A rope is put around the equator all the way around the earth. The rope length is increased by a yard. If we pull it to make another very slightly bigger circle with the rope, how high will the rope be above the Earth?
My initial thought (and surely yours too), is that it would be utterly insignificant. Much less than 1 mm as a yard is so incredibly small compared to the circumference of the earth! But apparently, it's 5.73 inches. Eh, wtf?? But it's correct.
Watch this video.
The narrator says we are convinced by the rope because we can offer a proof. But we can't offer a proof in politics, or philosophy etc. Since, without a proof, we would be wrong about the rope, how can we have good reason to be convinced in our political or philosophical views?
I'm not convinced at all by his argument. I don't think we can conclude that because mathematics confuses people, that this applies in all areas. Also, we don't need a proof in the rope example. Yes, increasing the length of the rope by 1 yard is utterly trivial compared to the circumference of the earth. So how can the rope be 5.73 inches above the earth? It's because 5.73 inches is equally trivially small compared to the radius of the earth! In another words, we have a miniscule increase in the length of the circumference. But also a minuscule increase in the radius. So nothing puzzling here and we can see this without a proof.
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