Tuesday, September 05, 2023

The Coastal Paradox And Its Application To Life

I'm not sure how I wound up in the coastal paradox rabbit hole, but I did. 

Here's a brief description (from Wikipedia);
The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal curve–like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox of length" was previously noted by Hugo Steinhaus, the first systematic study of this phenomenon was by Lewis Fry Richardson, and it was expanded upon by Benoit Mandelbrot.

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. Various approximations exist when specific assumptions are made about minimum feature size.

That's interesting, just by itself, and how this was "discovered" was fascinating:
Shortly before 1951, Lewis Fry Richardson, in researching the possible effect of border lengths on the probability of war, noticed that the Portuguese reported their measured border with Spain to be 987 km, but the Spanish reported it as 1214 km. This was the beginning of the coastline problem, which is a mathematical uncertainty inherent in the measurement of boundaries that are irregular.

Investigating the discrepancies in border estimation, Richardson discovered what is now termed the "Richardson effect": the sum of the segments is monotonically increasing when the common length of the segments is decreased. In effect, the shorter the ruler, the longer the measured border; the Spanish and Portuguese geographers were simply using different-length rulers.

As I often do, I see this as a metaphor for something in life; in particular, how people's view of obstacles depends on their personality type.

As an introvert, I tend to use a smaller length of measurement when I'm considering whether to do something. Very small, actually, and it tends to make every prospective trip (whether it's to Japan or just to a restaurant downtown) seem much, much longer. That length symbolically represents the obstacles in my way, and because I use such a small ruler, doing anything can sometimes seem like more trouble than it's worth.

Eli 22.1, though, uses a much larger length when he measures. It's not that he doesn't see obstacles, but rather that has a more appropriate method of measuring real difficulty instead of personality-induced difficulty. I add my own difficulty to anything because of my unit of measurement, creating my own, unnecessary problems. 

Like I've often said before, I've learned much more from my son than I've taught him.

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