Monday, May 20, 2019

Intuition, Disagreement, and a Rope Around the Earth

Check out this awesome new philosophical video by philosopher Jon Ellis at Santa Cruz.

The video starts with this thought experiment from Wittgenstein:

Suppose that a very long piece of rope is wrapped around the equator of the Earth. Now imagine that the rope is lengthened by one yard, but its circular form is preserved, so that the rope no longer fits snugly but occupies a circle at some slight constant distance from the Earth's surface. How great would that distance be? (reported in Horwich 2012, p. 7).

Your attitudes toward philosophical and political propositions might be kind of like your attitude toward that rope -- but with no clear mathematical means to resolve the disagreement.

If you like the video, you might check out Jon's on my paper Rationalization in Moral and Philosophical Thought.


Anonymous said...

The video brings up another compelling rationalization for you Eric. When your car breaks down, and you call a friend to come and tow your car home using a chain: Does the chain pull your car home, or does the chain push your car home?

SelfAwarePatterns said...

Have to admit, even fully knowing that intuitions are not to be trusted, I didn't buy this until I did the calculation myself in terms on the circumference and radius, in inches, of the whole Earth. Even then, it's like one of those visual illusions. Even after you know it's an illusion, you still can't stop seeing it.

Chris McVey said...

This is super interesting! I think I see the move that confuses people (myself included!), and it involves a subtle shift in perspective.

When we deliberate about what the addition of the yard would do to the circumference of the rope, we, as the video suggests, think about it from the perspective of the earth as a whole. The earth is SO BIG, so adding a yard would be insignificant from that perspective. But you see, that actually IS true, 5.73", looked at against the entirety of the earth's circumference, is in fact vanishingly small.

The problem only arises when we shift back to our own (in my case 5'10") perspective to evaluate what constitutes a significant increase in the circumference. Why, 5.73" is rather large! After all, I can trip over that!! But I was certain it would be insignificant!

Just a thought. Perhaps, as with most areas in life, problems like these crop up when we fail to take into account the proper perspectives.

Callan said...

I don't know how to actually calculate it, so I just treated the earth as a cube. Then I guess you're just taking the extension amount and dividing it by four for each side. Then dividing it by two for how much each side of the squared rope will be extended on each side. I guess it extends a fair bit more than I thought. I guess I'm not very good at working with circles, because if the earth is a cube and one side is 12742km plus a quarter of 2 yards, well that's half a yard more. So it'll extend a quarter of a yard in either direction. Thats straight forward enough but the circle version is confusing.

Eric Schwitzgebel said...

Thanks for the comments, everyone! Chris, I like way of thinking about it.