After lunch today, I ate a Reese's Peanut Butter Cup, which came individually wrapped in a surprisingly thin tin foil wrapper. Using the back of my fingernail, I smoothed the foil out into a perfect square with only the tiniest wrinkles remaining. Then I started folding the foil repeatedly in half, flattening it out between each fold. After 7 foldings, a tiny rectangle remained, unwilling to be further folded. I started to think that if I had a larger piece of foil, I could have folded it again, but then I remembered that old chestnut from adolescence (that was repeated in college as fact): it's impossible to fold a piece of paper in half more than 8 times. Thwarted.
Then I started thinking, why is the limit 8 times? Given an extremely thin, large piece of paper, you should be able to fold it more than that. I figured someone must have debunked this conventional wisdom and sure enough, a quick google revealed that the number of folds depends on the length and thickness of the piece of paper. In practice, the high school student who derived the formula for paper folding limits folded a piece of paper a whopping 12 times. So much for conventional wisdom.
Side note: Given Richard Feynman's interest in flexagons, this paper folding bunkum seems like something he might have solved in his spare time, the solution perhaps lost amongst the many things he never published or even wrote down anywhere.