Length of the Border

When it comes to measurement, old data often turns to be wrong. But the reasons are not as obvious as might appear at first thought. But let’s get the obvious reason out of the way first:

-       The length of the Spanish-Portuguese border was 987 km as per the former but 1,214 km as per the latter. Why? The size of the ruler used made the difference.

 

Ok, that reason’s trivially obvious, so let’s move onto more interesting reasons.

 

But if you thought the solution to the problem was to use a smaller ruler, that’s not always the answer either. Take the borders of countries like Britain or Norway: notice how they are not straight lines, rather they are broken and twisted? Ok, but doesn’t that just mean we need smaller rulers? At some point, the measured value would be close enough to the correct answer for all practical purposes, right? Aha, no, that won’t do because the term for such borders is one from maths: the borders are “fractal”. Ignoring the technical details, here is what it means in the context we are discussing, namely the size of the border. David Darling and Agnijo Banerjee describe it in their book, Weird Maths:

“(As you smaller and smaller rulers), The length actually grows exponentially, the more precise the measurement gets, rather than approaching, even more closely, a final ‘true’ figure.”

If this were pure maths, the length could keep increasing to infinity even though the area it encloses is still very finite! But for something from the real world, like a border, we’d hit the limit at the atomic level. Still, who’d have thought?!

 

Moving on to a different reason. Centuries back, navigating at sea was a nightmarish problem because there was no way to know one’s longitude (Unlike the latitudes, the longitudes aren’t parallel, so the distance between longitudes is not a constant).

 

With all maritime navigation at stake, even men like Galileo tried to come up with ways to know one’s longitude. He came up with a method based on the periodicity of the movement of the moons of (drumbeats) Jupiter! (Hey, he’d found those moons via his telescope, now he was going to put them to use). While that method wasn’t found practical for the seas, it got accepted on land, as Dava Sobel writes in her book, Longitude:

“Surveyors and cartographers used Galileo’s technique to redraw the world… Earlier maps had underestimated the distances to other continents and exaggerated the outlines of individual nations.”

So much so that:

“King Louis XIV of France, confronted with a revised map of his domain based on accurate longitude measurements, reportedly complained that he was losing more territory to his astronomers than to his enemies.”

 

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