There is one problem along these lines that allows for some rather precise mathematical statements: What is the condition for a hitch to hold? A hitch is a knot around a rigid object (a pole). Because the pole is not compressible, and assumed to be much thicker than the rope, the problem whether or not the knot holds (meaning, friction wins no matter how hard you pull on the rope) can be formulated and solved preciselyas a problem in linear algebra:
