In one perspective, a *knot* is defined as a tying algorithm, and so by definition one knows two such knots in the debated situation --there is no efficiency gained should the resulting structures prove identical !
I hope that this is not
your perspective ! ! Our knots, the physical knots we use, are determined by their geometry, not by their topology. Two identical, topologically, knots, can be very different geometrically. Now, geometry requires dressing, which, in its turn, requires inspecting of what has been set up, and careful manipulation of the segments of the knot, before and perhaps even after the initial tensioning. When you keep doing this for one knot, each and every time you do this, you gain knowledge and experience, which, for each and every knot you tie,
even for two identical, topologically, knots, is different. I said that it is better to keep tying one knot, than two, because, each and every time you tie it, your knowledge and experience becomes a little broader and a little deeper. I have been tying bowlines all my long life, but I keep noticing little subtle details I had not noticed before, and my tying "style" still changes ( among other things, that change on me !
) ! You may know the "tying algorithm" of two knots, ( if, by this "knowledge", you mean anything more than just parroting the tying procedures...), but this is not equal to the knowledge of two tying algorithms plus
all the other things about the structures and the mechanisms of the knots you keep learning each and every time you tie them ! We can extrapolate quantitatively this syllogism, to check its validity : If you knew how to tie, say,
one million different knots, and each and every time you had to tie a knot you had chosen a different one, at the end of your life, how much would you really "know" of any of them ?
