system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How sharp is paper?

It doesn't take a lot to get a paper cut, which makes me think it must be pretty sharp, especially because paper isn't all that rigid. I'm not totally sure how to define "sharpness" but is it comparable in sharpness to a knife? If it were more rigid, where would that place it?
gpt
Sharpness, until recently, has not been a very well defined term. Unfortunately, explaining sharpness is actually more complicated that an ELI5 because it requires an understanding of fracture mechanics.

The good news is that your question can be answered without actually defining sharpness! The first thing to understand is that being "sharp" entirely depends on the shape of the thing doing the cutting. It's a common misconception that "sharpness" depends on hardness, but it does not (for anyone interested, hardness affects how sharp something can stay, but not how sharp it is). For this reason, butter that has the exact same shape as very hard steel knife is technically just as sharp as the knife. So why does this make a difference? Because this also means that if you had a piece of steel that was as thick as a sheet of paper and had a microscopically flat edge like paper (assuming that's the case), it would be exactly as sharp as the paper itself. It may not be intuitive as to what that steel piece would be like, so you can imagine it'd basically be like a very dull razor. In other words, paper is not very sharp because, as thin as it is, its edges are still very broad.

So if paper is not sharp, why the paper cuts? Think about this: if the paper wasn't gliding across your finger and was simply pushing directly into it instead, do you think you'd still get a paper cut? Probably not, since we'd end up with many, many more paper cuts if we could get them simply by pushing. But when the paper glides over your finger, it manages to cut well. The key difference is that it's much easier to break skin by tearing it along the surface than it is to break it by pushing directly into it. You ultimately don't need all that sharp of an edge to cut yourself by drawing the edge across your skin; paper will do just fine!