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.

Mandelbrot, Knuth, and open-ended citations

A citation reproduced verbatim from Benoit Mandelbrot's The Fractal Geometry of Nature (1983):

Knuth, D. 1968-. The art of computer programming. Reading, MA: Addison Wesley.

The "1968-" is not Knuth's birth date, of course, but the date at which he started writing the work in question, which was fifteen years in the making when Mandelbrot wrote. It's still not done.

Incidentally, Mandelbrot's book is a good one, full of pretty pictures (although of course not as intricate as one might see now, because the book is a quarter-century old); it's also fairly casually written. Mandelbrot describes it as an "essay", in what I take to be the original Francophone sense of the word that means roughly an "attempt" at something, and so it's rather discursive, personal, and nonrigorous; these idiosyncrasies are good for a book one wants to read casually, as I do right now, but someone who wanted a rigorous understanding of the concepts might look elsewhere. I'm tempted to say it's a good series of lectures crystallized into paper form, although as far as I know it was never intended as such.

I think I'd heard of the book before, but it was Nova's Hunting the Hidden Dimension (aired on Tuesday night) that got me to actually head to the library and find it. I suspect I'm not alone, because apparently it's selling quite well on Amazon.

(The usual disclaimer on books I'm reading that I borrowed from the library applies: ignore my recommendations if you're at Penn, because I have the library's copy.)