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No. 3294:

Today, how long is a coastline?  The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them. 


     My wife looks up from her book and says: “Did you know that Maine has the fourth longest coastline of any US state?”  Interesting!  So, just for the fun of it, I look it up.  Oops!  I find it ranked ninth, not fourth.  So I look further.  Turns out, people measure coastlines in different ways.

     The closer we see a coastline, the more jagged it gets. The straight distance along Maine’s coast from New Hampshire to Canada is 228 miles – ninth longest among states. But the National Oceanic and Atmospheric Administration, NOAA, follows jagged ins and outs of the coast.  They get a coastline fifteen times greater

Now I find a curious graph.  It shows how long Britain’s coastline would be if we traced it with different measuring sticks.  If our stick were a huge thirty miles long, we’d get a two-thousand-mile coastline.  Reduce the stick to the width of a football field, and we’d get well over ten thousand miles.

Wikipedia image showing how the length of Britain’s coast varies with the length of our imagined “measuring stick

So, what’d happen if our measuring stick were just a common ruler?  Now, as we work our way around each bay, each tiny inlet, each large rock – the coastline becomes unimaginably long. 

This business catches the attention of mathematicians.  Should we view a coastline as a fractal object – like a snowflake?  If we could, the length would go to infinity as our measuring stick approaches zero in length.  But coastlines don’t replicate their shape as they shrink.  They are not fractals.  And – we have to stop at some reasonably small measuring length. 

Now: another wrinkle: Some coastline lengths increase much faster than others as we shrink our unit of measure.  Compare, say, the states of Hawaii and Maine.  Hawaii’s coast is far smoother than Maine’s.  So: A very large measuring stick shows Hawaii with the fourth longest coastline, and Maine with the ninth.  A shorter unit – the one used by NOAA – ranks Hawaii down at 18th longest.  And it raises Maine to fourth. 

This business can get tense when nations argue about boundaries. Boundaries are often defined by features, almost as messy as coastlines.  The boundary between Portugal and Spain is a twisting line of rivers and mountain ridges.  As late as 1951, the two countries disagreed on the length of their boundary by over twenty percent.

A portion of Australia’s relatively smooth coastline

Now, of course, the ravages of climate-change throw another monkey wrench into such measurements.  Coastlines change.  Rivers alter their courses.  Volcanos recently increased Hawaii Island’s coastline by adding seven hundred acres to it. 

A message lurks is all this.  It is: Let’s not be too quick to accept a simple answer.  The world doesn’t stand still for us to measure it.  And, even in-so-far as it does, we have to stay wary.  These coastlines are just one more reminder: It is that I’d better stay ready to question things I thought I already knew.

A portion of Norway’s impossibly complex coastline

I’m John Lienhard, at the University of Houston, where we’re interested in the way inventive minds work. 


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Here is the Wikipedia list of coastline lengths of US states.  It gives the simple lengths and NOAA lengths that I mention. 


This Wikipedia page gives a similar listing by country, and it also provides an extensive discussion of the coastline length problem.  It includes the moving graphic which indicates the effect or refining the measure measurement of the British Coast that we include in the text above.


See also this paper by B. Mandelbrot: “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” Science, New Series, Vol. 156, No. 3775. (May 5, 1967), pp. 636-638. 


I have not used a common term for this business, here.  It is, “The Coastline Paradox.”  That’s because I do not see a paradox here – merely a situation that results in confusion. However, I recommend an excellent YouTube video titled, “The Coastline Paradox.”  See:


Photos by John Lienhard. Britain graph is courtesy of Wikimedia Commons.


This episode was first aired on February 16, 2024