Author Topic: A most simple bend .  (Read 12957 times)

alpineer

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Re: A most simple bend .
« Reply #30 on: July 10, 2011, 04:45:03 PM »

It is a shame that Ashley called them both the Whatknot, because although the difference in topology is only tiny, the difference in functional structure is massive, and there is no way we should be countenancing calling them the same. 

Derek

The "UnKnot", or the "NoKnot" would be an appropriate name for ABoK #1407 as it really isn't a knot at all.


DerekSmith

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Re: A most simple bend .
« Reply #31 on: July 10, 2011, 04:52:31 PM »

It is a shame that Ashley called them both the Whatknot, because although the difference in topology is only tiny, the difference in functional structure is massive, and there is no way we should be countenancing calling them the same. 

Derek

The "UnKnot", or the "NoKnot" would be an appropriate name for ABoK #1407 as it really isn't a knot at all.



Agreed

xarax

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Re: A most simple bend .
« Reply #32 on: July 10, 2011, 05:00:34 PM »
It is a sad reflection of the sloppy (or should I say organic) 'history' of knots that puts us in the position of having knots named by numerous aspects that have nothing to do with the form and function of those knots.

   Yes, but it is even more sad, when people continue to spend their valuable time talking about knot names, and not about the knot themelves ! I have not yet read anything about the re-tucked parent Whatknot (ABoK#1406), presented in this thread ...

...the difference in topology is only tiny...

  :) A "tiny" (?) difference in topology makes a knot or not, and turns a no-knot, into a knot...In such simple knots with so few crossings, there are no tiny changes. Even a change of dressing can make or brake a secure knot, so any change in topology is a huge change !
« Last Edit: July 10, 2011, 05:01:31 PM by xarax »
This is not a knot.

DerekSmith

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Re: A most simple bend .
« Reply #33 on: July 10, 2011, 05:25:35 PM »
It is a sad reflection of the sloppy (or should I say organic) 'history' of knots that puts us in the position of having knots named by numerous aspects that have nothing to do with the form and function of those knots.

   Yes, but it is even more sad, when people continue to spend their valuable time talking about knot names, and not about the knot themelves ! I have not yet read anything about the re-tucked parent Whatknot (ABoK#1406), presented in this thread ...


HI Xarax,  I might hazard a guess that this might be due to the fact the as 1406 / 1490 already works so well, there is little interest in changing it for better or for worse, especially when the reader will have to judge for themselves if the change is an improvement worth learning.


...the difference in topology is only tiny...

  :) A "tiny" (?) difference in topology makes a knot or not, and turns a no-knot, into a knot...In such simple knots with so few crossings, there are no tiny changes. Even a change of dressing can make or brake a secure knot, so any change in topology is a huge change !

I think? we are agreeing with one another here, that even the small topological change of swapping over the orientation of the ends can, and in the instance of discussion, has a huge impact on functionality - but I would not agree that 'any' (i.e. all) change is 'huge' - that would depend on your assessment criteria...  But I take your point.

Derek

xarax

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Re: A most simple bend .
« Reply #34 on: July 10, 2011, 06:17:58 PM »
   I might hazard a guess that this might be due to the fact the as 1406 / 1490 already works so well, there is little interest in changing it for better or for worse, especially when the reader will have to judge for themselves if the change is an improvement worth learning.

   I might hazard a guess that this might be due to the fact that, even if the 1406 / 1490 does not work very well - because there is the danger of the tails re-positioning themselves -  there is no interest in changing it for the better, especially when the casual reader prefers to talk about something written on stone, 70 years ago, and fears to judge any possible improvement - that is asking for real work to test and evaluate, and real judgement and courage to criticize, something not as easy or safe as the mere parroting of the scripts...Come on, Derek, do you see many people around that find anything worth of learning ? Knowledge is something that does not pay the rent... :) O tempora, o mores.
This is not a knot.

DerekSmith

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Re: A most simple bend .
« Reply #35 on: July 10, 2011, 06:41:28 PM »
Nice one Xarax,

But - knowledge pays the rent for my soul,

and

Just because something is 70 years old, does not make it wrong or of poor value - but then I would say that because I am nearly that old myself, and my mother and kids still think I am pretty special...

As for O tempora, o mores, - well, I love these times - all this knowledge, all this facility to learn and communicate, and the children of today - they are just amazing... ( at least - most of them are)

Derek

DDK

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Re: A most simple bend .
« Reply #36 on: July 12, 2011, 06:51:55 AM »
...the difference in topology is only tiny...
  :) A "tiny" (?) difference in topology makes a knot or not, and turns a no-knot, into a knot...In such simple knots with so few crossings, there are no tiny changes. Even a change of dressing can make or brake a secure knot, so any change in topology is a huge change !
I think? we are agreeing with one another here, that even the small topological change of swapping over the orientation of the ends can, and in the instance of discussion, has a huge impact on functionality - but I would not agree that 'any' (i.e. all) change is 'huge' - that would depend on your assessment criteria...  But I take your point.
Derek

It is interesting to me that mathematical knot theory would consider ABOKs 1406 and 1407 to be topologically equivalent, i.e. zero difference.  In this theory, any arrangement of a knot that can be obtained if one were to have kept each of the working ends of the ropes connected to the end of their standing parts would be topologically equivalent.  I prefer to imagine all standing parts and working ends to be infinitely long so that, for example, no untucking and retucking may occur.  So for example, a Reef Knot or Thief Knot is topologically equivalent to a Cow Hitch hitched to a rope and a Granny Knot or Grief Knot is topologically equivalent to a Clove Hitch hitched to a rope.

It would seem to me that mathematical knot theory only takes one so far (not very far?) in understanding even the structure of a practical knot.  For example, the relative positioning of the elements of a knot are not considered.

DDK

xarax

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Re: A most simple bend .
« Reply #37 on: July 12, 2011, 08:56:38 AM »
... mathematical knot theory would consider ABOKs 1406 and 1407 to be topologically equivalent, i.e. zero difference.

   No, not exactly...With the hope to offer Roo the opportunity to be right for once ( if he tells me that this Forum in not the proper place for such a discussion), I will reply here... :)  ABoK#1406 is L6a1, while ABoK#1407 is L6a3. (See (1) and (2))

1) http://katlas.math.toronto.edu/wiki/Image:L6a1.gif
2) http://katlas.math.toronto.edu/wiki/Image:L6a3.gif
This is not a knot.

DerekSmith

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Re: A most simple bend .
« Reply #38 on: July 12, 2011, 11:48:29 AM »
snip...

It would seem to me that mathematical knot theory only takes one so far (not very far?) in understanding even the structure of a practical knot.  For example, the relative positioning of the elements of a knot are not considered.

DDK

True, but then 'Knot Theory' is only a tiny and highly stylised subset of the realm of Knots.  Indeed, the field we study (more correctly that should be 'fumble around in') is in itself a tiny subset of the realm of knots our universe plays with.  'Knot Theory' deals only with topology, while we are attempting to get to grips with (pun intended) Force Machines within which 'Topology' is itself only one aspect.

Sadly (or not depending on your perspective), our chosen field is so mind numbingly complex, we tend only to sit around the camp fire and semi randomly twiddle cordage, then marvel at the Force Machines that knots can create.

Unlike the mathematicians, we have not yet attempted to simplify / stylise our field so that we might start to comprehend the workings of the machines we so effortlessly make, use and discard.

Unlike the Chemists, we have not yet sought to identify the component 'elements', identify their properties, understand their 'Stable energies' and the energy needed to morph them to higher or lower energy forms, to formulate how they interact with other components and most importantly, to understand how they process FORCE.  A knot is a tiny analogue, 3D, real time force computer.  We - make a knot - put force in - and study the final consequence - we have virtually no idea what happens within our knots, and so consequently we have virtually no idea how to rationally refine or optimise them.

But that leaves a whole lot of exploration for those minded to try to go there...

Derek

DerekSmith

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Re: A most simple bend .
« Reply #39 on: July 12, 2011, 11:50:21 AM »
... mathematical knot theory would consider ABOKs 1406 and 1407 to be topologically equivalent, i.e. zero difference.

   No, not exactly...With the hope to offer Roo the opportunity to be right for once ( if he tells me that this Forum in not the proper place for such a discussion), I will reply here... :)  ABoK#1406 is L6a1, while ABoK#1407 is L6a3. (See (1) and (2))

1) http://katlas.math.toronto.edu/wiki/Image:L6a1.gif
2) http://katlas.math.toronto.edu/wiki/Image:L6a3.gif

For a two cord link - yes.  But for a single cord loop, both 1406 and 1407 are 3_1, the overhand knot.

Derek

xarax

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Re: A most simple bend .
« Reply #40 on: July 12, 2011, 12:31:54 PM »
For a two cord link - yes.  But for a single cord loop, both 1406 and 1407 are...

    No. That is the good thing with the mathematics, compared with the field of practical things, in general, and with practical knots, in particular : We first have to define exactly what we mean, and then we can argue no more about any well defined mathematical fact:)
   So, WHICH loops ? We can connect the four free ends, of each bend, in a number of ways, and have various different single cord loops ! Do the connections, and you will see immediately that what you say is not accurate, or correct. ( Of course, this thread was meant to deal only with the properly tied bend, the ABoK#1406 - that is, the doubled symmetric Sheet bend -, and not with the various loops that have the structure of ABoK#1406o and/or ABoK#1407  )
   
This is not a knot.

DDK

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Re: A most simple bend .
« Reply #41 on: July 12, 2011, 03:09:23 PM »
... mathematical knot theory would consider ABOKs 1406 and 1407 to be topologically equivalent, i.e. zero difference.
  No, not exactly...With the hope to offer Roo the opportunity to be right for once ( if he tells me that this Forum in not the proper place for such a discussion), I will reply here... :)  ABoK#1406 is L6a1, while ABoK#1407 is L6a3. (See (1) and (2))
1) http://katlas.math.toronto.edu/wiki/Image:L6a1.gif
2) http://katlas.math.toronto.edu/wiki/Image:L6a3.gif

Yes, I see what you mean.  I will say, though, that it seems somewhat ambiguous (the assignment of L6a1 to ABOK 1406) in that it does depend on how one connects the working ends to the standing parts whether an additional crossing is generated (L6a1) or not (L6a3).  The direction of the working ends as they leave the knot appears to have been considered (seems odd).  Possibly, this is a shortcoming (strength?) in the use of knots with no ends for the purpose of understanding knots with ends.  

I must admit I prefer my definition making use of infinitely long ends (no connecting of ends, no cutting of loops) which you have helped me see to be substantially different from the connecting of ends which then requires the cutting of loops.  That is, going in the reverse direction, from the knot with no ends to a knot with ends, that where one makes the "cuts" in, for example, L6a1 will determine whether ABOK 1406 is produced or different knots are produced (edit: i.e. the ambiguity I mentioned actually another type of ambiguity).

DDK
« Last Edit: July 12, 2011, 05:21:24 PM by DDK »

DDK

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Re: A most simple bend .
« Reply #42 on: July 12, 2011, 07:26:24 PM »
It is a sad reflection of the sloppy (or should I say organic) 'history' of knots that puts us in the position of having knots named by numerous aspects that have nothing to do with the form and function of those knots.
  Yes, but it is even more sad, when people continue to spend their valuable time talking about knot names, and not about the knot themelves ! I have not yet read anything about the re-tucked parent Whatknot (ABoK#1406), presented in this thread ...

Nomenclature does serve a useful purpose.  Better to imbibe ETHanol (2 carbons), responsibly of course, than the deadly METHanol (1 carbon).  Just calling them alcohol will not do.

Your point is taken, however, and so I will mention that like most of the retucked bends, eg. the overhand bends, I find this retucking of half hitches in the Grass Bend to be somewhat jamming.  The Figure 8 Bend (retucked through outer collars - Thief Knot) and its cousin, the retucked Reef Knot http://igkt.net/sm/index.php?topic=3196.msg19099#msg19099, are notable exceptions.

DDK

xarax

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Re: A most simple bend .
« Reply #43 on: November 01, 2011, 07:11:49 PM »
   Another, slightly different, retucked Whatknot. In this variation, the tails, situated closer to the central "embrass", are probably more functional to the overall mechanism of the knot.(See the attached pictures)
This is not a knot.