Perfect rope is an idealization. It can be bent without any effort and the
bending cannot deform its perfectly circular section. It is frictionless.
No wonder some of the knots which are used in the real life do not work properly
when tied on the perfect rope.
Let me give a few examples.
One of the simplest knots used in practice is the overhand noose.
It is used sometimes to shorten the rope. But, the knot cannot be used when
the rope is too slippery. Why is that so can be seen in a simulation I performed
recently. Pulling apart the ends of the rope does tighten the knot but then
... unties it. Have a look here.
A better version of the knot is the overhand loop.
What happens to it when it is tightened on the perfect rope can be
If you are a professional, you do not use loops to shorten ropes. You use
for instance the sheepshank knot.
It works perfectly well on real rope and it perfectly fails when tied on
the perfect rope. Just watch this.
Well. Is it possible then at all to shorten the perfect rope? It seems to
us, that the answer to this question is positive. What you have to do is:
use one of the open Gordian knots.
This is how to tie one of the particular knots:
Will it work? It seems to me that it will. Simulations
I performed suggest it. Look here.