A video at Aeon well worth checking out on what wrapping a rope around the Earth reveals about the limits of human intuition:
If you tied a rope tight around the Earth’s equator and then added a single yard of slack, would the extra material make any noticeable difference to someone standing on the ground? Yes, actually. The answer comes as a surprise to most people, but the additional bit of rope raises it high enough off the ground for our eyes to easily discern it, and our feet to easily trip over. That fact might seem trivial, but the early 20th-century philosopher Ludwig Wittgenstein believed that this chasm between human intuition and physical reality revealed something important about the fallibility of our thinking. After all, if something that seems obvious to almost everyone can be totally false, what else might we be wrong about?
See the video at Aeon (It’s about 6 minutes long.)
I have to admit that I didn’t buy this at first. Even knowing full well that our intuitions are not to be trusted, I could not accept it until I did the calculation myself in terms of the whole Earth.
The Earth is 1,577,756,568.96 inches in circumference. Its radius is about 251,235,122.45 inches.
Add 36 inches to the circumference, making it 1,577,756,604.96 inches, and you make the new radius about 251,235,128.18 inches, or 5.73 inches larger.
Adding a yard of rope raises it almost 6 inches off the ground, all around the world. Despite the mathematical proof, that still seems utterly wrong to me. It’s like one of those visual illusions that, even after you know it’s an illusion, you can’t stop seeing it.
In both science and philosophy, we have to be very careful about our intuitions. Often they will lead us astray.