The wonderful ever-lengthening Great Wall of China

Author: Julian Champkin

Part of the Great Wall.

Part of the Great Wall.

Image by Rux - ReadyForTomorrow/Wikimedia.

How hard can it be to measure a wall? You get out the tape measure, plonk the end of it at one end of the wall and read off the answer at the other end. You might be a centimetre or two out if you are not paying attention, but that should surely be about all. To miss a kilometre of wall looks like carelessness. To miss 12,345 kilometres of it...what were they up to?

It has just been announced that the Great Wall of China is not 8,851 km long, as previously measured back in 2008. It is 21,196.18 km long – more than twice as long as it was four years ago. Where were they measuring it from to get an error that big – the moon? (Great Myths of Our Time: the Great Wall of China is the only man-made structure on earth that can be seen from the moon. Great Corrections of Our Time: No it isn’t. It cannot be seen from the moon at all. Ask an astronaut if you don’t believe me.) (There is also, while we are at it,  a dispute about the height of Mount Everest - do you measure to the highest part of the rock, or the snow and ice covering it? And that's without talking about geodetic datum, spheroids and ellipsoids amongst other necessary measurement tools.)

Ok, I do admit it is harder to measure a wall that long (or a mountain that high), whether ‘that long’ is 8,000 km or 21,000 km. They don’t sell tape measures long enough for a start, and if they did they would be too heavy to carry around. What else went wrong to make that colossal error?

Several things.

A): Definitions: the bit they measured in 2008 was the Great Wall of China that was built during the Ming dynasty, which lasted from 1368 to 1644, to keep out the hostile hordes of Mongolian and Manchurian tribesmen. It is a stone and brick job, with towers and battlements and a road along the top. It’s the one that you see on the postcards. The longer wall that they have just finished measuring is that wall, plus the original, much (much) earlier wall that Qin, the first Emperor of China, commanded to be built between 220 and 206BC. In some places it follows the same path as the other wall (in which case do you count it as two walls or as one?), in other places it doesn’t. It was made mainly of mud and rammed earth, or of sticks pushed into the ground, and almost nothing of it remains visible today. The longer measurement also includes lots of other walls, built at varying times and places, both before Qin and after him, by varying local rulers and warlords, in branches and sub-branches and stand-alone bits that might or might not later have been joined up to other bits; so it all depends on what you mean by ‘The Great Wall.’

It also depends (slightly bizarrely, but bear with me) on what you mean by ‘length’. Do you mean length that is visible above ground today? Or length of wall whose foundations can still be traced, even if buried under drifting sands or accumulated soil? Or length of wall that ever existed, even if all physical trace of it has now disappeared and we know only from written records where it once stood? 

The Great Wall of China at Mutianyu

The Great Wall of China at Mutianyu. Image by Y/Wikimedia.

B) Methods: The 2008 measurement was done largely by looking at historical records – the orders that went out to the builders, to connect this place with that place via this route and those towns and villages along the way. The most recent measurement was an on-the-ground job, using the latest survey and archaeological technology. They might try again, this time using satellite photos. It would probably give them yet a third answer. Which leads to:

C) Uncertainty. There is no such thing as an exact measurement anyway. You can count things exactly: you can know exactly how many apples or pears you have, or how many children. But length isn’t like that: you cannot measure any length exactly. How exact would exact be? To the nearest kilometre? Metre? Centimetre? Millimetre? Hundredth of a millimetre? Ten-millionth of a millimetre? You would still be a fraction of an atom or electron-width out one way or the other. Length is a continuous variable, like weight or size, which means you need to know how accurately you want to measure it, or how accurately you are able to measure it. The latest measurement, of 21,196.18 km, claims accuracy down to the nearest ten metres, which is not at all bad over 20 thousand km – pointless, mind you, but not at all bad.

MORAL: A) If you are measuring something, make sure you know what you are measuring. B) If you are naming something, make sure you know what you are including in your name. C) Know what your error band or degree of uncertainty might be.

And if your error band is 12 thousand kilometres, then perhaps consider that somewhere along the line A) or B) or C) might have gone wrong...

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great Thank you that helps a lot

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Sumit Rahman

This reminds me of the question posed by Mandelbrot: "How long is the coast of Britain?"  The point here is that the coastline is a fractal object so in a sense the answer is "It depends how long your ruler is.  The shorter your ruler, the more wiggly will be the line you are effectively measuring, and the longer will be your answer to the question."  But the issues described above about the Great Wall are those that arise even for non-fractal objects.

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Allan Brimicombe

This is an interesting piece. In general, the more accurately you try and measure something like a coastline or Great Wall of China, the longer it will be. Because it goes up and down steep slopes the 3-D travelled distance will be quite a bit more than the 2-D map distance. Fractal geometry tells us that, in theory, any coastline could be infinitely long, so perhaps too might be the Great Wall of China. It would certainly feel like that if you tried to walk it.

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I think we are into the realm of a Mandelbrot set and fractals.

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