[BalinKing]

Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat....

The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!

[travisjungroth]

> The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect.

Maybe it’s because I’m a pilot and we never account for altitude when measuring distance, my intuition puts the difference at “effectively zero”. I also have it internalized that the earth’s atmosphere is very thin.

[gsf_emergency]

This could be why dimensional analysis is one of the few things from physics class that can't be drilled enough..

Without forcefully dumping the geometric "intuition", this would still feel counterintuitive to me!

[nayuki]

And the text about the airplane problem was added on 2024-11-26: https://en.wikipedia.org/w/index.php?title=String_girdling_E...

[shortrounddev2]

(2pi * (n + 1)) - (2pi * n)

-> 2pi * (n + 1 - n)

-> 2pi * 1

-> 2pi

If I remember my algebra correctly. Someone else check my work I'm a dropout

[freeopinion]

For convenience, we set τ=2pi. :-)

x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ

[shortrounddev2]

How do you pronounce that symbol?

[Tistron]

Tau. cf vihart: https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s

[freeopinion]

https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU...

https://docs.python.org/3/library/math.html#math.tau

https://www.google.com/search?q=tau*1

https://docs.oracle.com/en/java/javase/21/docs/api/java.base...

https://learn.microsoft.com/en-us/dotnet/api/system.math.tau...

[layer8]

https://tauday.com/tau-manifesto

https://en.wikipedia.org/wiki/Tau

[kurthr]

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?).

[seanhunter]

We 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".

[kergonath]

> 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]

Bet 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]

Yes, 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]

But 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?

[davrosthedalek]

A spherical cow /in vacuum/

[Dylan16807]

> 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]

Exactly, 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.

[aardvark179]

Just 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.