Madisyn (left), 11, Raighyn, 5, and Peightyn Henry, 11, of Portsmouth play on a rock at Odiorne Point State Park in Rye on Monday. Determining the length of the coastline is more difficult than you may think – some say it’s 18.57 miles, others claim it’s 13 miles and several contend it’s 235 miles. GEOFF FORESTER / Monitor staff

This box, taken from the state's Coastal Access Map, gives the two official N.H. lengths for our coastline - with and without the Great Bay and tidal areas. —Courtesy

It’s summer, which means you have probably spent some time on New Hampshire’s 18.57 miles of seashore, the shortest ocean coastline of any state.

Except maybe it’s actually 13 miles long. Or 235 miles. Or almost anything else you can think of. And maybe it’s not even the shortest.

Very confusing; no wonder I hate going to the beach.

Such uncertainty over something as straightforward as the length of the seashore reflects something interesting: Measuring coastlines is quite tricky, in ways both geographic and mathematical.

The geographic trickiness comes from which definition you use.

Again, that seems straightforward: Surely the coastline is every place where the ocean touches the shore, and the thing that differentiates ocean from lake is salt water. So the coastline is everywhere that salt water comes into contact with land, right?

If so, New Hampshire just lost the title of “shortest ocean coastline.”

Counting all the places where salt water sometimes makes it to the land means you have to include the Great Bay, the huge estuary that helped make the New Hampshire colony such a fabulous place for oystering. This bumps our coastline up to 235 miles, which means we have to hand that coveted “less is more” title to Pennsylvania, a seashore-less state that says it borders 112 tidal miles of the Delaware River, where seawater can flow north from the Chesapeake Bay.

Among those who use the 235-mile figure is the state Department of Environmental Services. Its Coastal Program includes the Great Bay when discussing our shoreline because it’s concerned about environmental stuff, but I don’t think most of us have tidal estuaries in mind when thinking about the seashore. We think about beach, rocks, seaweed and small children screaming from sunburn, not oyster beds.

So let’s ignore the tidal-basin dispute and turn to mathematics, where the issue is more interesting.

Although mathematicians are not a group normally associated with the beach, they have long been familiar with the coastline conundrum, which came to public attention in a 1967 article in the journal Science titled “How Long is the Coast of Britain: Statistical self-similarity and fractional dimension.” In that piece, fractal pioneer Benoit Mandelbrot, using earlier work by a British polymath named Lewis Fry Richardson, discussed how the measured length of a coastline changes, depending on the size of the scale used to measure it.

Mandelbrot was actually interested in applying the concept of fractional dimension, which blossomed into the much-loved field of fractals, but we’re interested in the coastline itself.

The issue is that if you measure a coastline map with a great big ruler, you’ll have to jump over lots of small inlets and bays, making the result straighter than if you’d use a little tiny ruler that could fit into those inlets. Straighter lines are shorter than wiggly lines between two given endpoints, which means that using a bigger ruler will produce a shorter measurement for a given coastline.

New Hampshire’s official tally is 18.57 miles. The Coastal Access Map put out by DES lists this figure as our “Atlantic shoreline,” as compared with 235 miles of “estuarine shoreline.”

The 18.57-mile figure was developed more than a decade ago by Ken Gallager, principal planner with the Office of Energy and Planning. He calculated it via the state’s geographic information system, or GIS, when maps were updated to a then-new federal standard of 1:24,000, in which 1 inch equals 2,000 feet.

(A side note: When I wrote about this topic in 2006, I said that Gallager spread out a physical map and measured the coast with a physical ruler. When I touched based with him again this month, Gallager said he wanted to “revise that statement,” a polite way of saying that I am an idiot who had misunderstood him, since GIS has been around since the 1990s and no way he was crawling over a paper map.)

All fine and dandy, but the National Oceanographic and Atmospheric Administration, the federal authority on coastlines, used its maps and came up with just 13 miles as the length of our Atlantic seashore. That is the number you’ll find cited in Wikipedia and on VisitNH.gov, the official tourism website for the state, although the 18-mile figure is much more commonly found online. (Oddly, VisitNH.gov claims the 18-mile figure “include our islands,” which Gallager says is not true. No matter what scale you use, there’s no way the coastline of New Hampshire’s few islands is 38 percent as long as the coastline of the mainland.)

NOAA uses a variety of map scales, some as small as 1:5,000, so that’s why its tally differs from the state tally. It’s a perfect example of Mandelbrot’s dictum about measurement depending on the size of your ruler.

So which number is “right”? Both are, and neither are. In fact, you could make our coastline almost any number you wanted by using a small enough measuring stick. Take a 1-inch-long ruler and start tallying at the Massachusetts border, adding up the distance every bolder and rock at high tide, and I’m sure you could double or triple the official length.

Plus, that would be a lot more fun than most things you can do at the beach.

One last note, to make it more confusing: Wikipedia also gives NOAA’s figure for overall “shoreline mileage,” which NOAA says is 131 miles for New Hampshire. That includes “offshore islands, sounds, bays, rivers and creeks . . . to the head of tidewater or a point where tidal waters narrow to a width of 100 feet,” a definition difference that at least partly explains why it is barely half the total of the estuarine boundary number used by DES.

What’s weird, though, is that NOAA also says our shoreline mileage figure is slightly shorter than Pennsylvania’s shoreline mileage, even though our estuarine coastline is longer. I’m not quite sure why this is so, but it does mean that New Hampshire always wins the shortest-seawater-coastline category as far as NOAA is concerned.

(David Brooks can be reached at 369-3313, dbrooks@cmonitor.com or on Twitter @GraniteGeek.)