What does one do while eating a falafel with NITI friends on St. Patrick's Day before heading to a pub for a couple drinks? I don't quite remember why, but pmccurdy, wlach and I decided to determine how many times you would have to fold a piece of paper in half for it to reach the sun.
We were quite sure the sun is eight light-minutes away, and assuming the sheet of paper is 1 mm thick (unlikely, yes, but it made it easier), we figured in our heads that 47 folds ought to do it.
Challenges included: (a) a magnitude error that rendered the sun somewhere in between the earth and the moon, and (b) eventually having to estimate the base-2 log of 144 trillion.
But we succeeded, and then made plans to win lots of bets with drunk people.
If one were to actually do this, I imagine amusing things would happen to the earth's centre of gravity, and things would start falling slightly sideways.
Also, upon reaching the sun, your paper would catch fire.