Why You Can't Measure Coastlines 🤨

Why is it impossible to accurately measure the coastline of a country?

Take the United States, for example. The Congressional Research Service estimates the coastline at around 20,000 miles, while the National Oceanic and Atmospheric Administration puts it at 95,000 miles.

But how can the same coastline be measured so differently?

Well, the answer lies in how coastlines are measured and the level of detail considered. Coastlines aren’t straight; and the more you zoom in, the rougher and more intricate they appear.

Let's use Great Britain as an example, If you use a larger unit of 100 miles, you'll use 18 units and get around 1,800 miles. But if you switch to 25 miles, you'll end up using 108 units and get 2,700 miles. You see, the shorter the unit, the longer and more accurate the coastline becomes.

But here’s the catch—even if you keep zooming in, it’s impossible to get a perfect measurement. You could measure every grain of sand and still be far off. And to make it more complex, coastlines are constantly changing with the tides, making them even harder to pin down.

#geography #facts #shorts

[stevengreidinger]

Measure the amount of fencing required to fence off the ocean from property. At high tide, chop off any details less than two meters long.

[gospelofrye]

"The shorter the unit, the more accurate the coastline... ladies."

[koteswararaoatluri]

1-Coast lines change by submergence of land or creation of deltas or melting of glaciers or expansion of ice age and making more glaciers and lowering sea coast levels 2- plate tectonics and continental drift 3- the units of measurement changes the length the larger the unit, the lessor the coast length, the shorter the measuring unit, the longer coast line so length of coast is always an approximation 4- the waves ebb and flow changes coast by time .

[stevoplex]

Coastlines, in particular and other fractal measurements and parameters in general should always be expressed and defined as a measurement limited by the degree of precision (limit of resolution). So that, for example, the coast-line of the island of Babaloon is 876 km at resolution 1km. 1275.4 km at resolution of 500m. Varies with daily tides by 6%.

[hola-hola-]

This is essentially about calculating a line integral. This is the result we would get if we made those measuring lines infinitily small.

Maybe it's hard to calculate it exactly, but it is not infinite. We could try and find an upper bound for it, which is a large enough value that we are 100% sure it it bigger than this value.

Let me give you an example. We estimated that, if we measure the coastline of Britain using 100 mile lines, we use 18 such. Now, this obviously is too small, as it doesn’t capture all the curves. What about taking those 18 lines and making them 1k miles instead. Wouldn't those combined be bigger than the coastline? So maybe 18k miles is an upper bound, albeit an inaccurate one?

Edit: indeed the length can get infinite as we take smaller and smaller measuring units. This is because coastlines are fractals and, as a result, they have a dimension between 1 (a line/curve) and 2 (a 2D shape with area). That means fractals have an infinite length, but zero area, kind being "more" than a line but "less" than a 2D object.

In fact, the rate at which the (logarithmic) measured area increases as we increase the (logarithmic) measuring length determines the dimension of the coastline. This means the line integral I describe above is infinite and my previous answer is wrong. Check out the comment below for more details.

[sujesh]

There are numerous Islands which also add to the country's coastline

[MikeMalik-ueen]

Hey i really like how you create your videos. Which tools do you use?

[the_aaaa]

Basically, we need to standardize the coastline interval measurement worldwide

[condude]

Hence why every coastal (optional) country has a coast line of 100.

[garbagecan]

Coastlines are fractals, and so there’s more “stuff” in a fractal than there is in a line or (rectifiable) curve that you could calculate the line integral of. As a consequence, calculating the “length” of a coastline isn’t exactly a well defined question. It’s the same as if you asked someone to find the length of a plot of land—you can have an arbitrarily long curve contained inside of it, and so any measure of length you could assign to it would be trivially infinite. One way around this researchers have found, which in particular can be applied to coastlines, is to measure something called the fractal dimension (the technical term is Hausdorff dimension). This assigns a number between 1 and 2 to a coastline, with a fractal dimension of 1 meaning the coastline is actually some curve (and in all but the most pathological cases one could actually compute a length there) while a fractal dimension of 2 means that the coastline is so jagged that it actually “sweeps out” some nontrivial area (as opposed to a set with area zero). In reality, all coastlines (which formally are thought of as the topological boundary of subsets of the sphere) have a fractal dimension somewhere between 1 and 2, and so coastlines have “infinite” length and zero area. As an aside, another (perhaps more practical) way to resolve the issue is to fix a minimum distance that one can resolve, and measure the coastline by approximating the coastline with line segments of at most that length. Though since coastlines are fractal, letting this minimum resolution tend to zero does not mean that the length obtained from these approximations approaches a finite limit, in fact it means they balloon to infinity, which is exactly the phenomenon described in the video.

[michaelh]

I believe we could accurately measure use a drone with LiDAR and scan the coast… it would take a while but if say we could use increments of 1/8 mile etc 😊

[Preix]

I think that scandinavia went for the grain of sand mode

[neverseenbeforenow]

Just use 1m units to the max of where the waves reach

[CryAlpha]

Correction. smaller measurements don’t lead to more accurate coast lines, it only correlates with longer coasts

[poolbwoy]

its almost like earth is one place instead of a place divided

[Frozen_Egg]

Technically the principality of Sealand has a set coastline bc the poles holding them up don't shape like coasts do around water

[samuelpotters]

Um actually, all we need is a really really big tape measurer

[Whoppær]

Use 2 or 5 meters as a estimate. It cant be exact but its prob close.

[TheDarkKnight]

And then there is Norway with all the Fjords that are technically coastlines, which if you want to you can count that and then they suddenly have the biggest in the world.

[Mahoraga-hl]

20, 000 miles and 95, 000 miles 😭😭😭 what are these people thinking bro its bigger than earth then