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Benoit Mandelbrot: 2 ideas and puzzles worth knowing

2 ideas and puzzles from Benoit Mandelbrot, each explained in a minute and credited to the original work. Free on Savvy.

• A coastline's length changes depending on the size of ruler you measure it with

  Measure Britain's coast in 100km segments and you get about 2,800km; switch to 50km segments and it jumps to roughly 3,400km, because finer rulers catch more inlets and bends. Math…

  — Benoit Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

• How long is Britain's coastline? Honestly, the question doesn't really have an answer

  Measure a coastline with a 100 km ruler, then a 1 km ruler, then a 1 m ruler, tracing every inlet and headland the shorter ruler can reach that the longer one skipped. What happens…

  — Benoit Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

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