No, you can only get an answer up to the limit imposed by the fact that the coastline is actually composed of atoms. The fact that a coastline looks like a fractal is misleading. It makes us forget that just like everything else it’s fundamentally discrete.
This has always bugged me as a case of especially sloppy extrapolation.
Of course you can’t really measure on an atomic scale anyway because you can’t decide which atoms are part of the coast and which are floating in the sea. The fuzziness of the “coastline” definition makes measurement meaningless on scales even larger than single atoms and molecules, probably. So you’re right, and we can’t measure it arbitrarily large. It’s just wordplay at that point.
And assuming an arbitrarily large world, as the area of the island increases, the ratio of shoreline to area decreases, no? Not sure what that means in terms of the metaphor, though...
Modal realism says “all possible worlds are as real as the actual world” (Wikipedia). In different possible worlds there are different laws of physics, almost all of which don’t allow for life. In some proportion of those where they do allow for life, there’s no life anyway (it seems to be rare in our universe). In some proportion of universes with life, there is no sentient life...
Without sentient life, there’s no knowledge, so no shore. No shore means no land.
But the cutoff is obviously not “continent”/”not continent”, but rather “takes up more than half the world” versus “doesn’t take up more than half the world”—possibly with an additional constraint of a sufficiently simple shoreline...
This is answer is about as informative as answering “Why do aeroplanes fly?” with “Calculus. Differential equations with forces.”.
If you are talking about continents larger than half the world, then DanArmak has already pointed it out and much more politely. However, as dlthomas points out the distinction is not based on it being a continent or not, but on it covering more than half the word.
Also, everything we call a continent on Earth takes up less than half of it, and for such things there is a minimum perimeter that increases as the area increases. (The minimum perimeter is something a little bit like 2*sqrt(pi*Area) (except different because the Earth is a sphere rather than a plane).)
The larger the island of knowledge, the longer the shoreline of wonder.
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Only while the island is smaller than half the world :-)
Anyway, I can always measure your shore and get any result I want.
No, you can only get an answer up to the limit imposed by the fact that the coastline is actually composed of atoms. The fact that a coastline looks like a fractal is misleading. It makes us forget that just like everything else it’s fundamentally discrete.
This has always bugged me as a case of especially sloppy extrapolation.
The island of knowledge is composed of atoms? The shoreline of wonder is not a fractal?
Perhaps it’s composed of atomic memes ?
I think this conversation just jumped one of the sharks that swim in the waters around the island of knowledge.
Of course you can’t really measure on an atomic scale anyway because you can’t decide which atoms are part of the coast and which are floating in the sea. The fuzziness of the “coastline” definition makes measurement meaningless on scales even larger than single atoms and molecules, probably. So you’re right, and we can’t measure it arbitrarily large. It’s just wordplay at that point.
And assuming an arbitrarily large world, as the area of the island increases, the ratio of shoreline to area decreases, no? Not sure what that means in terms of the metaphor, though...
Eventually the island’s population can’t fit all at once on the shore, and so not everyone can gather new wonder.
And when you discover modal realism, you realize that everything is known in some universe and there is no sea after all.
Then you realize that in almost all universes there is no life, and consequently, no land...
Now I’m confused, so I guess I’m out.
Modal realism says “all possible worlds are as real as the actual world” (Wikipedia). In different possible worlds there are different laws of physics, almost all of which don’t allow for life. In some proportion of those where they do allow for life, there’s no life anyway (it seems to be rare in our universe). In some proportion of universes with life, there is no sentient life...
Without sentient life, there’s no knowledge, so no shore. No shore means no land.
Well, shoot.
Cf. Larry Niven’s early short story “Bordered in Black”.
A short shoreline of wonder is a good sign that the island of knowledge is small.
UNLESS IT’S A CONTINENT!!!!!! BOOM.
I don’t understand. Continents are just big islands, they have shorelines too.
If a continent takes up more than half the world, then the shorter the shoreline, the bigger the continent.
But the cutoff is obviously not “continent”/”not continent”, but rather “takes up more than half the world” versus “doesn’t take up more than half the world”—possibly with an additional constraint of a sufficiently simple shoreline...
“Continent” vs. “island” is an arbitrary line, a matter of definition. Whereas smaller/bigger than half the world is precise and objective.
Geometry. Big areas with less big corresponding perimeters.
This is answer is about as informative as answering “Why do aeroplanes fly?” with “Calculus. Differential equations with forces.”.
If you are talking about continents larger than half the world, then DanArmak has already pointed it out and much more politely. However, as dlthomas points out the distinction is not based on it being a continent or not, but on it covering more than half the word.
Also, everything we call a continent on Earth takes up less than half of it, and for such things there is a minimum perimeter that increases as the area increases. (The minimum perimeter is something a little bit like
2*sqrt(pi*Area)
(except different because the Earth is a sphere rather than a plane).)Were you trying to point out that the shoreline’s length varies as the square root of the size of the island?
Doesn’t that depend a lot on how convoluted the shoreline is?
Yes, but only if the shape varies too.
I’m not sure immediately what it means for the shape not to vary if you are growing a complexly shaped island on a sphere.
You’re right. I was imagining it on a plane.
Edit: Only later did I look at this comment out of context and start daydreaming about making some sort of Snakes on a Plane joke.