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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!
by Lucasoato 6mo ago
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 6mo agoIndeed, 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
- linzhangrun 6mo ago[flagged]
- colechristensen 6mo agoThe meaning of "coastline" breaks down far before you reach quantum levels. I challenge you to go to the beach and pick a square inch where the "coastline" splits it half and half, this part England, that part the sea.
- BobaFloutist 6mo agoThis is also ignoring the time component, where individual fluctuations in water will change the measurement, tides will as well on a daily and monthly cycle, and as years go by erosion and global climate change will shrink the land and grow the sea.
- anonymars 6mo agoRelevant 3blue1brown (20 min) https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=gB9n2gHsHN4
- random3 6mo agoThat 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 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.