I completely understand why measuring the length of coastlines is not possible but surely measuring a trail should be doable quite easily, you could simply use a gps tracker and it would be precise enough.
Why it’s impossible to measure England’s coastline
11–20 of 42 posts
Re: Why it’s impossible to measure England’s coastline
#12How on earth can you write an article that practically plagiarizes the title, mention the paradox, and neither mention mandelbrot nor cite the original paper anywhere!?
https://www.researchgate.net/profile/Ion-Andronache/post/Wha...
Re: Why it’s impossible to measure England’s coastline
#13I guess I could understand why this would be borderline impossible if you did it manually, but surely today with satellite images and computer vision it really shouldn’t be that difficult to agree on a standard unit and then just automate it. Surely just make the scale human at its smallest (meters works and can get converted from there, assuming you have sufficient zoom level data for the coastline) and call it a day - I have no clue why we are discussing atomic fractal calculus approaching the limit as if that's a real problem for agencies trying to give a cogent answer about a particular country's coastline.
Re: Why it’s impossible to measure England’s coastline
#14I completely understand why measuring the length of coastlines is not possible but surely measuring a trail should be doable quite easily, you could simply use a gps tracker and it would be precise enough.
Beginning of the 3rd paragraph agrees with you:
> But while the length of the newly designed path is easily measurable, the coastline that it follows is not.
Re: Why it’s impossible to measure England’s coastline
#15I completely understand why measuring the length of coastlines is not possible but surely measuring a trail should be doable quite easily, you could simply use a gps tracker and it would be precise enough.
[deleted]
Re: Why it’s impossible to measure England’s coastline
#16I completely understand why measuring the length of coastlines is not possible but surely measuring a trail should be doable quite easily, you could simply use a gps tracker and it would be precise enough.
I think the idea is to show we don't know the exact lengths of any paths that aren't constructed from our handful of mathematically known curves and must approximate using them instead.
If you measure with GPS coordinates, you still run into the same problem. The number of points plotted onto a curve affects the result, and then you are possibly also adding more error than you'd have compared to tracing from aerial photos.
Re: Why it’s impossible to measure England’s coastline
#17This 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…
Relevant 3blue1brown (20 min)
Re: Why it’s impossible to measure England’s coastline
#18I 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…
Re: Why it’s impossible to measure England’s coastline
#19This 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…
[flagged]
Re: Why it’s impossible to measure England’s coastline
#20How on earth can you write an article that practically plagiarizes the title, mention the paradox, and neither mention mandelbrot nor cite the original paper anywhere!? https://www.researchgate.net/profile/Ion-Andronache/post/Wha...
This kind of comment always strikes me as the textual equivalent of the Youtube thumbnail with the big yellow characters and multiple people making an O face and pointing.
The article mentions who observed it in history first, Lewis Fry Richardson, and then links to an encyclopedia article about it which describes Mandelbrot. On top of that, Mandelbrot explicitly named his paper that because he is referencing Richardson.
"Practically plagiarizes the title" because it references the same original referent that Mandelbrot was referencing is really stretching it, mate. Honestly. It would be like calling a book review of Wuthering Heights by Bronte "practically plagiarizing" Fennell's 2026 movie by the same name.