6 ms·

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

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

shortrounddev2 2y ago
(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 2y ago
  For convenience, we set τ=2pi. :-) x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ
  - shortrounddev2 2y ago
    How do you pronounce that symbol?
    - Tistron 2y ago
      Tau. cf vihart: https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s
    - freeopinion 2y ago
      https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU... https://docs.python.org/3/library/math.html#math.tau https://docs.python.org/3/library/math.html#math.tau https://www.google.com/search?q=tau*1 https://www.google.com/search?q=tau*1 https://docs.oracle.com/en/java/javase/21/docs/api/java.base/java/lang/Math.html#TAU https://docs.oracle.com/en/java/javase/21/docs/api/java.base... https://learn.microsoft.com/en-us/dotnet/api/system.math.tau?view=net-9.0 https://learn.microsoft.com/en-us/dotnet/api/system.math.tau...
    - layer8 2y ago
      https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto https://en.wikipedia.org/wiki/Tau https://en.wikipedia.org/wiki/Tau
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 ago
    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.
- seanhunter 2y ago
  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".
  - davrosthedalek 2y ago
    A 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?
gsf_emergency 2y ago
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 2y ago
And the text about the airplane problem was added on 2024-11-26: https://en.wikipedia.org/w/index.php?title=String_girdling_Earth&diff=prev&oldid=1259596804 https://en.wikipedia.org/w/index.php?title=String_girdling_E...
travisjungroth 2y ago
> 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.

shortrounddev2 2y ago

(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 2y ago
For convenience, we set τ=2pi. :-) x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ
- shortrounddev2 2y ago
  How do you pronounce that symbol?
  - Tistron 2y ago
    Tau. cf vihart: https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s
  - freeopinion 2y ago
    https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU... https://docs.python.org/3/library/math.html#math.tau https://docs.python.org/3/library/math.html#math.tau https://www.google.com/search?q=tau*1 https://www.google.com/search?q=tau*1 https://docs.oracle.com/en/java/javase/21/docs/api/java.base/java/lang/Math.html#TAU https://docs.oracle.com/en/java/javase/21/docs/api/java.base... https://learn.microsoft.com/en-us/dotnet/api/system.math.tau?view=net-9.0 https://learn.microsoft.com/en-us/dotnet/api/system.math.tau...
  - layer8 2y ago
    https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto https://en.wikipedia.org/wiki/Tau https://en.wikipedia.org/wiki/Tau

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 ago
  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.
seanhunter 2y ago
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".
- davrosthedalek 2y ago
  A 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?

gsf_emergency 2y ago

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 2y ago

And the text about the airplane problem was added on 2024-11-26: https://en.wikipedia.org/w/index.php?title=String_girdling_Earth&diff=prev&oldid=1259596804 https://en.wikipedia.org/w/index.php?title=String_girdling_E...

travisjungroth 2y ago

> 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.