It is an open question as to whether there is a polynomial time algorithm for recognizing the unknot.

Consider the following procedure for doing so on an actual physical string: Suppose there is a physical string that is tangled and I am holding both of its ends. To determine whether the string is knotted, all I have to do is pull on both ends, tightening the string. If we end up with an unknotted string, then the string is unknotted. Otherwise, the string is knotted. I would think if we simulated this process on a digital computer, it would take polynomial time, since in real life it is quick, at least in my experience. Has this idea ever been considered in the literature?