Sunday 7 June 2015

Bend it like Mercator

After their win in the Champions League final yesterday, the 101 Great Goals blog published a piece on the relative location of FC Barcelona's triumvirate of South American strikers. They picked up a map from Reddit that showed their birthplaces as being positioned in such a way that you can draw a perfectly straight line between them on Google Maps.

Here's the map:

A headline writer's dream...arguably the three best strikers in the world all born in formation as well as playing in formation for the world's best team. An easy map to make...take a pen and draw a line across the map to link three red symbols, each of which is about 50 miles in diameter in real world units. Job done.

Except the map is incorrect...which makes the headline potentially incorrect too. A straight line between two places on the globe becomes a curved line when projected using Web Mercator (which the Google Map used by the author is in this case). You cannot simply draw a straight line on the map and infer that it represents a straight line on the curved surface of the globe - because it doesn't.

Here's what the line looks like on a virtual globe as if looking from Messi's birthplace to Neymar's birthplace:

And when we place that line back onto a projected flat map, here's the outcome:

The line now has a slight curve to it but with symbols about 10 miles in diameter it still just nicks the edge of the town where Suarez was born. If I'd used smaller symbols I could have shown the line doesn't pass through Salto, Uruguay. If I'd used big red blobs like the original then of course the line would pass through Salto. Built correctly, we not only get an accurate map...but one that supports the story even better!

OK, we're talking small margins here but the author of the original map got very lucky simply because of the quirk of geography relating to the three players he chose to link on the map. Because the three locations are relatively close to one another (in global terms) and they are also only 30 degrees or so south of the equator we don't see a massive distortion in the line. It has a curve, yes...but only a slight one.

But what if we look at three other footballers? Wayne Rooney was born in Croxteth, Liverpool. Harry Kewell in a Sydney suburb in Australia; and C. V. Pappachan, the famous (?) former Indian footballer born in Thrissur. Here's their map:

As far as I know there is nothing at all to link these three footballers but if we'd taken the mapping approach used to link Barcelona's strikers we'd also get a perfect straight line passing from Liverpool in the UK, all the way to Sydney, Australia via Thrissur on the southern tip of India.

If you got in a plane and flew the straight line route between the UK and Sydney the closest you get to Thrissur is about 2,500 miles. The red line shows the planar version of a straight line projected on Web Mercator. I included the Barcelona striker's line for scale which shows that smaller distances, particularly near the equator, 'appear' less curvier.

News aggregators, blogs and, well, pretty much anyone should question maps. They lie. They are terrible at telling porkies. Worse. Most map readers don't know they're being fed a lie because they look authoritative; and they don't know that the maker of the map they're looking at didn't know the pitfalls of their approach either.

As it turns out, Barça's strikers do happen to have been born close enough to almost lie in a straight line on the globe and on the map. The curve on the projected map tells the accurate story. Try telling the story using three other footballers who appear to have been born along a straight line on a map and chances are, they weren't.

Hat Tip to Brian Timoney for the tweet about this map.

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