Any symmetric bend, where the links are topologically equivalent to the unknot ( the "A" bends" of Miles s "Symmetric Bends" book ), can be turned into a PET loop, almost
by definition... So, if you take a PET loop and turn it back into a bend, either you have completed a
round turn ( that is, a perfect 0 ...
), or you have tied a non-symmetric bend - which, most of the time, is not an interesting knot... There are some rare cases where we have tried to do the opposite, i.e., to turn interesting non-symmetric bents into loops - as, for example, in the case of the simple non-symmetric bends presented by Hoban (1) - no luck (2) !
The original simplicity of the parent bend is lost, and the loading of another, third, limb of the initial end-to-end knot can deform it to the point it becomes unrecognizable.
Now, regarding your attempt, as a result / consequence which, perhaps, should have been expected, the nice flow of the strands into the parent loop s nub leads to a nice non-symmetric bend, looking like an enhanced Sheet bend. However, as a potentially practical knot, does it offer anything more than a symmetric bend ? I doubt it. In a sense, the simpler link begs to be completed, and acquire the same amount of complexity - and the same degree of participation in the workings of the knot - as the other one. And if you re-tuck the end of this end, you end to some known symmetric bend
- or you "tie" some ugly tangy, a desperate act which you would nt even think to do, of course.
Balance of the amount of complexity of the path each rope follows into space, as it turns around the other and itself, is not just a demand of aesthetics - it is a requirement of the mechanics of a tool, so the forces that run within its parts are evenly distributed along greater areas. Look at a humble
nut-and-bolt simple machine : the male and the female parts are equally complex, you can not say the one is more "worked", more sculptured into the metal, than the other. Look at the common bowline : the nipping loop and the collar, although they play different roles, are equally simple. Look at Buster Keaton
! Although the form and the material of his body are sooo different from the form and the material of the current of air, those two things are in a perfect balance - a situation which, of course is such a rare thing in life, so it makes us admire it, or laugh with it.
I am not convinced by any non-symmetric bend - and I am not even convinced by any
too-clever-by-half knot
, where we add 1 and 1 to make 1, = we interlace two hitches to make one bend... There should be a sound reason for the addition and the duplication, in place of a new creation. On the same footing, there should be a sound reason for the subtraction of a symmetric bend s portion / part, and the resulting unbalanced knot, in place of a simpler, right from the start, symmetric bend. However, as Ashley says,
"There are always people who believe that if a single thing is good, two are bound to be better." Well, I can only say that I am not among those...
1.
http://igkt.net/sm/index.php?topic=41162.
http://igkt.net/sm/index.php?topic=4116.msg27762#msg27762
