I guess you were already aware of the connections between the Gleipnir & Bull hitches.
You mean, if I was aware of the Gleipnir before I had tied the Bull Clove hitch or any other of the "tight hitches" ? Of course I was, and that is what enabled me to "see" the binders and hitches with an entirely new way - but not only that ! I believe I would nt even had tied most of the other knots I had ever tied, if the Gleipnir had not been invented and I had not been lucky to learn about it. Perhaps I would nr even had been seduced in the hobby of knot tying at all. You see, the Gleipnir, for me, but also for most of the members of this Forum ( I say "most", because there are always some people who simply can not understand, or do not wish to understand, for their own personal reasons ), was a revolution. And revolutions change the Weltanschauun, the World view
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If you take one of the lines out of the closing clove hitch and don't reinsert it any where else, you do not get a Gleipnir.
In the Gleipnir, and all its variations, both ends are secured when they pass through the "central" nub. If the one of them is not secured there, but somewhere else, you do not get a Gleipnir, indeed. However, I was not talking about that ! I was talking about HOW do those ends pass through the central nub, regarding their orientations when/while they do that : Do they pass by entering into and exiting from different sides, or the same side ? That, in my opinion, is not an important structural difference - at least in the case of the Clove-hitch based Gleipnir variations.
In the asymmetric Clove-hitch Gleipnir you show in this thread, both lines enter into and exit from the same side of the Clove hitch, in the symmetric one ( which I think it can be more secure, because there the lines can be twisted around each other ), they enter into and exit from different=opposite sides. So what ?
I should also remind something you may not be aware of. In Dan Lehman s Gleipnir variation ( which, probably, just like you, its author will never accept that it just a Gleipnir variation...
), both lines converging to the "central" nipping structure arrive there coming from the same direction. Not much difference. The "nipping tube", having had a turn more, is longer, so it can encircle the pair of ends better, but that is not a structural difference that makes it a new knot. If we just use a three-turn Gleipnir, we get an even longer nipping tube, which allows us to twist the ends around each other inside it more easily, but that is, perhaps, just an improvement, not anything else. The inventor of the Gleipnir had probably tried all those variations, but he says that he prefers to just add one classic Gleipnir after the other, in a series - and he may well be right in this.
I think that what you mean is that in the way you've learned to think about knots you associate your concept of the Draw Knot "with something subtracted" with your notion of the Gleipnir. The way you've learned to think about knots clearly has merit because you've devised a lot of neat new designs based on it..
Nooo, it is not the "way" ! It is the Gleipnir itself ! That is what I am trying to convey to you. A great idea, a great knot, is not only great because it does what it does, but because it is what it is, and so it teaches what it teaches : Its mere existence has an educational value. It is not the pupil that has learned something, it is the teacher that has taught him that !
The term 'structure' is generally synonymous with 'form'.
that different forms may produce some functions in common.
"Generally" ? ? ?
Never ! Not even in the so-called "modern movement", which only declared that "Form follows function".
Form is akin to the shape, the geometry. Structure has to do with the distribution of forces within the elements of the form, which make something "work" : either be stable and on its feet ( when it is a building, for example ), or move without its parts be spread all over the place ( when it is a vehicle, for example ). Form can be seen, structure has to be understood, that is, "seen" by the mind s eye. The distribution and the equilibrium or not of the forces within a rigid or flexible material is invisible.
Indeed, different forms may/can produce the same results, regarding structure. Perhaps that is why we have infinite different forms, but few different structures.
You consistently discount whatever distinct handling properties I mention. You seem to be fixated on the 'mechanics' of knots.
You do not seem concerned about the 'user interface' aspect of knots .
your concern for what makes a knot 'practical' is rather limited..
It is !
It is concentrated in one, and one only, point ! The better is the knot, per se, the more practical it can be.
Of course, as I said, there are some good knots which are extremely unfortunate, as practical knots, because there is not ( or we have not yet found ) an acceptably easy and quick method to tie them - but they are rare exceptions of the general rule.
You see, practical knots are, almost by definition, simple knots, and, in general, simple knots can be tied easily and quickly. The small differences in this "easily and quickly" are not enough to make a serious knot tyer prefer an inferior knot from a better one.
However, the asymmetric Clove-hitch-based Gleipnir variation you show is NOT tied or untied more easily and quickly relatively to the symmetric one ! Do not try to shift the goalposts !
...you seem to be operating in some higher-level conceptual space were you decide what is similar and then declare that things that you consider as similar to be equivalent. I don't really trust you to take every relevant factor into account. Every representational system has biases.
Starting from the last sentence, which is the only one that makes semse to me :
True, but you hide the most important thing in the representational systems : they are structured ! They can be placed into an hierarchy of systems, when some "belong" to others, some can be "derived" from others, and some can not. ( Unless you are talking about art or religion, of course ).
Let me give an example : You see a circle, and you see an ellipse. Are they different ?
To ancient Greeks they were, so the representational system of Ptolemy was based only on circles, which were thought to have some divine substance, which "ovals" did not. Until the time of the great Kepler, this was the mode of thinking, and Kepler himself was sad when he was forced, in a way, to abandon his beloved previous system, the "Mysterium Cosmographicum" (1), based on perfect Platonic solids, in order to "save the phenomena", and accept the ellipses.
You know only Euclidean Geometry - your "conceptual space" is filled only with that. The circle is different from the ellipse.
Then, suddenly, out of the blue, there comes Desargues, and "Projective Geometry", and your conceptual space is filled with a new, more general way to "see" the same ancient geometrical forms - and, as consequence of that revolution, the circle and the ellipse become one and the same thing. ( Notice that the work of Desarques around 1600 was re-discovered after 250 years, so there is plenty of time to you to "see", at last, that the knot you show is but a variation of the classic Gleipnir.
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So, yes, the more we tie, the more "sophisticated" our "conceptual space" becomes - and more general, more powerful in its task to describe, explain and, if possible, predict reality.
The field would benefit from a well thought out taxonomy.
Say that again !
Hic Rhodus his saltus.
What do you mean by: "the integrity of the binder"?
Not the secondary characteristics, which there may be quantitative differences : the balance of the nub in mid0air or on the surface of the hitched/bound object(s), or its tightness, which may be more or less efficient in immobilizing and "locking": the ends. The primary characteristic, which is to enable the binder to "work", to enable the nipping structure to : 1. Be tensioned by its limbs. 2. nip both penetrating ends. If the nipping structure is not tensioned by both limbs ( attention : I do not say " both limbs pointing to different or opposite directions" ), and it is not forced to shrink, to grip, to nip anything that penetrates it, we do not have a Gleipnir. If it does not nip both ends, and, by this nipping, it secures them, we do not have a Gleipnir.
There may be differences in the efficiency a particular Gleipnir variation does those things - but this does not change the identity of the knot : A not-so-effective Gleipnir variation, is still, and will remain, a Gleipnir variation. Same thing with Zeppelin-like bemds, bowlines, etc.
readjusting your definition to reinforce your current point of view..
Do you really want me to re-adjust my definition to reinforce the point of view I had in the past ?
Perhaps even before I had learned about the Gleipnir, or about how to tie my shoelaces ?
Would you feel safer if the pilot of the airplane you are on finds his way using sextant and Ptolemaic astronomy ?
1.
https://en.wikipedia.org/wiki/Mysterium_Cosmographicum