Bill Trandum

How long is our Key Peninsula coastline?

The length of our coastline depends on the length of the ruler used to measure it. By simply using prominent points around the peninsula and measuring by the mile, Google Maps says our coastline is about 37.75 miles long. What do you bet it’s twice that? Four times? More?

In 1983 mathematician Benoit Mandelbrot proposed the notion of fractals to describe coastlines. The term “fractal” was first used by Mandelbrot in 1975. He based it on the Latin frāctus meaning “broken” or “fractured,” and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature. Hang in there, it gets simpler.

The underlying notion is that as the measurement unit gets smaller and smaller, there’s more and more stuff to measure and more decisions to be made about what and where to measure.

So, if instead of using mile-long milesticks to measure our coastline, we use yardsticks, we’d include measurements inside Whiteman Cove, Taylor Bay, Filucy Bay, VonGeldern Cove, Mayo Cove and Glen Cove in doing our calculation. And if a stream emptied into a bay, like it does in Rocky Bay, Vaughn Bay, Dutcher Cove, and Minter Bay we’d need to decide what part of each estuary was bay, and what part was stream bed.

Mandelbrot would point out that if we were to use inches, we’d have to include thousands of little indentations, lagoons, points, outcroppings and other coastal features in our measurement. It’s actually endless, according to him, because the measurements could get infinitesimally small in which case variations in sand, gravel, rock and clay buildup along the shore would have to be included as part of the length of our shoreline.

And, how would we account for boulders or tidal islets that appear and disappear with the tide? Are their circumferences part of our shoreline measurement?

Absurd, you’re thinking, but not to Mandelbrot. He used his fractal theories to explain mathematically how many things in nature come to be ordered the way they are. Coastlines are just one of them.

While there’s not been a great deal of study of our little Key Peninsula coastline, there has been detailed study of the west coast of British Columbia. Of course our Canadian brothers and sisters did the measurement in kilometers, probably to confuse us, so I converted them to miles.

If the measuring stick is a hundred miles long, the B.C. coastline is 600 miles from the southern tip of Alaska to the north-westernmost tip of Washington state. But measured using a mile-long measuring stick, the coastline measures 15,985 miles. That’s more than 26 times as long. Same coastline, shorter yardstick.

That is known as the paradox of the coastline. Whether you gaze upon our shoreline from a thousand feet high or from five feet high, the indentations, variations, bays and other features are quite similar. They are fractals, the same geometric patterns on a much smaller scale. So let’s go to the shore, observe some coastal fractals, and while we’re at it, let’s pick up litter. That will shorten our coastline because there will be fewer things to measure. Hmm, there’s a question: Should man-made objects be included in coastline measurements?

Bill Trandum is a guest columnist of the Key Peninsula News and a self-described student of all things winds, tides and waters.

Winds, Tides and Weather
Winds, Tides, and Weather