.

"you can't rely on the market to weed out inaccurate maps" is a misleading statement, particularly in the context where people are contending that the size of Taiwan has intentionally been inflated worldwide for political reasons.

THAT kind of inaccuracy bears almost no resemblance to gripes which emerge about the tradeoffs in 2d map projections regarding inevitable (as opposed to highly arbitrary, political) shape and area distortions.

Maps which have south at the top ARE sold and do just fine in the Southern Hemisphere.

The point actually remains that the market has not rewarded any maps which have the kind of distortions which would be required to specifically and artificially inflate the size of Taiwan relative to China, without much affecting anything else.

There are a bunch of parallel conversations spawned from this 2 year old blog post. For reference, here's the area the author talked about in current google maps:

http://maps.google.com/maps?q=Huashan+Road,+Shanghai,+China&...

The locations are all still off and they're consistently off by an offset throughout Shanghai. There might be some deliberate dishonesty by map makers in China, but I don't think this is evidence of it - I think this is just an inaccurate projection. If you want to make bad maps to confuse people - first, that's probably pretty impossible with current information systems, even in China, and second, this would be a really bad attempt at it.

Yes I was familiar with that at the time, but I don't recall if it was mentioned in our particular discussion. In any case, Taiwan is relatively far South in its region so the projection effect would tend to be reduced. It would actually have the effect of making mainland China look larger.

Yes, the mercator projection is not at play here, but I'm pointing out how you can sell a 'wrong' map and not be commercially penalized.