[Lucasoato]

This 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...

[interroboink]

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_paradox

[random3]

That is the article. There’s no article, just a rehash of the coastline paradox. All while missing most interesting parts. The Wikipedia article is a much better exposition https://en.wikipedia.org/wiki/Coastline_paradox).

First, it can’t have an exact length because it’s not a static thing, but a process. Second, as opposed to fractals that can be zoomed in forever, our measurements seem to hit some limits, so the reality is not quite like fractals in this sense.

Of course, it all makes sense if you think about it. What’s perhaps more interesting is we can’t “really measure” anything absolutely and the whole idea of absolute measures becomes rather tricky once you get to physics. In fact it gets philosophical and disputed and you realize that nothing is quite certain, nor quite agreed upon.

I think Quanta Magazine does a good job making justice to these things though.

[anonymars]

Relevant 3blue1brown (20 min)

https://www.youtube.com/watch?v=gB9n2gHsHN4