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anotherblackhat comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 118 - Less Wrong Discussion
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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.
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