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No One Knows How Long the US Coastline Is (discovermagazine.com)
How long is the U.S. coastline? It's a straightforward question, and one that's important for scientists and government agencies alike. From a report: The U.S. Geological Survey could give you an answer, too, but I'm going to tell you right now that it's wrong. In fact, no one could give you the right answer, and if you look around, you'll find a number of estimations that differ by seemingly improbable amounts. One government report lists the number as 12,383 miles. The same report admits that a different government agency says the figure is actually 88,612 miles. That's an almost eight-fold disparity for a fact that seems simple to obtain. We all know how to use a ruler, right?
Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines. Though the border between land and sea may look fairly straight when seen from far away, they're anything but. Coastlines jut and dip, curve and cut, and each deviation from a straight line adds distance. Some of these features are massive, like bays, while others are miniscule.
Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines. Though the border between land and sea may look fairly straight when seen from far away, they're anything but. Coastlines jut and dip, curve and cut, and each deviation from a straight line adds distance. Some of these features are massive, like bays, while others are miniscule.
It can not be shorter than the longest straight line distance between any two points on the coast line.
Of course it can.
A: Not all land between points of coastline is coastline. We don't even have a solid definition of coastline to start measuring.
B: In strict 3 space, measuring coastline makes little sense. Lines are 2D, the coast is 3D, and you first need strict rules for tracing the path before you can measure it. How do you handle a cliff on a beach? What if it juts out over the water? When considering 2D projections, it makes a bit more sense. But "the longest straight line distance between any two points on the coast line" in such a projection is infinite. Consider "the longest straight line distance between" your dick and your ass based on a 2D projection (flat map) of Earth. That line would simply wrap around the Earth forever in an infinitely tight spiral. Or consider the simpler scenario of wrapping around Earth once. That's "the longest straight line distance", yet we can show the actual distance is shorter, even if we don't know the true position of either point. Start by drawing a bounding box around each point with whatever accuracy/precision we want / can achieve, then measuring the distance between the outer edges of the bounding boxes. This gives us an upper bound for the actual distance. (You can simply draw a line segment between the points, then draw lines perpendicular to that segment at each point, and find where those lines intersect the bounding boxes to determine the "outer edge" of each bounding box.)
Read the article. It turns out that this is not a scientific journal or communique, not a technical report or abstract, not detailed information written by experts for experts. It is a general interest blog discussing items of scientific interest. It makes no claim to be novel or current. Furthermore, the article is not about the coastline per se. The second half of this very brief article discusses fractals and the relevant concepts about measuring length with respect to scale. While many people on Slashdot know this subject and its implications, many other people out there might not. So, as an informative article for laymen, it is perfectly reasonable for the forum it was published in. Even by those standards, it was still brief and naive, but if you have never encountered the concept before, it was a reasonable enough introduction to the idea. It does make one wonder though why it was posted on Slashdot, being as basic as it is.
However, the post has elicited many comments, and now, a challenge. For those who say the coast length is moot, well no, not really so. True, we can quibble the details, and the coastline is dynamic rather than static, and it all depends on length of your ruler. But that does not invalidate that the measure is important based on context. Examples:
- A boat is tasked to follow the coastline, maintaining a tangent or parallel course at all times, 200 meters of the shoreline. The boat has an aft screw, a certain length (e.g. 60 meters), and a certain rudder turning radius. Assume that the boat is laying cable and furthermore that it must to perform to perfect efficiency so that it can maximize the amount of cable it carries rather than excess fuel. How many kilometers will it ply, how many kilometers of cable are needed, how much fuel in its tanks?
- A coastal highway is being built 100 meters back from the high tide waterline. The road will be 10 meters wide. It will go from town A to town B, 20 kilometers from each other as the crow flies. Concrete and asphalt must be specified. How much of each are needed to complete the project?
- Recent seismic or volcanic activity has altered a coastline, creating a new large rocky mass along the coastline near an urban area. The altered contour creates new wave or current or tidal patterns that threaten erosion to coastline. How much rock, timber, concrete, or whatever will be needed to create a new seawall or jetty to protect human structures? Or, based on the metrics of those waves and tides, what will be the erosion rate along nearby beaches?
In each example, the length of the coastline has a tangible meaning. A rowboat that wants to follow the coast 10 meters away will have a different measure than an oil tanker following 2 kilometers away, but for the problems presented, their relative lengths matter. Based on the physical scales of each problem, the shorter rulers with longer coastlines, and the longer rulers measuring shorter coastlines must all be filtered out to yield the Goldilocks answer. As Obfuscant stated in a response above, "If you're estimating how much it will cost to install coastal protection you will measure how long the protection measure is, not how long the coast is behind it."
So, here is the challenge or invitation. Please respond below with realistic scenarios of a scientific, mathematical, engineering, or commercial nature where the length of the coast does matter for the problem or project at hand. They could be hypothetical or imagined, or they could be real world examples of prior endeavors or ordinary practices.
Post here . . . . . .