Some time ago I came across a fun article. I got curious, and embarked on a journey that took me to the source of a famous internet myth and even to explore what it means to be a physicist.
But let’s not get ahead of ourselves. The article was about the myth that it’s impossible to fold a piece of paper more than 7 times, and about the nice Finnish gentleman who tested it in this popular YouTube video.
At the seventh fold, the paper collapses spectacularly under the intense mechanical stress. After just one fold, it seems we get a new sheet, half as big as the original, and twice as thick. Clearly, that is just an approximation: the folds are in fact arcs, and the paper on the outside has to go all the way around the layers in between.
Moreover, the number of layers goes up exponentially. First it’s 2, then 4, 8, 16 and so on: at fold number seven, the outermost paper has to go around over 120 layers. At that point the stress on it is unbearable.
Bigger sheets could allow more space for the folds, strain the material less and avoid the problem. Some years ago, the people at MythBusters actually took a football-field-sized piece of paper and managed to fold it 11 times.
The world record belongs to a girl that reached 12 using a huge and very thin sheet. Personally, I wasn’t satisfied: giant sheets are cheating!
In physics, however, we can ignore some rules—say, the mechanical resistence of the paper—to answer bigger questions. For example: how many times could I fold an indestructible A4 paper if I could always make folds as perfect as the first?
A back of the envelope calculation told me that, always folding along the longest available margin, I can get to… 7 (that’s where it came from!). At that point I’d be holding a cubeish piece of paper, and further folding wouldn’t change it anymore following this rule.
But we could get as high as 22 changing the rules. For example, folding always along either the initial length or width of the paper, I’d end up with an object as wide as the initial sheet was thick (and a few hundred meters thick).
Can I keep folding something that small? And if I can, what to do when it reaches the width of an atom? or of a proton? The very idea of “fold” would lose meaning.
The issue, now, becomes: what rules are reasonable to ignore?
That is the art of physics: to decide what rules are important and what can be ignored, to walk the fine line of the reasonable approximations to answer a question. Albeit only… on paper.