The coastline paradox, a popular illustration of fractal geometry, posits that a coastline’s length is impossible to definitively measure because each scale of measurement gives a different result. The edges that appear as straight lines on a map are just simplified representations of the jagged outcroppings that you’d observe if you explored the same coastal area on foot, and if the contours of each rock were measured and added up, the “length” of said coast would obviously be much higher than the lengths of the simplified straight lines. No individual measurement of the coastline is correct; getting an authoritative answer requires an agreed-upon scale of measurement and a consensus about which details are too small to matter. One quirk about fractal phenomena is that increasingly advanced measurement tools can reveal additional levels of detail, thereby decreasing certainty about the answer to the original question. As that’s frequently inconvenient, we often just stick with the old answer.
#91: Music for Airports
#91: Music for Airports
#91: Music for Airports
The coastline paradox, a popular illustration of fractal geometry, posits that a coastline’s length is impossible to definitively measure because each scale of measurement gives a different result. The edges that appear as straight lines on a map are just simplified representations of the jagged outcroppings that you’d observe if you explored the same coastal area on foot, and if the contours of each rock were measured and added up, the “length” of said coast would obviously be much higher than the lengths of the simplified straight lines. No individual measurement of the coastline is correct; getting an authoritative answer requires an agreed-upon scale of measurement and a consensus about which details are too small to matter. One quirk about fractal phenomena is that increasingly advanced measurement tools can reveal additional levels of detail, thereby decreasing certainty about the answer to the original question. As that’s frequently inconvenient, we often just stick with the old answer.