30 March 2011

How long is the coast of Maryland?

Last night's Final Jeopardy clue: "With 301 miles, it has the most coastline of current states that were part of the original 13 colonies." (Thanks to the Jeopardy! forum for the wording.)

This agrees with the Wikipedia list which is sourced from official US government data.

But as Mandelbrot told us, coastlines are self-similar . (Link goes to the paper How Long is the Coast of Britain as reproduced on Mandelbrot's web page, which unfortunately doesn't have pictures. I'm not sure if the original version of this paper in Science did. Wikipedia's article on the paper does.) That is, the length of a coastline depends on the size of your ruler. Furthermore, I would suspect that the fractal dimension of some states' coastlines is larger than others. Wikipedia states that "Measurements were made using large-scale nautical charts" which seems to imply that all the measurements were done at the same length scale, but if you did the measurements at a smaller scale, the states whose coastline have higher fractal dimension would move up the list.

So last night I spent twenty seconds yelling this at the TV, and ten seconds getting out the answer Maryland. Which is wrong. Also wrong: Maine, New York. (Maine used to be part of Massachusetts; the wording is a bit ambiguous.) It appears that only the south shore of Long Island counts as "coast"; the north shore, which borders Long Island Sound, doesn't.

And of course Chesapeake Bay doesn't count either.

1 comment:

dricheson said...

I had to look this up for an article I wrote for the College Math Journal ("Centers of the United States") several years ago. It turns out NOAA has technical definitions for coastline and shoreline. The coastline is measured with a ruler of 30 minutes of latitude, so it is very coarse. Shoreline measures "every feature" (I don't recall their ruler length)—including islands, bays, mouths of rivers (up to the head of the tidewater or where it narrows to 100'). For example, the coastline measurement of the Pacific coast is 1293 miles and the shoreline measurement is 3863 miles.