testing physical theories of knots

Practical Knots
41

Hi Derek,

Nice try, attempting to characterize my argument as “simplistic” , but sorry, it is not simplistic at all. There are only a few expert mathematicians in the word that study ideal links, and they do not think that my example is simplistic…In fact, they have tried to calculate the dimensions of the loop of maximum perimeter, that would allow a number of ideal ropes to sip through, yet they will not allow the knot to be untied - i.e., retain its character as Gordian knot. It is an open mathematical question, but well defined, and interesting.

Yet it is involved, in the form of a wedge of an infinitely small angle. Or this is what I understood by reading your post.

Noope ! :slight_smile: If you do the math, you will see that there may be configurations where a nipping loop can not be forced by a penetrating object to open, indeed, not because of any infinite constricting power, of course, but because the object/“obstacle” itself forces it to close more than it forces it to open. Study the Gordian bends I have shown, and you will see that, although the nipping loop can open, it will not open - and this has nothing to do with the need of an infinite force, but just with the need of a force greater than another one ! The trick is this : Figure out an “obstacle”, a tangled segment of rope, that, when it will tend to go through a nipping loop, it will force, by its geometrical shape, the nipping loop to close more than it will force it to open - something like a 'reversed wedge", to use your term.

Yes, only an infinitely great mechanical advantage, achieved by an infinitely small wedge… :slight_smile:

Ouaou ! A girth hitch ! A dead zebra ! How on earth I had not seen that ingenious mechanism ! Yes, there is life on earth ! :slight_smile:

Please, Derek, tell me ONE f knot or hitch that is tied around a hook or ring, and which you hold by both its ends, that will not do what your ingenious counter example will… And then tell me why on earth you have chosen the girth hitch, and not the ring hitch, and not a single round turn, and not any hitch, and not any knot, to tell me the obvious, that the topology of a knot can not change ! Because that is the only thing that your dead zebra does, your ingenious counter example, the girth hitch : it retains its topology, - and its integrity, so it can not pass around or through the pole ! :slight_smile: And it does not even do this, because a girth hitch without friction will slip alongside the sutface of the pole, going to the one or to the other direction. You need an alive zebra, a ring hitch and a ring/hook, to point out the obvious tautology that knots have topology ( which I have not been able to understand, the dumb extra-terrestrial…)…and that there are living things on earth, indeed - even if they are trying to bite and eat each other alive, like we do in this silly dialogue of deaf knot tyers…

42

[s]Really? When did ‘we’ agree to this?

If indeed I have come to such an agreement, then I must now recind it, for although the sensible use of the SB requires constant tension, it remains entirely practical for all applications requireing line shortening which satisfy the provision of remaining under tension.[/s]

Edit:

I must accept having made an error in the above statement as I was refering to the SB and had not realised the distinction that Constant had made by refering to the ‘Symetric SB’

Most knots have limits to their practical usage, but few of those knots are deemed impractical simply because they have a usage limitation. After all, knowing what knots are suitable for a particular application is part of the pleasure and skill of the Knot Tyer.

Finally, a Girth Knot formed utilising a loop of cord is not impractical. And, for very low cF cords, making a stopper knot by back splicing a braid is certainly not impractical, be it used to block slipage through a strangle or any other knot. So, even in this simple and highly practical example of a stopper knot, you are presented with yet another example of a practical knot which does not rely on friction for its function.

Derek

43

Really ! :slight_smile:

http://igkt.net/sm/index.php?topic=3716.msg21506#msg21506

It would be “foolhardy and irresponsible” (sic) to suggest it to anyone as a Practical knot, but we can suggest to anyone to melt the free end of a practical knot, that would otherwise be unknotted at a glance ! THAT would require a lot of “cerebrionics” to understand… :slight_smile:

So, now it is me the one who will try to narrow the field of “practical” knots…What a difference a few days can make !
I had come to believe that if the dressing of a knot is unstable, i.e. if the knot should be dressed to one stable form that very easily ( by a " tiny tug" ) degenerates to another, less stable or completely unstable form, from which it can easily be untied, then it should not be considered as a “practical” knot.
Of course, if the knot demands melting, gluing, fastening with metal parts, the involvement of segments of other rope, etc., it is not a 'practical knot" either.
I have to remind that I am the least able to speak about the practicality or impracticality of a knot, because I never use knots for practical purposes ! :slight_smile: I use knots to admire them as rope mechanisms, as potential tools, and in an effort to understand what a knot is…

You would have to adress this statement to knot tyers of other universes, to get a reply ! Try 4 dimensions… :slight_smile:

I doubt that any back splicing of a braid would remain in place in the complete absense of friction - unless it replicates a “Gordian knot” that I had mentioned. If it does, it would be probably so complex and hard to tie that it would NOT qualify as a practical knot.
I myself had tried to figure out a knot that does not rely on friction ( or topology, of course ! ), and I had presented the Gordian links and bends I had mentioned. If you would find another such knot, you should present it properly, not by talking only about it, but by pictures !
So, I am NOT presented with yet another example of a practical knot that does not rely on friction, just because I am not presented with EVEN ONE example of a practical knot that does not rely on friction - because to say that any knot or hitch, when it is wrapped around the pole, bollard, hook or ring, and you hold both its ends by the friction of the fingers of your hands, is such an example, is a great misunderstanding of what I was talking about - and of what an example, any example, is ! It is a tautology, void of any meaning, good only for rhetoric purposes, of which we have enough in this Forum. Knots, presented with pictures, THAT is what we do not have ! So, try to figure out a tangle of ropes that is not topologically linked in the first place, but can remain tangled even in the absense of any friction. It is called “Gordian knot”. You will soon discover that it is NOT so easy as you think…

Please, let us move our discussion at (1), because I feel guilty I have destroyed this very interesting thread. Sorry, bcrowell, it was my fault.

1). http://igkt.net/sm/index.php?topic=4183.0

44

Hi Constant,

I have acknowledged your first point and corrected my previous post accordingly.

I failto see why you keep addressing me to the fourth dimesion re the Girth Hitch made using a loop, and it is simplicity itself to make a stopper in braid by splicing. However, I do take your point that this has been a significant hyjack of bcrowell’s thread, so I agree, we should take the discussion elswhere.

Derek

45

Thank you Derek.

Just a quick reply : Because a knotted closed loop can be unknotted in 4 dimensions, without any loss of continuity. Topology does not preserve closed tangled ropes remain tangled in 4 dimensions, as they do in 3. The extra dimension somehow provides additional space, another degree of freedom, from which they can slip through. A curious thing, imdeed.

46

Again, just a quick rejoiner,

I am not talking about a knot in a closed loop, I am talking about a knot made with a closed loop, by flattening the loop, passing one end bight through a ring, then back through the other end bight. This forms a simple knot in 3D which relies on topology rather than friction, and can be easily undone in 3D.

47

THAT is your problem ! :slight_smile: Because you are talking about it ! :slight_smile: It is like there is a intelligent being in the universe, be him/her an extra-terrestrial or knot, that could have said something else ! :slight_smile: You simply state the obvious - inherent in the definition of a knot, any and every knot -, that the topology of a knot can not change…but it seems you have not YET realized that you are not saying/ talking about ANYTHING ELSE. So, you had not explained why on Earth you chose the “Girth hitch”, and not any other hitch which we hold by both ends, or the ring hitch, or the single round turn, or the single loop. Moreover, if you wished to state a tautology, that knots are knots are knots are knots( because that is all you say, and nothing else…), for rhetorical reasons, you could well had talked about the overhand knot, for knotGod s sake…No, you are talking about the “Girth hitch” , because there is something in Girth hitch other than what is inherent in the overhand knot, something that makes it THE ingenious counter example against your extra terrestrial interlocutor - something that will be revealed AFTER Dec. 21, I suppose ! :slight_smile:

Extra-terrestrials, Mayans, the Girth hitch, and a rose is a rose is a rose :
http://igkt.net/sm/index.php?topic=4183.0

P.S. It is an improvement you have replaced the pole with a ring. Now, if you replace the ring with a second Girth hitch, made with a closed loop or not (), you will arrive at the Cow hitch bend I was talking about at a previous post… just in time for the DEC. 21 party ! :slight_smile:
(). When the two ends of the open loop, or the end of the one bight of the closed loop, are/is now inaccesible, while previously was not ( you used it to form the knot, remember ? ), you have CHANGED the topology, without talking about it… :slight_smile: