Why it’s impossible to measure England’s coastline
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Re: Why it’s impossible to measure England’s coastline
#2I was thinking about this recently, the way to do is to define a radius, and then imagine rolling a circle of that radius around the outside of the coastline (or around the inside! Define that as well) and then take the length of the equivalent track that never leaves contact with the circle.
So you get a different length depending on the radius you choose, but at least you get an answer.
You could define the radius in a scale-invariant way (proportional to the perimeter of the convex hull of the land mass for example) so that scaling the land mass up/down would also scale our declared coastline length proportionally.
Re: Why it’s impossible to measure England’s coastline
#3I was thinking about this recently, the way to do is to define a radius, and then imagine rolling a circle of that radius around the outside of the coastline (or around the inside! Define that as well) and then take the length of the equivalent track that never leaves contact with the circle. So you get a different length depending on the radius you choose, but at least you get an answer. You could define the radius…
A radius of plank length is the only true answer
Re: Why it’s impossible to measure England’s coastline
#4I was thinking about this recently, the way to do is to define a radius, and then imagine rolling a circle of that radius around the outside of the coastline (or around the inside! Define that as well) and then take the length of the equivalent track that never leaves contact with the circle. So you get a different length depending on the radius you choose, but at least you get an answer. You could define the radius…
It's in no way a meaningful solution. If you're settling for a resolution, you don't need a ball-rolling analogy. We already know the length of a given coastline at given resolutions (ignoring the constant changing of the coastline itself). What's practically not feasible is getting every country on earth to agree on the right resolutions. And that's for good reasons, because the desired accuracy depends on many factors, some situational and harder to quantify than just size of the enclosed land mass.
Re: Why it’s impossible to measure England’s coastline
#5tl;dr - for the same reason as any other coastline or complex border.
Also, it annoys me that the trail in question is advertised as allowing one to walk the entire English coast - but fails to mention Wales and Scotland are in the way (the trail is not contiguous).
Re: Why it’s impossible to measure England’s coastline
#6[dead]
Re: Why it’s impossible to measure England’s coastline
#7This article says that by using a smaller unit of measure, the measured coastline increases.
The concept of dimension in fractals is backed by a similar idea! Take the Koch curve for example, at any iteration it gets longer and its 1-dimensional length loses the usual meaning because it diverges to infinity as you continue iterating. Intuitively the fractal dimension allows you to calculate how fast the measurement increases as the scale to measure it gets smaller.
In a more precise way, for most self-similar fractal made of N copies of itself, each scaled by factor r, the dimension is defined as: D = log(N)/log(1/r)
In the case of Koch curve it’s 1.2619...
Re: Why it’s impossible to measure England’s coastline
#8I was thinking about this recently, the way to do is to define a radius, and then imagine rolling a circle of that radius around the outside of the coastline (or around the inside! Define that as well) and then take the length of the equivalent track that never leaves contact with the circle. So you get a different length depending on the radius you choose, but at least you get an answer. You could define the radius…
Not a bad idea - one issue would be when the circle approaches a 'narrow' section that widens out again. If too big to fit into the gap, the circle method would simply not count any of this as land. I think it would be unreliable compared to moving along the coastline in fixed increments (IE one-mile increments or one-foot increments, depending on your goal)
Re: Why it’s impossible to measure England’s coastline
#9This article says that by using a smaller unit of measure, the measured coastline increases. The concept of dimension in fractals is backed by a similar idea! Take the Koch curve for example, at any iteration it gets longer and its 1-dimensional length loses the usual meaning because it diverges to infinity as you continue iterating. Intuitively the fractal dimension allows you to calculate how fast the measurement i…
Indeed, the Wikipedia page on fractal dimension[1] uses the coastline paradox[2] as a leading example.
[1] https://en.wikipedia.org/wiki/Fractal_dimension
[2] https://en.wikipedia.org/wiki/Coastline_paradoxRe: Why it’s impossible to measure England’s coastline
#10tl;dr - for the same reason as any other coastline or complex border. Also, it annoys me that the trail in question is advertised as allowing one to walk the entire English coast - but fails to mention Wales and Scotland are in the way (the trail is not contiguous).
Assuming they specifically do advertise that you can walk the entire English coast, then it is accurate, as Wales and Scotland are not England.