Wittgenstein's rope

I don't remember hearing of this before.   It's a very surprising bit of maths.  Apparently, Wittgenstein used it as an example of how wrong our intuition can be.

Add a metre to an Earth equator spanning rope and how high does it raise it off the ground?

Watch the 6 minute video to find out.

Update:  for those who can't watch a video, here is an explanation from a book footnote.  For a yard of extra rope, it's nearly 6 inches:

So for a metre, it's going to be something similar.  Enough to trip over for the entire length of the equator. 
 
I'm still having trouble getting my brain to accept this...