Hi Keystoner, hi Knot4U,
Sorry about the delay, out all day.
Gentlemen, I have good news: a resolution (I hope) of the single vs double twist question.
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.
1. I now see that I was wrong about the morphology of what the man is tying, and that you both were right about that. He produces what I have been calling the "single twist".
The reason is quite subtle, and, not to diminish your "rightness" about the overall question in any way, there is one fundamental aspect where I believe I was at least as right as you guys, and I believe this was the source of the problem:
2. To produce the "single twist", the man twists twice---nearly exactly the motion I use for the double twist.
I believe this is the source of the confusion.
Believe it or not, this whole confusing discussion may therefore be a story of wasted motion (or, since "wasted" can antagonize, "different motion"): all along, with a single twist, we have been producing different loops, and therefore talking about different things.Lee twists twice to produce my single twist. Do you guys also twist twice? You must do, as you have said that you do what he does? Please come forward, I have given you the cake and changed my mind about the morphology produced, as I always said I would do the second I was convinced.
For the record, here is the "single twist" motion that produces my "single twist" on my picture below, which differs from where the man is after one twist, and is in fact his double twist.
When I grab the rope to make my first twist, I sweep my right forearm counterclockwise. The elbow points away, and the right hand points towards me. The right hand's fingers crosses the rope from the left, except for the thumb, which stays on the left side, creating a fulcrum opposite the four fingers which grab the rope from the other side. The hand twists clockwise, and we have what I have been calling a "single twist".
I am so used to this gesture that I never considered that a single clockwise twist might be producing a different structure. Will post pictures in the next post.
You guys weren't mad that the man on the video produces a "single twist" (I thought you were).
And I wasn't mad that he twists twice (in what looks like my "double twist").
I am amazed that we didn't get here sooner. How very odd that it took all this time.
Glad indeed to have that resolved! I was on the verge of pulling my hair a few times and I'm sure some of you were too.

Thank you all for your patience. I'm sure we all learned something on this ride, whether about knots or about the challenge using words to make each other see the same thing.
Wishing you all a beautiful day,
Andy