Why it's Impossible to Accurately Measure a Coastline Coastline Paradox Why it's Impossible to Accurately Measure a Coastline

Coastline Paradox Described The coastline of a landmass does not have a well- defined length therefore cannot be measured consistently Why? Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious size of the smallest feature that should be measured around, and hence no single well-defined perimeter to the landmass.

Coastline Paradox Example Great Britain is measured using units of 100 km – the length of the coastline is approximately 2,800 km When measured using units of 50 km, the total length is approximately 3,400 km (~600 km longer)

Animated Example

Mathematically Speaking… The coastline paradox was studied in detail by Benoit Mandelbrot in the 1950s His work resulted in the invention of the mathematical concept: fractal geometry, i.e., a curve that gets more complex the more closely you look at it.

Practically Speaking… …from a data perspective Geographic Information Systems (GIS) must always consider the scale of geographic data when conducting analysis Disparate scales between geographic datasets will result in analysis output inaccuracies Equal scales between geographic datasets will result in higher analysis output accuracy, with defined +/- error ranges Regardless of scale, there will always be discrepancies resulting from the digitizing of the feature, i.e., it will never exactly match the real world feature, nor can the data be replicated exactly by another digitizing method.

So, ultimately… We are likely to never know the exact length of any coastline Length of Canada’s Coastline Source 202,080 km CIA World Factbook 243,042 km Stats Canada 265,523 km World Resources Institute

Sources https://en.wikipedia.org/ http://mathworld.wolfram.com/ https://www.atlasobscura.com/