A New Binding Knot?

[InTension]

   To me, there in no "fundamental" structural difference in all those Gleipnir variations whatsoever - however, evidently, if you wish to see that there is so much, at the very end you will manage to do so !

It changes the form of the knot. It changes how the knot is tied. And it changes the functional properties of the knot.
 Perhaps, one can love one particular thing so much that everything else is of secondary importance..

  By "form", you mean the geometric shape of the knot, which is not the only thing, or the most important thing, that determines the structure of the knot, the way the knot "works". The structure of the knot is based on the ends which are constricted, and immobilized, by a middle-line nipping structure ( be it a double nipping loop, a Clove hitch, a Constrictor, etc...). The way the ends penetrate this nipping structure, the "nipping tube", is secondary : they may enter and exit through the same side, or not. If they do not disturb the overall balance of the knot in mid-air, there is no structural difference.
   Any knot which is somehow different, geometrically, than another, can also ne tied differently - this is no big deal either ! The way a knot is tied ( if it is not veeery easy and quick, or the exact opposite ), is not of much importance in the evaluation of a knot. And you should not forget that any knot can be tied in maaany ways, many more than you can think of !

   

 

 
 

   Cut the four limbs of the Bull Clove hitch, some cms further away from the nub itself, and connect them the "other" way, to get the asymmetric Clove-hitch based mid-air binder you show.

   Since you can cut a clove hitch and turn it into a ring knot are they essentially the same knot ?

   ... Yes, those two hitches, the Bull Clove hitch and the asymmetric Clove-hitch Gleipnir variation you show are essentially the same knot. The two limbs of the Clove hitch can point to the same direction ( as they do in the case of the Bull Clove hitch ), or to opposite directions, as they do in the asymmetric Gleipnir variation  you show, but this changes nothing, regarding the structure of the knot. The angle the ends leave a Clove hitch is only of secondary importance. Do you believe that a Clove hitch where this angle is 60 degrees, and one where it is 90 degrees, work differently ? That they have "different functional characteristics" ? That they are a different knot ? The Clove hitch is a Clove hitch is a Clove hitch, in both knots - and the ends, since you pay sooo much attention to it, both enter into and exit from the nub through the same side.   

Is your concept of "no 'fundamental' structural difference" transitive?

If so, given that:
You are arguing that there is no 'fundamental' structural difference between the Draw Knot and the Gleipnir family of knots.
And you are arguing that there is no 'fundamental' structural difference between the Draw Knot and the Bull Clove hitch.

Implies that there is no 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots.

[xarax]

   There is a lot to be learnt from it, but please keep learning new things from new and different knots.

   I doubt that we can really learn new things from every new and different knot we happen to tie... We can, and we do gain experience, and dexterity, and familiarity with convoluted paths in 3D space with which our brains are not accustomed to deal - but we can not / do not learn new things. I have not learned anything new from the asymmetric Clove-hitch based Gleipnir you show that I had not already known, and I believe I am no exception on this. 
   The great knots, are the knots that are but the implementation, in its most pure form, of a general knotting idea. Those are the knots that can teach us new things - in just a few days after I think that I had learned something from a common knot, I realize that what I learned was already present, in a much more clear and genuine form, in one of the great knots, but I had not paid the required attention to it. Learn from the masters - and learn from the great knots !
 
 

  The Draw Knot is not topologically equivalent to the Gleipnir 

  Topological equivalence has nothing to do with two practical knots having the same structure, working the same way, playing the same role, doing the same job, etc.

   

 
...it is not an embellishment to the Gleipnir since nothing is added to the Gleipnir to create the Draw Knot.

   Nothing ... except a second nipping loop, connected to the first with the help of the Clove hitch s riding turn !
   See it the other way : Since something can be subtracted from the knot you show, and what will be left will be the Gleipnir, the Gleipnir is the fundamental knot where this particular variation of the Gleipnir is based.

   

   
   It has a different form; its tied in a different way; .

   
   Completely irrelevant things, regarding the similarity / identity of two knots, the way they "work", their structural idea.

   

...although it can perform some functions in common with the Gleipnir, it has many distinct handling properties..

   It can perform ALL the functions a Gleipnir performs - and nothing else !
   It may be more tight or stable, as we should had expected from the use of the Clove hitch ( which is a very tight, self-locking knot when it is tied around compressible and elastic materials ), but that remains to be proven experimentally.
   However, the "many distinct handling properties"(sic) are just another way for you to tell that you are in love with your brain child, and nothing else, I am afraid.
   The symmetric Clove-hitch-based Gleipnir, on which it seems you do not wish to refer, does everything the asymmetric does, and better : because the tails can be twisted around each other, in an ABoK#34 arrangement, and this multiplies the friction forces between them, as we all know since the invention of the Reef family of knots !

   It is not legitimate to say that two knots have "no 'fundamental' structural difference" if only you run the lines through them in different ways ! 

   Strictly speaking, the "ways" are identical, and only one - the directions the ends enter and exit are different, but the way their segment which are encircled into the "nipping tube" are gripped and immobilized, is the same. In a "toggled bend" we were talking about recently, for example, you can pass the toggle from the any one side to the other, without changing the structure of the knot.

 

Does the community of knot tyers have any rigorous way of determining if two knots are structurally equivalent, or is it just a matter of opinion?

   No, this "community", if it exists, has not any such rigorous way to determine the "structural equivalence" of two knots - for the simple reason it has no rigorous way to determine any-thing ! And it may be the case that it is not even a matter of opinion, but a matter of definition. -
   However, speaking about me, I am pretty sure that two knots I see as equivalent, are equivalent ! This knot is an asymmetric Clove-hitch based Gleipnir binder, very similar, and, most probably, inferior, to the symmetric one. It is the exact opposite I am afraid of :  two knots that look different to me, but they are nothing but the same thing, into a different package...

   Last thing:  A mid-air binder is self-locking, by definition. This means that both ends, the "Standing" and the "Tail" end are immobilized and secured in/by the nub of the binder : precisely this is what characterizes a 'tight hitch" as well . There is no other difference - except the fact that, in some cases, the interaction between the hard surface of the hitched object and the nipping nub of the knot plays some positive role in how tight the nub can become after some pre-tensioning. ( Also, as I have mentioned in passing, the binders utilizing same-direction wraps can be transformed into "Tackled"  hitches ).

   Now, how the direction the lines of the wraps turn around the object ( both clockwise or counter-clockwise, or the one clockwise and the other counter-clockwise )does not matter in the integrity of the binder. It may alter the way you form the knot in the first place ( although I do not see why this is so important ), but it does not alter the way the knot works. In general, there are two different classes of binders : The binders where the multiple wraps form a single multi-line loop, and the handcuff-type binders, where we have two loops connected in the "middle", by the nub of the binder.
   http://igkt.net/sm/index.php?topic=4821.msg32017#msg32017
   In the past, I, too, had tried to make a distinction between binders belonging to the one or the other class, as you do, but I had soon realized that this was an artificial, too narrow and perhaps myopic distinction :
   http://igkt.net/sm/index.php?topic=5014
   So, I do not blame you when you try to distinguish 50 shades of grey...

[xarax]

...there is no 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots.

  There is not.
 
   Try to "feel" the knot, as if you were a small creature crawling inside the lines, and "eating" tensile forces as you proceed forward.
  All those differences we see are secondary : There is a nipping structure, a whatever nipping structure, tensioned by the two limbs/lines, which, in their turn, and after some binding or hitching action around something, return to the place where they were born, and die there ...  
   For just another essentially Gleipnir-like binder, see :
   http://igkt.net/sm/index.php?topic=4819.0

[InTension]

I have not learned anything new from the asymmetric Clove-hitch based Gleipnir you show that I had not already known, and I believe I am no exception on this. 

I guess you were already aware of the connections between the Gleipnir & Bull hitches.
If you look into the Draw Knot, you might find a family of Draw Knots.
You seem to be the exception in terms of being the primary person engaging me in a dialogue. - Thank you for that.
   

 
   See it the other way : Since something can be subtracted from the knot you show, and what will be left will be the Gleipnir, the Gleipnir is the fundamental knot where this particular variation of the Gleipnir is based.

Structurally that simply isn't true: 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.

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.
 

 
   

   
   It has a different form; its tied in a different way; .

   
   Completely irrelevant things, regarding the similarity / identity of two knots, the way they "work", their structural idea.

The term 'structure' is generally synonymous with 'form'. I think that what you mean here by "their structural idea" is how their form gives rise to their function. But you seem to factor out that different forms may produce some functions in common, mixed in with some other different functions.
 

 
   

...although it can perform some functions in common with the Gleipnir, it has many distinct handling properties..

   It can perform ALL the functions a Gleipnir performs - and nothing else !
   ...
   However, the "many distinct handling properties"(sic) are just another way for you to tell that you are in love with your brain child, and nothing else, I am afraid.

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:
- How easy it is to tie?
- How fast it is to tie?
- How fast & easy it is to tie around awkward or unwieldy bundles?
- How easy it is for a novice to learn to tie?
- How memorable it is, when infrequently applied?
Those aspects have a big impact on the practical application of a binding knot. Ashley did not ignore such properties. How can you, without acknowledging that your concern for what makes a knot 'practical' is rather limited.

 

 
   Strictly speaking, the "ways" are identical, and only one - the directions the ends enter and exit are different,

Strictly speaking if the lines run in different ways, as in: "the directions the ends enter and exit are different" then they are not identical.

Again, 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.
 

 
   No, this "community", if it exists, has not any such rigorous way to determine the "structural equivalence" of two knots - for the simple reason it has no rigorous way to determine any-thing !

Pity. The field would benefit from a well thought out taxonomy. Balancing form, function, practical use, and lineage would be a real chore.  It would make one hell of a dissertation topic, but what field today would support such research into organizing the field of practical knots? Is their anything beyond ABoK that comes close to providing a general taxonomy of practical knots?
 

 
   Now, how the direction the lines of the wraps turn around the object ( both clockwise or counter-clockwise, or the one clockwise and the other counter-clockwise )does not matter in the integrity of the binder.

That makes no sense whatsoever to me.
- The Double Ring hitch and the Bull Clove hitch are examples where the lines of the wraps turn around the bundle in the same direction. When tied in braided nylon they will not hold when pushed apart from within by the dynamic bundle that they are meant to bind.
- The Gleipnir and Draw Knot are examples where the lines of the wraps turn around the bundle in opposite directions. When tied in braided nylon they will hold when pushed apart from within by the dynamic bundle that they bind.
- So how can you claim that the direction the lines of the wraps turn around the object does not matter in the integrity of the binder? What do you mean by: "the integrity of the binder"?
 

 
   In the past, I, too, had tried to make a distinction between binders belonging to the one or the other class, as you do, but I had soon realized that this was an artificial, too narrow and perhaps myopic distinction :
   http://igkt.net/sm/index.php?topic=5014

There you go again, readjusting your definition to reinforce your current point of view. Yes, there are good insights in that posting, but its really more of a collection of design principles relating to Gleipnir-like constructs than part of an objective classification scheme.

[InTension]

Is your concept of "no 'fundamental' structural difference" transitive?  If so, given that:
You are arguing that there is no 'fundamental' structural difference between the Draw Knot and the Gleipnir family of knots.
And you are arguing that there is no 'fundamental' structural difference between the Draw Knot and the Bull Clove hitch.
Implies that there is no 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots.

  There is not.

I cannot interpret your response: "There is not."
Does it mean: There is not a 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots?
Or does it mean: There is not such an implication?

If you believe that there is no 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots, then you would have to deny that the Gleipnir represented a new knot, since the family of Bull hitches predated it.

If you believe that the Bull Clove hitch and the Gleipnir family of knots are 'fundamentally' structurally different, then please note that the Draw Knot is closer in FORM to the Bull Clove hitch than the Gleipnir.

[xarax]

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 .   

  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. )
    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

[xarax]

  There is not a 'fundamental" structural difference between the Bull Clove hitch and the Gleipnir family of knots?

  There is not, indeed. However, we are NOT talking about that in this thread, are we ? We are arguing if there is a fundamental structural difference between a Glove-hitch based, or a whatever-tight-hitch based Gleipnir, and the knot you show, are nt we ? You have tried to push the whole argument to its limits, hoping, perhaps, that there your view may confront less objections, but it did nt work... I could simply / bluntly had replied : " This not is nothing but a Clove-hitch based Gleipnir, and, because it is asymmetric, it is probably inferior from the symmetric one ", period - but I did not. I had tried to explain my view, for whatever it is worth. Other people will have other views, but I guess you are more interested to the views of the people who happened to have more experience in this particular class of knots ( and had proved that they have more experience, because they have tied more similar knots ).
 

   If you believe that there is no 'fundamental' structural difference between the Bull Clove hitch and the Gleipnir family of knots, then you would have to deny that the Gleipnir represented a new knot, since the family of Bull hitches predated it.

 
   Going even before the Bull hitches, there is the bowline, and the Sheepshank, and the Captain Mullin s knot, which have elements of the Gleipnir - but not in the PURE, minimal, non-reducible form they exist in the Gleipnir. Elements of something may exist for many years, merged with or hidden under other things, but only when they are revealed in front of our eyes in their purest form, we appreciate what was there, just under our nose, invisible from the "common sense" - which is, oftentimes, just the current prejudice.

   the Draw Knot is closer in FORM to the Bull Clove hitch than the Gleipnir.

   No, because, regarding the form ( NOT the structure, which is about what we are talking for ages...), the orientation of the LIMBS that converge to the nipping structure, does matter. So, Dan Lehman s variation of the Gleipnir also looks more ( in form ) like a Bull-like hitch/binder, than a Gleipnir - but it IS a Gleipnitr variation, no question about that. As I said at least a dozen of times, neither the topology, nor the particular form/shape of the knot determines its structure, its identity as a "knot" tied on rope/material, the way it "works", which is all what matters for a practical knot.

[InTension]

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 .

Your classification system is based entirely of the particular way and order in which you studied and learned to tie knots. It is a subjective, rather than an objective classification system. I'm sure it works for you, as a designer of knots.

  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 !

Here you are classifying knots (variations of the Gleipnir) based on a high-level description, grounded in your principles of design. That is a perfectly legitimate way of constructing a classification system, but it also fraught with peril. Every different set of design principles will generate a different classification system. One can have multiple sets of design principles coexisting at the same time, intended to stress different design goals.

The underlying problem with this approach is that it is difficult to ground it on a stable, agreed upon set of characteristics.

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.

Here's my central point, and it illustrates how one can ground the classification of a knot in their low level characteristics.

Back in Reply 12 you provided a fine explanation of how the Bull Clove hitch can be transformed into the Draw Knot by reversing the direction of one of its coils runs. That is accomplished without taking the knot apart and putting it together again, as is required to convert the Draw Knot into a symmetric Clove-hitch Gleipnir. The act of extracting a line from a knot and pushing it back through a different part of the knot can be used to turn many knots into other knots that have little in common with the original.

Thus I argue that in terms of these low level, well-grounded characteristics, the difference between the Draw Knot and the Bull Clove hitch is smaller/less significant than the difference between the Draw Knot and the Clove-hitch Gleipnir. Therefore the Draw Knot should be classified as a variation of a Bull hitch, rather than a variation of the Gleipnir.

(Running the lines of a Bull Clove hitch surrounding the bundle in different directions changes how the knot is formed around the bundle. This transforms the Bull Clove hitch into an effective binding knot, with some of the functional qualities found in the Gleipnir family of knots.)

   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".

When the architect Louis Sullivan stated that he meant that it is the duty of an architect to design buildings to facilitate the function(s) they are intended to serve. (He wrote a great book entitled "Kindergarten Chats" that I think you would enjoy.) This is applicable to the design of practical knots.

Many people try to apply "form follows function" to biological systems, but in that case form and function are so intimately intertwined that they arise together. This may be applicable to the objective classification of practical knots.

    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.

Please don't redefine the meaning of the term 'structure.' It means: "the arrangement and interrelationship of parts in a construction, such as a building", as you will find in any dictionary. The moment you start talking about forces or functions you need to apply a different word. In the field of mechanics they divide the analysis of how forces operate on structures into statics (which applies to structures that do not move) and dynamics (which applies to structures that move). You might consider using the word 'mechanics', however, I suspect that your focus is really on the 'mechanical principles' that apply to knots rather that the detailed mechanics of how knots operate (quantitative differences, which you consider secondary). Alternatively, you might adopt a modifier and refer to it as the 'functional structure' that conveys that you're referring to something more than just the structure.

   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 .

It is ! It is concentrated in one, and one only, point ! The better is the knot, per se, the more practical it can be.

I like the way George R.R. Martin makes the point in "A Song of Fire & Ice": You can have the best sword blade in the world but if the bade has no handle it is not very useful. The handle is the user interface of a sword.

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.

I've got to wonder how many people who tie practical knots are "serious knot tyers".

   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 !

As I keep saying, its easier & faster to pull two lines together through an open clove hitch then it is to individually pass them through in different directions. This is probably insignificant if you're tying a static object sitting on a table in front of you, but if you are trying to tie an unwieldy bundle it can make a significant difference.

   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.

If one bases the design or selection of a knot around the use it will be put to (form follows function) then, in some cases, what you designate as secondary characteristics may become significant or even the deciding factor.

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 ?

No, but if your classification of knots is based on your current set of design principles, and your system of design principles is constantly evolving, then your classification scheme changes over time.

If the classification scheme was codified it could be updated at specified dates. You are performing a free-form version of that by posting articles of the forum describing your latest set of design principles. ? Bravo!

[InTension]

  There is not a 'fundamental" structural difference between the Bull Clove hitch and the Gleipnir family of knots?

  There is not, indeed. However, we are NOT talking about that in this thread, are we ? We are arguing if there is a fundamental structural difference between a Glove-hitch based, or a whatever-tight-hitch based Gleipnir, and the knot you show, are nt we ? You have tried to push the whole argument to its limits, hoping, perhaps, that there your view may confront less objections, but it did nt work...

We are engaged in a discussion of how to best classify knots, determine how similar they are to other knots, and if they are equivalent to other knots. I am 'drilling down' because I'm trying to figure out how you do that, and how your approach compares to the classification techniques I've seen applied in other fields. (The mother of all taxonomies is Linnaeus' "Systema Naturae" and its modern day 'derivatives'.)

I could simply / bluntly had replied : " This not is nothing but a Clove-hitch based Gleipnir, and, because it is asymmetric, it is probably inferior from the symmetric one ", period

Had you done that I would have written you off as a hack.

- but I did not. I had tried to explain my view, for whatever it is worth.

I truly appreciate that, and hope that you are enjoying this discussion as I am. I am a designer at heart, and like to interact with others who exist in that realm.

   the Draw Knot is closer in FORM to the Bull Clove hitch than the Gleipnir.

   No, because, regarding the form ( NOT the structure, which is about what we are talking for ages...), the orientation of the LIMBS that converge to the nipping structure, does matter.

Yes it matters, but does it matter more or less than the orientation of how the LIMBS pass through the nipping structure? This is the question on which the classification hangs.

As I said at least a dozen of times, neither the topology, nor the particular form/shape of the knot determines its structure, its identity as a "knot" tied on rope/material, the way it "works", which is all what matters for a practical knot.

As pointed out in previous posts there are many different ways of describing the operating principles by which a knot works. If the design of the Gleipnir is the cornerstone of your design principles, then the orientation of the limbs that converge to the nipping structure may be stressed more than the orientation of how the limbs pass through the nipping structure.

I respect your knowledge and opinion. I'm sure that is a very effective way to think about designing new knots. But it does not satisfy me in terms of a classification system. I favor systems based on more concrete, lower-level characteristics, because they provide a more stable grounding for building an objective, long lasting classification scheme. Although I cannot offer you a full blown taxonomy, I previously explained why I consider that reversing the direction of one of its limbs of a knot is a less significant change then reversing the direction in which one of its limbs pass through the nipping structure (which requires taking the knot apart and putting it back together).

[xarax]

   

   Your classification system... is a subjective, rather than an objective classification system.

   I do not see any "objective" classification system around, so, until you or somebody else finds one, allow me to use mime !
   

... you are classifying knots based on a high-level description, grounded in your principles of design.
... how one can ground the classification of a knot in their low level characteristics.

   Why do you want to base your classification scheme of knots on their low-level characteristics ?
   If you do that, you run the danger to get more classes than the knots that were ever tied in the Universe - because some of them might had been tied, dressed or loaded slightly differently, their forms might had became slightly different, so, those slightly different FORMS should belong to even more different classes of knots than the knots that were actually tied...
   The form/shape of a knot is a very superficial criterion of its identity. "See" deeper, in how do they wok, why they do not fall apart.
   

...it is the duty of an architect to design buildings to facilitate the function(s) they are intended to serve. This is applicable to the design of practical knots.

   If you believe in this "modern movement" s BS, you may manage to be happy to live in, and see around you, those mass-produced BOXES, which were the implementation, in concrete and brick ( like" flesh and blood" ) of this utilitarian ( like "totalitarian" ) ideology. Fortunately, architecture was,is and will be an art, and does not do this - just as painting does not fill canvases with colour. "Duty" to "serve" ? Come on !
   And practical knots do not exist because we need them - they exist, period - and because they exist, we can use them for our needs, or not. Unless you believe that numbers exist because we made them, to count our fingers.
   We do not "design" practical knots ! Just as we do not design mathematical theorems. We find them - and after we find them, we decide if they can be used for something or not.
   

   Please don't redefine the meaning of the term "structure". It means... , as you will find in any dictionary.

   I do not need to define or re-define what is a structure, thanks KnotGod ! And, of course, I do not learn what IS a thing, by looking in a dictionary.
  To "feel", in your bones, what a structure IS, you must build structures - and some of them must collapse, to teach you what you did wrong. A nice, small, clear booklet on structures, is the :
   Structures, or why things don't fall down, by J.E.Gordon
   Just three lines of this marvelous book :
   "Science"...has subtly warped our system of values by teaching us to judge things on grounds which are excessive functional. The modern man asks : What is this man or thing FOR ? rather than : What IS this man or thing ? Herein, no doubt, lie the cause of many of our modern sickness.
 

   I like the way George R.R. Martin makes the point in "A Song of Fire & Ice": You can have the best sword blade in the world but if the bade has no handle it is not very useful. The handle is the user interface of a sword.

   OK. I will make the best steel, and the best blades, and you will make the best handles... ( And please, do not tell me after that what "noble" function those swords will "serve"...)
   

   I've got to wonder how many people who tie practical knots are "serious knot tyers".

   Are you interested to learn only in what "maaany" people do ? Then, I suggest you should study LOTTO, or toothpastes, not knots !
 

...its easier & faster to pull two lines together through an open clove hitch then it is to individually pass them through in different directions. .

   HOW do you know this ? Have you actually MEASURED the time to tie the symmetric and the asymmetric Clove-hitch based binders, and found any difference, or such a big difference that would persuade somebody to tie the one instead of the other ?
   If THIS is the advantage of the asymmetric variation you think it is critical, well, think again !
   I have to notice that, again, for the n-th time, unintentionally or intentionally, you remain notoriously silent about the real advantage of the symmetric variation over the asymmetric one - but sorry,  I am not going to repeat it here again !
   

...what you designate as secondary characteristics may become significant or even the deciding factor.

   I have seen, in use, that a very significant factor which can determine the outcome of a knotting activity is how WET is the rope I pull - remind me to take it into account the next time I will "design" a knot, which will "serve" a purpose.
   Secondary characteristics should be offered the fair amount of attention they deserve : not much. 
   

... your system of design principles is constantly evolving, then your classification scheme changes over time.

If you mean that, in the future, pilots of airplanes will, again, use sextants and the Ptolemaic astronomical system to orient themselves, the meaning of the word "future" in your dictionary is different than in mine.

[xarax]

   We are engaged in a discussion of how to best classify knots, determine how similar they are to other knots, and if they are equivalent to other knots.
   This is the question on which the classification hangs.
...it does not satisfy me in terms of a classification system.
   I favor systems based on more concrete, lower-level characteristics, because they provide a more stable grounding for building an objective, long lasting classification scheme.

   The issue of classification is important - up to a point.
   When we see a great knot, it is not important any more... If we "classify" the Gleipnir, this would mean we have not understood nothing about it, in particular, and about practical knots, in general.
   Van Gogh may be classified as an "impressionist" - but he is simply a great painter.
   Great knots should define the classes we better use, not the other way around.
   The knot you have presented is an asymmetric Clove-hitch based binder. It belongs to the Gleipnir "class" of knots, even if it "resembles", in form, the Double Ring knot, the Bull Clove hitch, or the Mona Lisa !

[InTension]

... you are classifying knots based on a high-level description, grounded in your principles of design.
... how one can ground the classification of a knot in their low level characteristics.

   Why do you want to base your classification scheme of knots on their low-level characteristics ?

"I favor systems based on more concrete, lower-level characteristics, because they provide a more stable grounding for building an objective, long lasting classification scheme." The opinions of subject matter experts vary over time & between experts.

...it is the duty of an architect to design buildings to facilitate the function(s) they are intended to serve. This is applicable to the design of practical knots.

   If you believe in this "modern movement" s BS, ...

What makes you think that? I cited the master architect who coined the expression "Form follows function" and recommended his book. I also pointed out that form & function arise together in biological systems. - For the record, I'm pro modern movement and fascinated by biomorphic designs.

   And practical knots do not exist because we need them - they exist, period - and because they exist, we can use them for our needs, or not.

Yes, but if you explore the 'design space' of knots with a particular focus or goal in mind you're apt to try out certain approaches and ignore others. People don't really invent knots they 'merely' discover them. The trick is to use your time wisely to discover more useful knots than useless ones.

   

   Please don't redefine the meaning of the term "structure". It means... , as you will find in any dictionary.

   I do not need to define or re-define what is a structure, thanks KnotGod ! And, of course, I do not learn what IS a thing, by looking in a dictionary.

You can alter the meaning of terms for your own internal use to your hearts content. The problem arises when you attempt to discuss or explain something to others who are not aware of how you have altered the use of common terms. It took me a long time to figure out that when you said "structure" you meant more than just "the arrangement and interrelationship of parts in a construction".

...its easier & faster to pull two lines together through an open clove hitch then it is to individually pass them through in different directions. .

   HOW do you know this ?

It's generally faster to perform an action once than twice.

... your system of design principles is constantly evolving, then your classification scheme changes over time.

If you mean that, in the future, pilots of airplanes will, again, use sextants and the Ptolemaic astronomical system to orient themselves, the meaning of the word "future" in your dictionary is different than in mine.

It is the nature of designers to be ever looking forward to new ways to think about and do things. I'm afraid we need someone who enjoys organizing things (like a librarian) to construct classification systems that are useful and stable. - I'm not applying for the job either.

[InTension]

The issue of classification is important - up to a point.
   When we see a great knot, it is not important any more... If we "classify" the Gleipnir, this would mean we have not understood nothing about it, in particular, and about practical knots, in general.
   Van Gogh may be classified as an "impressionist" - but he is simply a great painter.
   Great knots should define the classes we better use, not the other way around.
   The knot you have presented is an asymmetric Clove-hitch based binder. It belongs to the Gleipnir "class" of knots, even if it "resembles", in form, the Double Ring knot, the Bull Clove hitch, or the Mona Lisa !

Thank you for being clear about your preferences.

   "The crow wish'd every thing was black, the owl that every thing was white." -- William Blake

I believe that the only unbiased solution is to split the difference: Observing that the knot I presented is like the Bull Clove hitch but with the direction of one of its limbs reversed, and like the symmetrical Clove-hitch Gleipnir but with both limbs entering the nipping structure from the same side, I conclude that the Draw Knot is half way between the symmetrical Clove-hitch Gleipnir and the Bull Clove hitch.

I will leave it to others to determine the usefulness of this knot, and, once a better perspective has been gained, to determine if it is worthy of being considered a new binding knot.

[xarax]

...it is the duty of an architect to design buildings to facilitate the function(s) they are intended to serve. This is applicable to the design of practical knots.

   If you believe in this "modern movement" s BS, ...

  What makes you think that ?

   Maaaany years of experience - and of study, but, most of all, of just looking around with an innocent/honest eye...
   The so-called "modern movement", this "utilitarian"/"functionalistic" ideology, in architecture, produced b o x e s - cheap boxes. I lost so many years of my life in the bottom of this dark pit, and I know. Do not listen what the "modern movement" was saying ( better : preaching ), just LOOK what it had built - how it had destroyed the cities, and transformed humans into subway rats.
   ( Moreover, the same ideology which considered that houses are/should be just "machines a habiter", was responsible for much worse things.... One step further lurks the "modern" idea that man himself is also machine, which "functions", and his function/behaviour is/should be controlled accordingly. As a comment on a recent debate about the dangers of artificial intelligence, read this :
   " Some prominent scientific gurus are scared by a world controlled by thinking machines. I am not sure that this is a valid fear. I am more concerned about a world led by people, who think like machines..." )   
   
  The "modern movement" did not produced "biomorphic designs", it produced rectangular cuboids = boxes, and rows of boxes, made from cement, glass and steel, we have to call "cities".
   

   It took me a long time to figure out that when you said "structure" you meant more than just "the arrangement and interrelationship of parts in a construction"....

   You were unlucky ! It took me a fraction of a second to dismiss your statement :
   

   The term 'structure' is generally synonymous with 'form'.

   Because that is what we are talking about : how and why the knot you show "works", its structure, not how it "looks", its form.
   The structure of your knot is the structure of the Gleipnir ( more than the structure of the Bull hitch, which, after all, may be seen as just an attempt to "lock" the Cow hitch ). 

...its easier & faster to pull two lines together through an open clove hitch then it is to individually pass them through in different directions. .

   HOW do you know this ?

   It's generally faster to perform an action once than twice.

   When I read a supposedly devastating, "clever" one-liner, I usually smile.
   To pass, through the same side of a hole, the end of one line coming from the east. and then the end of one line coming from the west, is "generally faster to perform"(sic) than to pass the same ends, of the same lines, through the same hole, from different sides...
   However, I had not asked about anything "general" ! I asked if you had actually m e a s u r e d the time you need to perform those particular actions, on this particular knot, and if you had found that there is a difference, and that this difference is sufficient to make one tie the asymmetric rather than the symmetric variation. Read my lips - the whole sentence, please :
   

   HOW do you know this ? Have you actually MEASURED the time to tie the symmetric and the asymmetric Clove-hitch based binders, and found any difference, or such a big difference that would persuade somebody to tie the one instead of the other ?
 

[Dan_Lehman]

I believe that what you call the bull hitch is what Ashley called
the double ring knot (ABoK #1126, also called the double running knot).

No, what I mean is that  the knot is to the cow hitch
as the dbl. bowline is to the bowline --where the latter
of each pair has a full/round turn vice the single turh--; and your knot
is to the bull h. as the water bowline is to the d.b.
--the clove structure is more stable.

it doesn't matter whether you start with a Buntline or Two Half Hitches; an identical Draw Knot results in either case.)

Although you take the ends around in opposite directions,
and so it should matter --at least as far as "identical" is
concerned, as there will be the difference in tail direction.
(Note that there's interesting difference when using the
clove hitch in the Gleipnir structure to reeving ends
through it one way or the other, where the paired half-hitches
either pull away or towards each other --the latter case
seems to make for a tighter hitch (as seen in some
commercial-fishing knotting), but perhaps less grip!?)

--dl*
====

It's more a matter of starting with one part and finishing with the other, versus starting with the other and finishing with the one. - Simply the order in which they are passed around & through.

Well, I'm clearly right, but in the narrowest, most
technical sense --I was thinking that there was more
significance, but, no, you're right.  (If you tie the one
approach going the opposite way to the other, you
end up with identical knots (given appropriate dressing
and all, getting the two ends like-aligned through the
hitch part).)
Thanks,

--dl*
====