Hello Dennis / Alan,
Firstly - thank you very much for your efforts
It is appreciated.
per Alan:
For the presentation at reply #3 (Alan) - it is an interesting creation.
I like how Alan thinks 'outside the square' - I'll have a closer look at this over the weekend.
per Dennis:
We have 2 different posts/threads with double Butterfly's... its getting hard to follow and collate the progress made.
The example shown at reply #5 (using a carabiner) is an interesting way to establish a 'proof' - that avoiding twists/overlaps with the eye legs is not possible.
I'll quote you here...
What Mark wants is a way to insert a ring or pulley without any half twists. Below I show that this is not possible.
It is true to state that I would like to discover a way to add a ring (or pulley with a swivel eye) to one of the double eye Butterfly's without induced twists in the eye legs.
One thing I have realized in my life experience is to used the phrase "not possible" (ie impossible) with abundant caution.
There are incredibly talented people like
Xarax and
Alan Lee who have repeatedly demonstrated that the 'impossible' is merely an opportunity to show what is possible.
That's
not to in any way deride or ridicule Dennis Pence - quite the contrary!
I am both impressed and humbled by the progress and advances made by Dennis.
I remain cautiously optimistic that Dennis (or another creative genius) will discover a way to avoid twisted/overlapped eye legs in one of the double Butterfly's.
The
proof of the carabiner tying method is not necessarily a 'show-stopper'...
yet (I hope).
Note: The tying method depicted at reply #6 has a geometry that is almost identical to the 'Girth hitched double Butterfly'.
Look at the geometry of the eye legs... note that for each 'eye', both legs are situated to one side of the knot core (ie 1 pair of eye legs lies on the 'Z' side and the other on the 'S' side).
I feel that you are possibly on the verge of some important discoveries - and I hope you have the motivation to continue.