Coastline

Shortly before 1951, Lewis Fry Richardson, in researching the possible effect of border lengths on the probability of war, noticed that the Portuguese reported their measured border with Spain to be 987 km, but the Spanish reported it as 1214 km. This was the beginning of the coastline problem, which is a mathematical uncertainty inherent in the measurement of boundaries that are irregular.

The prevailing method of estimating the length of a border (or coastline) was to lay out n equal straight-line segments of length ℓ with dividers on a map or aerial photograph. Each end of the segment must be on the boundary. Investigating the discrepancies in border estimation, Richardson discovered what is now termed the Richardson Effect: the sum of the segments is inversely proportional to the common length of the segments. In effect, the shorter the ruler, the longer the measured border; the Spanish and Portuguese geographers were simply using different-length rulers.

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