Surely that wikipedia answer is wrong. I can't be bothered to try it, because I have, several hundred times before now, as i'm sure every child has, tried to fold a piece of paper in half more than 8 times. Don't think I ever made 7 proper folds. 12 folds(!) is that some mathematical jigger-pokery? If not I'd like to see a video of some high school junior fold the same piece of paper in half 12 times.
After folding a full open page sheet (~4sqft) of newspaper eight times I ended up with roughly a one inch cube which I was able to compress in a vice to nearly one-half inch in thickness. Assuming it would be possible to continue folding this lump thirty-two more times it would have a "thickness" greater than the circumference of the Earth.