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anotherblackhat comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 118 - Less Wrong
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So I've been thinking about the feasibility of cutting stuff with a thin wire. As the thickness of the wire goes to zero, and the tensile strength goes correspondingly up, does the effort required for cutting actually go to zero?
It seems to me that it can't go to exactly zero, because you still need to counteract whatever forces were holding the material together. But does it go to a small value or a large value, in the case of cutting a strong material like bone? Say, if we tried using a thin wire to decapitate a person standing up, would they actually get decapitated, or would they just fall over?
Seems to me the force needed to penetrate tracks the diameter, but the strength tracks the area of the cross-section.
That is, decrease the thickness by N and it decreases the force needed by N but the strength by N squared.
Below a critical thickness, the wire would just break.
Spiderwebs don't slice you up if you run into them.