Andy, your graciousness goes far to assuage my frustration with you. However, either you don't carefully and thoroughly read my arguments or you don't understand how to apply them, vis a vis how I defined Side 1 and Side 2. I exclude the possibility of that being false, and that you simply disagree, because I am 100% sure of my position. (I'm 95% sure with the Knot4u discussion.) If anyone else would like to engage, please do so, because I feel like I'm running a relay race and no one will take the baton from me. In any case, I will be taking a break from this thread for a while.
Please, for my sanity, TABULA RASA. Without any preconceived ideas, as if we were starting from scratch, please ponder my following arguments. Please do not respond impulsively. Sleep on it if you have to. Out of courtesy to you and Knot4u, I have exhaustively been verifying my statements and yours.
>> By looking at the two pictures below, I had an epiphany.
They are the picture of my single twist (the shape I produce with one single clockwise twist of my right hand), and the picture of what the man produces with one single twist of his right hand. I had always assumed that these are the same (we both seem to be doing the same motion in a clockwise direction). Looking closely at the two pictures, I see that they do not show the same loop. [Edit to clarify:] On mine, the "down rope" crosses behind. On his, it crosses in front.
>> Well yes and no.
Yes in suspended 3-D space they are topologically the same thing (a loop of rope), but if you push a bight through the front of the guy's loop, it won't hold, whereas if you push a bight through mine, it will.
They are EXACTLY the same loop. Choosing my words very carefully: They are EQUIVALENT. There is NO need for the qualifier "topologically." They are not a mirror image of each other. They are EXACT.
>> No they are not "viewed from different angles", they are viewed from the exact same angle, we both used our right hand, in front of us, and twisted clockwise, everything about the load, knot etc is in the same place, and so is the camera.
>> ps: on the pictures, notice whether the "down rope" crosses at the front or at the back. Also notice that the bight is pointing the same way.
Andy, PLEASE bear with me here. Look at your photo, Andy #1, the one under the warm Australian sun, the one that you've been showing with Lee #1. Imagine at that same moment in time a camera on the other side--a camera that would show the back of your hands. The loop in a picture from that camera would unmistakably be the same loop as Lee's. Please try to see this. You would immediately retract your "p.s."
>> I believe there's a point here. Perhaps some of the praise so lavishly spent on the method in that video could be retracted.
Absolutely NOT. There is no wasted motion at all (at least not in the sense that you claim--I wish I could show him Perry's motion). He demonstrates a topologically equivalent ABOK #173--the Clove Hitch variation. (I'd prefer to state that without the "topological" qualifier: It's equivalent to a pseudo-ABOK #173.) Lee is the man.
Cheers!