So How Long is the Coastline of Maine?

Benoît Mandelbrot, the pioneering mathematician whose name is popularly synonymous with fractal geometry, died last week.

(A music video for Jonathan Coulton’s song Mandelbrot Set by Pisut Wisessing made in Film 324: Cornell Summer Animation Workshop, taught by animator Lynn Tomlinson every summer for Cornell’s summer session, in the department of Theatre, Film & Dance.)

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  • Custador

    A great man who will be chiefly remembered for producing wicked cool tee-shirts…

  • Peter Cross


  • Aphoric

    In Maine Studies class that we all had to take in school, I faintly remember the number being about 4,000 miles.

    • Michael

      Unfortunately measurements of coastline length are not done on a standardized scale so they aren’t really meaningful. I could measure the coastline of Maine using different resolutions and get values ranging from a few hundred miles to millions of miles.

  • L.Long

    The Maine coast line is the same size as the NH coast line….
    Infinitely long.
    As Mandelbrot shows a coast line is a decreasing self-similar line that as your ruler shrinks and you look closer and closer the details get finer and you can never measure the fractal length of the coast.
    But since people can’t easily do that they ignore Mandelbrot and Aphoric is probably right.

    • Jerdog

      Well not quite infinitely long. Don’t confuse a mathematical model with the real world. There is a shortest possible ruler.

      • Elemenope

        There is a shortest possible *physical* ruler (being one planck radius in length), but there is nothing intrinsically wrong with measuring with infintesimals and interpolating indefinitely; you don’t need to build a physical ruler to interpolate smaller distances. Those distances may not be sensible in the context of physics, but they still exist in a spatio-temporal sense.

        • Peter Cross

          but there is nothing intrinsically wrong with measuring with infintesimals and interpolating indefinitely

          Yes, there is, if your “interpolation” is going to add new detail with a nonphysical basis.

          Wikipedia sez:
          “In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.”

        • Michael

          There is no particular reason the Planck length should be the shortest possible ruler. However, the definition of “coastline” definitely breaks down at the smaller scales anyway.

    • Kodie

      GENERAL COASTLINE figures are lengths of general outline of the
      seacoast. Measurements were made with a unit measure of 30
      minutes of latitude on charts as near the scale of 1:1,200,000 as
      possible. Coastline of sounds and bays is included to a point
      where they narrow to width of unit measure, and the distance
      across at such point is included. Most of … the general coastline
      figures are the same as those published in the First (1915)
      Edition, but all were remeasured in 1948. The coastline of
      Alaska was again remeasured in 1961, and again the 6,640-mile
      figure of 1915 was retained. The principal change in the 1961
      edition is the increase of Florida coastline from 1,1197 to
      1,1350 miles; this was checked and re-checked and reflects a new
      approach to measurement of the Florida Keys.

      TIDAL SHORELINE figures were measured in 1939-40 with a recording
      instrument on the largest-scale charts and maps then available.
      Shoreline of outer coast, offshore islands, sounds, bays, rivers,
      and creeks is included to the head of tidewater or to a point
      where tidal waters narrow to a width of 100 feet.

  • ClamCove

    I’m not sure. But I’m sure glad to be living on the coast of Maine!

  • Tom Coward

    I live on the coast Maine too. The cool thing about it is not how long it is, but rather how far it is from anywhere else! It may be the same length as New Hampshire’s coast, but it is infinitely longer than Vermont’s.