? ? ?
I can't help you. You will find the light when you are ready.
Read again my trash ! Dumb and naive people may be more correct than you think ( or you can imagine...)
If the loop is loaded by, say, 2 units of force ( that is, 1 unit and 1 unit on each eyeleg ), and the angle between the ends is 120 degrees, each end is loaded by 2 units of force.
However, if the same loop is loaded by the same load ( 2 units of force ), and the ends are parallel, each end will be loaded as much as each eyeleg, that is, by 1 units of force, 2 ( = two ) times less than previously !
What "part" of that you do not understand ?
but I will try anyway although I know that you must find the light for yourself. Your post is far to imprecise to clearly describe something such as vector addition. I think pictures suit your communication style better than words when it comes to technical detail.
I was not arguing about the values of the forces, but the angles. 120 degrees is a huge angle for a loop (at least a couple of adjustable loops will slip FAR before that) and I will assume you were only using that to demonstrate a point. That's fine. I cannot clearly decipher your words but if you have three legs tensioned at 120 degrees to each other all three will have the same force (unless the knot part is accelerating). If one of those is doubled (two standing ends) then obviously each half of the doubled line will have half that force. If that agrees with what you said, then great. Of course if two legs are at 120 but unequally tensioned, the third leg then will not be at 120. Let's restrict ourselves though for the moment to cases where the two eye legs are equally loaded.
But this was not my point. My point is that if two equally loaded eye legs are at 120 degrees the one tensioned standing end must point straight between them. If two eye legs are at 10 degrees and equally tensioned, the one tensioned standing end must still point straight between them, now only 5 degrees off of each from parallel, and in either case (10 or 120) the standing end at least is at the same angle relative to the knot structure. As for the eye legs being at various angles, well small angles are not uncommon at all, but large angles on the mobius correspond to a non-straight parent line on the alpine. So, as I said, the important difference is not the angle of loading so much as it is which line is not loaded, and even that can be reconciled by situations for either which would be outside their idyllic knot tyers view of their use, but not outside of realistic expectations. Ropes are quite often improvisational tools.
The difference in the end, comes down to not even angle or loadings that are possible or even will certainly happen, but that for different configurations different angles and loading are more convenient or likely.
It is the relationship between the possible loadings and angles to the manipulation of our attached object and rope that has changed. We have to do different things with our things to create the same loadings and angles for the two configurations and so the configurations are in that way different, but do not change names simply as/when or because the angles and loadings change, well they could I guess, but...
(added:)What this loop's knot surely shares with its twin loop's identical knot, is that both can tolerate a wide range of abusive loadings BEYOND their ideal use in a particular configuration while still holding. THIS is maybe the most important property of this knot beyond it's TIB nature, and anyway, both of those properties are the same exactly BECAUSE the knot part is identical. Differences in these LOOPS will bring some differences in behavior, but the identicalness of these KNOTS (parts) will bring the most important properties especially in a and even because of situations where the knot part loadings become indistinguishable too. The same cannot be said of the eskimo bowline.