To make the problem of tightening knots unambiguous we must specify a model of the rope on which the knots are tied.
The simplest of such models is the perfect rope: perfectly floppy and at the same time perfectly hard.
By perfectly floppy, we mean that it can be bent with zero force.
By perfectly hard, we mean that it cannot be squeezed, i.e. its perpendicular section always remains perfectly circular.