The Coastline Paradox

By Anupum Pant

The length of Australia’s coastline according to two different sources is as follows:

  1. Year Book of Australia (1978) – 36,735 km
  2. Australian Handbook – 19,320 km

There is a significant difference in the numbers. In fact, one is almost double the other. So, what is really happening here? Which one is the correct data?
Actually, it depends. The correct data can be anyone of them or none of them. It completely depends on the kind of precision you decide to use while measuring the coastline. This is the coastline paradox.

The coastline paradox

The coastline paradox is the counter-intuitive observation that the coastline of a landmass does not have a well-defined length. – Wikipedia

The length of the coastline depends, in simple terms, on the length of scale you use to measure. For example, if you use a scale that is several kilometers long, you will get a total length which is much less than what you’d get when you would use a smaller scale. The longer scale, as explained neatly in this picture, will skip the details of the coastline.

This is exactly what happened when the two different sources measured the coastline of Australia. The first, Year Book of Ausralia, used a much longer scale than the one, Australian Handbook used. Ultimately, the great disparity in the result had to do with the precision of measurement. Had they used a scale just 1 mm in length, the result would have been a whooping 132,000 km.

This effect is similar to the mathematical fractal, Koch’s flake. Koch’s snowflake is a figure with finite area but infinite perimeter. Veritasium explains it better in this video:

Another factor is to take into account the estuaries to measure the length. Then,what about those little islands near the coast? and the little rocks that protrude out of the water surface? Which ones do you include to come out with the data? ¬†And the majestic Bunda cliffs? Probably this article from the 1970’s clarifies what was included and what was not during the time the results were published.

So, the next time someone decides to test your general knowledge and asks you the length of certain country’s coastline, your answer should be – “It depends.”

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