“Uh, what?” you say.
A few weeks ago, I read a post on Hacker News about something called “the coastline paradox.” Despite my geology background, I hadn’t heard of this before.
The measured length of the coastline depends on the method used to measure it and the degree of cartographic generalization. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious size of the smallest feature that should be taken into consideration when measuring, and hence no single well-defined perimeter to the landmass.
Essentially, the smaller unit of measurement you use to try and measure something with a fractal pattern, the longer it becomes.
So, I’m currently reading a book called “Reading the Rocks” by Marcia Bjornerud and there is an entire section devoted to the coastline paradox, which I just learned about.
Mandelbrot’s point was simple: If you use a very long stick to measure a coastline, you will capture the broadest arcs but miss the fjords, firths, and coves, and you will conclude that the coastline is not terribly long. As you use shorter and shorter rulers, however, the coast actually stretches. Mandelbrot named such stretchy features fractals…
Neat!
This brings up the second TIL: What is the phenomenon called when you hear something for the first time and then suddenly start seeing or hearing it everywhere?
It’s the Baader-Meinhof phenomenon, also known as the frequency illusion:
The frequency illusion (also known as the Baader-Meinhof phenomenon) is a cognitive bias in which a person notices a specific concept, word, or product more frequently after recently becoming aware of it.
Well, here’s to seeing more coastline paradoxes.