The Coastline Paradox: Measuring a Nameless Island

Field studies, drawings, and published artist book (see The Artificial Magic ... book)

A nameless island, Odense Fjord, Denmark


An island with no name in Denmark had recently emerged from the sea. Measurements were made with rope, thumbs, hands, and arm’s lengths. Using different units of measure generated many different perimeter totals. Even establishing the boundary between land and sea was not easy – my team and I were relentlessly foiled by the fickle shoreline, its tiny, vulnerable perimeter made dramatically dynamic by the tides, waves, and rotting seaweed. Here, the fieldwork on one hand fell apart as science and, on the other hand, emerged as ontological situation, framing paradoxes of empiricism and imperialism: Cartography’s legacy of human empire and knowledge was momentarily dissolved in the relationship of body to shore, in a collapse of map and territory.

The coastline paradox is the counter-intuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal-like properties of coastlines. More concretely, the length of the coastline depends on the method used to measure it. 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 limit to the size of the smallest feature that should not be measured around, and hence no single well-defined perimeter to the landmass. For instance, if it were possible to wind an infinitely small measuring tape around every single pebble and grain of sand on an island’s – or puddle’s – perimeter, the coastline’s seemingly finite length would actually unfurl into millions upon millions of kilometers. The more precise mapping becomes, the more challenges it presents to quantification.