When my son was near the end of his primary school years, I thought that it was time that I should impart some of my Weird Freaky Science Wisdom – and have a little bit of fun as well. I told him that I would give him a million dollars if he could fold a piece of paper in half, and in half again, and so on for a total of 10 times. Of course he tried, and of course he failed.
I knew that this would happen, because it was “Accepted Wisdom” that it was impossible to fold a piece of paper in half 10 times (or seven, or nine, for that matter.). I told him that it couldn’t be done, even if he used paper the size of a football field. But I now know that I was wrong.
Suppose that you start with an standard A4 sheet of paper – about 300 mm long, and about 0.05 mm thick.
The first time you fold it in half, it becomes 150 mm long and 0.1 mm thick. The second fold takes it to 75 mm long and 0.2 mm thick. By the 8th fold (if you can get there), you have a blob of paper 1.25 mm long, but 12.8 mm thick. It’s now thicker than it is long, and, if you’re trying to bend it, seems to have the structural integrity of steel.