Turns out a high school girl in Pomona, California found otherwise, and even wrote up a couple formulas for it. One for folding in a single direction (using a rather long sheet of paper), and the other for folding in two directions (alternating). All it took was a little motivation (free math credit if she could accomplish it), some gold foil, and $85 of toilet paper (1.2 km worth).Of course, the first problem was thickness. Every fold doubles the thickness of what you're folding and halves its area. Doesn't seem like much, but it's kind of like that "you pay me 1 penny today and double it every day there after for a year..." little bits add up. She tried to get around that by using the thinnest sheet she could find, which was gold foil. Being a stickler for details, the math teacher reiterated that she must use paper (not foil). That proved to be a completely different problem, which was to find a manufacturer of paper that would be long enough (and/or) wide enough to test the formulas she came up with.
With an extremely long roll of TP, a large area of a mall (.6 km), and some precise measurements, she managed achieve her goal of 12 equal folds, reaching a thickness of 80 cm. A process that took over 7 hours. The strange thing is that this all happened back in 2002. What ever happened to the news? This is big news right? Oh, what's that!? Apple's releasing new iPods in 2 weeks, nevermind about that science thing.
Actually, Mythbusters covered it a while back too... must have missed that episode... wasn't that when the iPhone was looming?
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