It is you who see necessity in some collar, not I(who even sees more of collaring than you do!).
Yes, that is funny !
I believe that the
"proper" collar is an indispensable element of the bowline (albeit only the secondary one, after the nipping loop). You do not believe this, but you are ready to accept a more relaxed definition of the collar, and see collars where I do not...I explain it as following : I pay much attention to the collar, the particular "proper" collar of the bowline, where the second leg, after its U turn around some segment of the standing part, re-turns into the same opening it exited from, now pointing to the opposite direction. Paying much attention to this "restricted" kind of collars, it is natural and expected to distinguish the "proper" forms from the "generalized" forms you have in mind, and use this restricted definition to eliminate other loops from the bowline group ( like the ABoK#1033, the Angler s loop, the Myrtle...)
At the end of the day, incorporating the "proper" collar into the essential elements of the bowline group, leaves us with much fewer "bowlines" than you are ready to accept, and, given the plethora of them we already have, that is a good thing, I believe !
You are left in an indifensible position, to deseparetely try define as "bowlines" many knots that nobody will ever name like this, believe me. You might succeed to reduce their number a little bit, by the clever "direct / indirect " distinction of the feed of the nipping loop tension into the eye, but your net result will still be far greater than wanted !
My base is the turNip (not the Gleipnir,
Mine too ! I do not say that the Gleipnir is an element of practical knots, I say that it is the purest knot that incorporates the "basic element" of the practical knots that is the nipping loop. I say that
"the Bowline is related to the Gleipnir more than to the Sheet bend", because we
relate knots to knots, not knots to basic elements of them. We
explain knots by analysing them into basic elements, and the basic element of the Gleipnir is the nipping loop, exactly as it happens in the bowline. I think we are on the same page in this, for once...
On the question of the eskimo bowline, I'm going to straddle the middle, or be on both sides, as with that carrick loop-can be either, depending upon the setting.
Well, to walk on a tensioned rope is a difficult exercise...Good luck !
"SPart is that brings 100% tension into the knot; what runs from this into the eye --an eye leg-- is just that (eye leg), not SPart any more. So your bit about some "symmetry ..." with collaring going either direction loses me.
Just a minute ! I said about THE TEST LOOP that I submitted to Derek Smith, that the standing part there brings 50% of total tension into the eye ! ( The other 50% is brought by the combined presence of the two legs of the collar.) And I was talking about the Standing part AFTER the other structure of the compound knot, the mid line TIB loop I had used - to show that the two legs of the collar can be almost parallel to each other and to the standing art, yet the collar works. This was made in an effort to offer a counter-example to Derek Smith, who sees, in the one-sided loaded bowline, segments of rope perpendicular to each other, and so he relates the bowline to a hitch, the hitch element of the Sheet bend.The two legs of a collar can be almost parallel to each other, and this collar works : when the two legs of a hitch are parallel to each other, this hitch doen not work !
I characterize as "standing part" the segments of the rope before, within, and after the nipping loop, and also the eye leg of the standing part. I do not characterize as standing part the "rest of the knot", that is : the eye leg of the bight, the first leg of the collar, the second leg of the collar, and the tail - i.e. the segments of the rope that come "after" the standing part. According to this characterization, the lowest point of the bight separates the standing part from the rest of the knot : The sailor should tie the topologically-equivalent-to-the-unknot structure on the former, and pass through it the working end / tail of the later. So, when he unties the bowline, i.e. pulls the tail out of this unknot, the standing part is left with no knotted structure on it, and that happens
even before the rope gets out of the ring or the bollard- a necessary requirement for the mooring line.
What is your difficulty with the symmetry argument ? It is a
local symmetry, of course, not a symmetry of the whole knot ! Locally, in the proximity of the nipping loop, the segment of the rope is, from the one hand, the standing part end, and, from the other, the eye leg of the bight that belongs to the standing part. When the rabbit reaches the nipping loop, it does not have to
think/choose, in advance, from which end it will pass through : And, after it passes through, it does not have to think/choose around which particular end of this nipping loop - around which segment of the standing part - it will make its U turn. It just makes the U turn around the only leg
it can ( Otherwise, it will form a loop that will slip through the nipping loop, so the rabbit will be eaten by the fox, and it will not survive to describe to us its definition of the bowline...
) I think that the bowline should be defined
independently /without any reference to the particular side the working end / tail it passes through, ( be it as in the common bowline, or as in the Eskimo bowline ), and the collar should be defined
independently / without any reference to the particular side the working end / tail passes around the standing part segment of rope, in the vicinity of the nipping loop. See the picture of Reply# 82 : No indication which is the "front" or the "back" side of the nipping loop, no indication of which is the segment of the standing part inside the eye ( "after" the nipping loop) and which is the segment of the standing part outside the eye ( "before" the nipping loop). So, the bowline mechanism is defined with the fewer possible references to particular thoughts/choises of the rabbit, and only with references to the locally, symmetrically positioned knot structures in front of it, where the rabbit has no choice at all - if it does not wishes to be eaten by the fox, of course, i.e. if it wishes to form a collar loop that
can not bedeformed/untied by a pull of the eye leg of the bight.
P. S.
Fortunately, in science, a thing is either true or false !
How's that work for you with quantum mechanics?
Didn't the Law of the Excluded Middle get broken there?
(And, actually, there are reams of thoughts on what makes "true" ... .)
Oh, my dear Dan Lehman, your debt to me is now reduced by 100 worthless US dollars ( to -2650 $...) , just because you have mentioned
QM,
Excluded Middle, and all that, however erroneously you interpret them !
( US congress will not solve its debt problem with this gain of yours, but it is a positive sign nevertheless...) If you keep going like this, you will be free of debt in just a few
dozens of dozens years !
I would LOVE to talk about those things, because I have spent 35 years of my life, into the
mud, studying them !
When you were studying and tying knots, I was trying to un-tangle the various interpretations of QM, Brouwer s constructivist/intuitionstic interpretation of mathematics in relation to the Platonic/realistic one, and all that...However, I leave
you to be beaten by roo this time
, because those things have no relation to practical knots whatsoever.
Truth, that beloved and betrayed goddess, has indeed, and it is that truth we are here to unveil, I believe. ( I would be glad to discuss any questions about interpretations of QM and Constructivist/Intuitionistic logic and mathematics, through e-mail).
