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The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere. If, instead we approximate it as a fractal... then
by kurthr 2y ago
The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere.
If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope!
The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).
- Dylan16807 2y ago> infinite, or at least highly dependent on the thickness of the rope The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant. But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?
- kurthr 2y agoExactly, if you're only 1cm off the surface you follow every nook and cranny. If you're 10km off the surface only Everest is a blip.
- seanhunter 2y agoWe actually model the earth as a very large spherical cow. This is approximately the same for most purposes but ends up being more convenient. P.S. Not a physicist, but my child is studying maths and physics at Uni at present, so I have it on good authority that this is still going on. They told me in their first week one of their classes had a worked example where the lecturer used the phrase "Assume the penguin's beak is a cone".
- davrosthedalek 2y agoA spherical cow /in vacuum/
- kergonath 2y ago> I have it on good authority that this is still going on Do you mean making simplifying assumptions to make a problem tractable? Of course it’s still going on. It has to be, otherwise you just cannot do anything. > Assume the penguin's beak is a cone It is impossible to consider the true shape of a penguin’s beak for several reasons: - you’d need to go all the way down to the electron clouds of the atoms of the beak, at which point the very concept of shape is shaky - every penguin has a different beak so even if you describe perfectly one of them, it does not necessarily make your calculation more realistic in general. There is a spectrum of approximations one can make, but a cone is a sensible shape at a first order. It’s also simple enough that students can actually do it without years of experience and very advanced tools. What do you think they should do instead?
- seanhunter 2y agoBet you’re fun at parties as they say. I totally understand why simplifying assumptions are helpful in modelling and definitely don’t need you to explain that. It also is a bit ridiculous if you think literally about it which makes it something that is fun to laugh about as here.
- kergonath 2y agoYes, sure, I get the jokes. I just found it puzzling that someone would think it stopped. And I don’t talk about work at parties anyway :)
- eminent101 2y agoBut nobody in this thread thought it (simplifying assumptions) stopped. You seem to be making an assumption that someone thought that and then posting long explanations that nobody asked for. I read the "P.S." of grand-grand-parent comment as good humor. Nothing there implied that they really thought that simplifying assumptions would/should stop. Imagine a world where every bit of humor is interpreted literally and then refuted pedantically! What kind of a world would that be?
- aardvark179 2y agoJust because your initial fractal path is infinite does not imply that a line offset from it is also infinite (even for an infinitely thin rope), at least if the offset version is not self intersecting.
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