Recall from the chapter on Fractal Geography that a coastline – such as that of Britain – shows more and more detail the closer we zoom into it. If we ask “How long is the coast of Britain,” the answer is that it depends on how closely you look at it, or how long your measuring stick is. If you measure the coastline by taking a map and placing a ruler around the edge you can get a certain value for the perimeter. But if you were to walk around the beaches of Britain and add up all your steps, you’d arrive at a very different (and larger) perimeter. But that value is also an approximation. To get a more accurate value, you’d have to measure the length around every boulder, and every rock, every pebble, and even every grain of sand. And at a microscopic level, sand is a fractal as well, and cannot be easily measured. The answer is: the coastline gets longer and longer as you measure it more closely, and it approaches infinity. This is why the fractal dimension is a very useful concept to describe a coastline. Source: Fractal Foundation Online Course
Well. A coastline approaches infinity, does it? That helps to explain why coastal roads are the same wherever you go: slow. The ones in Newfoundland are no exception.
But the views are generally worth the effort and time it took to get to them.
Hmmmmmm…… So if every coastline, measured in enough detail, approaches infinity, does that imply that every coastline is thereby identical? Or does it mean that there are a multiplicity of infinities, each one different… perhaps like the decimal expression of pi, which is, apparently, a non-recurring decimal, so that even if you take it to infinity, it will not repeat its shuffling of the ten primary integers, which suggests… well, as you said, you’ve never seen a headline that says “Math is fun.”
Jim T – The conflation of infinite length with identity is likely offside. I do remember feeling (hah) astounded when I first heard this about coastlines, though (“Whaddya mean they can’t be measured? Who’s in charge here, anyway?”). So at the 30,000-foot level, math is fun – or, at least, its implications are interesting.
Jim T – You dog! What’s wrong with you that you can’t/won’t share your current feelings? I’ll keep your tactic in mind should I ever need to respond with something/anything to meet expectations.
How about a math joke: then we can say “Math is funny.”?
Barbara – OK, you go first.
At one time Barbie dolls had pulls on them. Pull the string and Barbie would say, “Math is hard.” That’s funny (pretty sad, though, too.)
Barbara – Sadness for the times, I guess; happiness that we’re making some progress. https://techcrunch.com/2016/06/20/dartmouth-graduated-more-women-than-men-in-engineering-this-year/
Barbara – OK, my turn (with a little Google help . . .) Not a joke so much as a riddle. Q: Why don’t they serve beer at math parties? A: Because you can’t drink and derive. (ba da bush) See more here . . .
Thanks for this shot of Rocky Harbour. There are many such beautiful, picturesque sights in Newfoundland, where we were privileged to live for a time in the late 60s.
Tom – My pleasure. Glad it brings back good memories.