The coastline paradox refers to the phenomenon that a single perimeter can yield multiple lengths, depending on the method of measurement. Measuring a shore in kilometers will yield a different total than measuring it in meters, or arm’s lengths, or thumb spans, or Planck lengths. The perimeter of a body of land or water cannot be precisely defined, since the distance is contingent on the unit of measurement – in other words, on the resolution of measurement. Each resolution reveals different edges; the coastline has features at all scales. Even the perimeter of a puddle approaches infinity: if one wound a theoretically infinite thread around the edge of every pebble, every grain of sand, every molecule, the resulting line might stretch for millions of kilometers. The smaller the unit of measure, the higher the resolution, and the larger the totality of the measurement. For any real-world coastline, a single absolute figure for the perimeter is impossible: not because of a lack of precision, but because of an excess of precision, an excess of information. The edges become multiplied by an endless fractal zoom.
For another project, called The Coastline Paradox: Measuring a Nameless Island, onsite measurements of a single island – in particular, a nameless island in Odense Fjord that recently emerged from the sea and may soon disappear again – were made with rope, thumbs, hands, arm’s lengths, and so on. These are examples of body-based units of measure used for that project.
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