Overs Index - First example

[Dan_Lehman]

... The idea is to mentally cut off the force-bearing parts of the knot in order to examine the knot in its forceless configuration.  Knot aficionados would understand that this means cutting off the Bowline's loop.  But when I try to apply the "neighbor test," I can't help but wonder if everyone is going to properly interpret what to do here.  ...
Therefore, I'm inclined towards keeping things as straightforward and simple as possible by examining the knots as-is, rather than trying to cut off their force-bearing components.  This would mean that if two ropes are joined with a Carrick Bend, then the OI is 8:16.  But if the two ends of the same rope are joined with a Carrick Bend then the OI is 8:15.

Thoughts?

The idea is to consider the nub of the knot, in Chisholm terms; the confusion that
you hypothesize is beyond the pale irrational, in most cases, at least (the Sheepshank
is one case I'm unsure of).  This entire exercise is done for what point, exactly?  It's
certainly not for the average Joe, who might not be up on exactly how shoes are tied,
let alone knot classification to any serious extent.
Note that ALL ends are cut off, so to speak--not merely load-bearing ones--; so as
to consider just the thing where they interconnect.
Having it matter whether a bend unites the ends of one vs. two PoFM is not any
help, so far as I can see.  (Conceivably, this aspect might be unknown!)

Incidentally, I could see that Clove hitch looked at where the ends go off in opposite
directions, and a count for that layout is 7:10; shifting the crossover part gives 7:9.
But Derek's minimal arrangement is down to 6 crossings but fully saturated.
(I can hardly wait to figure out a Bimini Twist!  )

--dl*
====

[DerekSmith]

Derek,

It would be helpful if we can find or invent some examples in which there are more than two thicknesses of cord at one point, so that we can describe how to handle such situations.

Dave

Hi Dave,  we already have a three layer knot - the Jug hitch covered on the Wiki.

Seen edge on, the jug hitch looks like this:-



but it can reasonably easily be pulled open without changing its structure as in this image:-



The big issue looming is - should a knot be counted in its 'in use' configuration?  The next example really brings this home.

[DerekSmith]

(I can hardly wait to figure out a Bimini Twist!  )

--dl*
====

While I have worked up an outline method for counting cylindrical knots such as the Fiador, I have to admit that linear multiwrap knots such as Slip/Grip hitchs, Icicle and other gripping hitches have all left me at a loss as to how to even begin to feature them into the OI.

I personally see the Bimini as a piece of double laid rope rather than a knot.  Ropes, Plaits, splices and weaves to me are outside the scope of the OI and that would include the plaited double featured on the forum recently.  But perhaps that is just me looking for a way out from having to tackle them.

However, if you are keen to take on the Bimini, tackling the multiwrap hitches should be 'fall off a log' easy.  I really hope you manage it, because I honestly do not have the slightest idea how to begin.

[DaveRoot]

The idea is to consider the nub of the knot, in Chisholm terms; the confusion that you hypothesize is beyond the pale irrational, in most cases, at least (the Sheepshank is one case I'm unsure of).  This entire exercise is done for what point, exactly?  It's certainly not for the average Joe, who might not be up on exactly how shoes are tied, let alone knot classification to any serious extent.

Will anyone do exactly what my pictures show?  Maybe, maybe not.  The pictures simply illustrate a point, and the point itself is valid, I believe.  For the vast majority of people who encounter an unfamiliar knot, they won't be looking at the knot in terms of "force components" and "nubs" and so on.  They will simply see a piece of rope which twists around itself in an unfamiliar way.

Anyone who has gained some Knot Knowledge, such as contributors to this forum, there was a time before we had any real Knot Knowledge.  At that time, if we looked at a knot then we would not have had much awareness of such things as "nubs" and "bights" and "standing parts" and "bitter ends," etc., because we had no real experience or knowledge of such things.  This is the case for the vast majority of people.  For example, a chemist can look at a chemical formula and get a feel for certain properties which the formula describes (based on his or her knowledge and experience), but the vast majority of people would see an arrangement of letters and numbers without really understanding the meanings in the way that a chemist would.  I would say that the same is true with knots.

If cutting off the ends and only examining the nub of the knot is a significant factor in properly determining the OI and saturation, I don't have a problem with that.  But the more complicated the procedure and the more steps involved, the greater the likelihood of user error and user confusion, which reduces the value of the product.

If the target audience of the Overs Index is the small group of people with an interest in a deeper study of knots, then the complexity of the procedure is less of an issue.  But if the intention is for the OI to be a valuable resource for anyone in the world, then it is helpful to occasionally step back and try to view our work through the eyes of an imaginary next-door-neighbor.  That was the point of the "neighbor test" which I mentioned, because as a software developer I have seen time and time again where people will take a product or a set of instructions and do all manner of unanticipated things!  Again, the more complicated the procedure and the more steps involved, the greater the likelihood of user error and user confusion.

But if cutting off the ends and the force-bearing components (for example) turns out to be an important factor in correctly calculating the OI and the saturation then that's fine, and we can try to come up with a fairly simple way to describe the procedure.

Dave

[DerekSmith]

We are just trying to classify knots by counting some characteristics of those knots - easy peasy?

So why do I feel like I am peering in through the doors of Dr Who's Tardis?

We have only looked at one example and already hit snags, the next example will expose yet more and there are some cord structures I cannot even begin to mentally resolve.

It is probably too early to start throwing out methods and perspectives when we as yet do not even know the size of the problems we have yet to resolve.

I have always been an advocate of standing back and considering a situation from other perspectives.  The 'Joe public' perspective may just turn out to be an important one - particularly if we hope that one day knot science will feature within our schools and to do that it must be comprehensible.

Perhaps for a while, if we can spare the mental energy and the time we should continue by considering and retaining all perspectives, at least until we have some feel for how deep is this hole.  We might even have to consider that we could end up recording every different arrangement that we can find for our knot.  The one we think it 'should' be and those that someone might by accident choose.  The Wiki can hold all of these possibles and the search function for say a 9:12 would then turn up not only the 'formal' 9:12's but also all those knots which have an alternative layout which counts it as a 9:12.

The objective after all is to be able to hold a knot in our hands, then find it in the WKI.  I just have a sneaky feeling that we should be prepared to end up utilising a whole bag of identifiers to make the task as easy as possible.

[DaveRoot]

The test is, if the knot still exists without the presence of the rigid part (CD in this case) then the rigid part is NOT part of the knot and should not be included in the OI assessment.  If however, the knot ceases to exist when the rigid part is removed, (as in this case) then the CD part has to be defined as part of the knot and has to be included into the Crossings count and the Saturation count.

We have seen that the idea of the rigid part (a spar, a tree, etc.) being considered as a component of the knot is fairly counter-intuitive.  However, perhaps the simplest solution is to specify that if a knot is tied around an external object, or if a knot requires an external object for its existence (e.g. Clove Hitch, Constrictor, Marlinspike Hitch, Lark's Head Hitch, Cat's Paw, etc.), then substitute a length of rope for the external object for the purpose of calculating the Crossing Points and Saturation.  This is essentially what you did by tensioning CD, but it appears to be a simple solution for the general case as well.  Edit: The purpose for this is to make it easy to see the points which need to be included in the Crossings count and the Saturation count, and to prevent disputes about what is (or is not) a part of the knot.

While I have worked up an outline method for counting cylindrical knots such as the Fiador, I have to admit that linear multiwrap knots such as Slip/Grip hitchs, Icicle and other gripping hitches have all left me at a loss as to how to even begin to feature them into the OI.

One idea for handling multi-wrap knots is to specify that only a single wrap should be used when calculating the Crossing Points and Saturation.  We would need to define exactly what a "wrap" is, and we would need to consider the case where there are multi-wraps within a knot (e.g. Double Dragon), but perhaps this is a straightforward way of handling multi-wrap knots.

Dave

[DaveRoot]

Ah ha....here's a reason for cutting off all of the entry and exit points of a knot.  I'm looking at a Bowline on the Bight, and I can see that if a knot has 2 or more loops then the loops will generally lay on top of each other.  This creates any number of Crossing Points which are not within the knot itself (depending on how a person has arranged the loops), so how do we devise a generalized solution for handling such cases?  Cutting off the entry and exit points of the knot seems to handle such cases quite effectively.

Now, I followed the Standing Part through the Bowline on the Bight until it exited the knot where I was mentally cutting off the loop.  That "cut off" point is now essentially a Working End, but it seems redundant to follow that Working End back through the knot since it is the exact strand which I had just followed.  But we can't make a rule that cut-off points should not be treated as Working Ends, because then the Saturation count would not include the part where the "rabbit" goes around the "tree."  Therefore, the most straightforward procedure for ensuring that all Crossings are included in the Saturation count is to say that all cut-off points must be treated as Working Ends, even if this results in strands being redundantly followed twice.

Following this procedure, I came up with {OI 16:34} for the Bowline on the Bight, does that sound right?

Dave

[squarerigger]

This is a very interesting thread to follow and I can see that you all are having a great time with it.  I wish that I had some suggestions of my own to make, but clearly you are all well able, and appear not to need any further input.  I like the idea of Joe-next-door idea as a role model for the person reading the method, by the way!  You had mentioned Budworth's prior treatment of a similar process for possibly classifying knots by counting overs and unders (I think!).  Have any IGKT Members contacted Geoffrey Budworth for his input?  Although he may not want to contribute to a public forum, maybe he has some private suggestions for what he envisaged and maybe he could help you all?  Just a thought...

SR

[DerekSmith]

This is a very interesting thread to follow and I can see that you all are having a great time with it.  I wish that I had some suggestions of my own to make, but clearly you are all well able, and appear not to need any further input.(my emphasis)  I like the idea of Joe-next-door idea as a role model for the person reading the method, by the way!  You had mentioned Budworth's prior treatment of a similar process for possibly classifying knots by counting overs and unders (I think!).  Have any IGKT Members contacted Geoffrey Budworth for his input?  Although he may not want to contribute to a public forum, maybe he has some private suggestions for what he envisaged and maybe he could help you all?  Just a thought...

SR

Hi SR,  glad you like the topic, but you couldnt be more wrong about needing additional input.  This pond is deep and we havn't even found the edges yet, let alone the bottom.  The more folks add their penn'th the better.  In particular, the task is going to advance faster if as many folks as possible start to count OI's.  Where we get dissagrement, then we know there is a need to resolve some issues.  So PLEASE dive in - the water's -- DEEP.

Re Geoffrey Budworth, yes I have had contact with him.  Sadly I have not been able to obtain a copy of his book on the subject and have just contacted him again to update him on the progress and to ask how we might access the text in his book.  He was very interested in the project and keen for his 'Crossings' method to come back into use.

[DerekSmith]

Ah ha....here's a reason for cutting off all of the entry and exit points of a knot.  I'm looking at a Bowline on the Bight, and I can see that if a knot has 2 or more loops then the loops will generally lay on top of each other.  This creates any number of Crossing Points which are not within the knot itself (depending on how a person has arranged the loops), so how do we devise a generalized solution for handling such cases?  Cutting off the entry and exit points of the knot seems to handle such cases quite effectively.

Now, I followed the Standing Part through the Bowline on the Bight until it exited the knot where I was mentally cutting off the loop.  That "cut off" point is now essentially a Working End, but it seems redundant to follow that Working End back through the knot since it is the exact strand which I had just followed.  But we can't make a rule that cut-off points should not be treated as Working Ends, because then the Saturation count would not include the part where the "rabbit" goes around the "tree."  Therefore, the most straightforward procedure for ensuring that all Crossings are included in the Saturation count is to say that all cut-off points must be treated as Working Ends, even if this results in strands being redundantly followed twice.

Following this procedure, I came up with {OI 16:34} for the Bowline on the Bight, does that sound right?

Dave

I agree Dave, the 'rabbit round the tree' is a functional part of the knot and must stay intact.  However, your example throws our newly framed 'end of knot rule' right out the window.

As tied, the knot is a double loop tied with a single strand of cord.



'Sense' has me count it as {OI-16:15} simply by following the single cord through the entire knot.

However, take away the non functional ends and we have a three cord knot.



At first sight it is still 16:15.  But wait !!  The new rule for the 'end of the knot' means that as the ends B and D come out of the knot they cross over two cords and account for four crossings.  But the rule says that because the second crossings are the same priority, then we have to go back one cord  and discard the second crossings.  Exactly the same happens as ends E and F come out under two cords.  Using the new rule the OI for this knot is 12:15.  The rule has made us dismiss a cord which is clearly part of the knot and therefore MUST be included.  A rule designed to help us distinguish between components integral and extraneous to the knot has in this case failed.

Clearly we cannot keep the rule as it would fail in situations such as this one.  Any thoughts on how to rephrase it so that it does not cause such problems or must we approach this problem from a new direction?

As for counting in from every end, each cord will have two ends.  I doesn't matter which end we start the count from, the count will be the same, so if we count it from both ends, we have just counted it twice, so counting in from every end simply doubles the counts we would have made by simply counting each cord once.  I do not see haw that will add clarity to counting the OI.  Following the KISS principle we should only count each cord once.

[DaveRoot]

At first sight it is still 16:15.  But wait !!  The new rule for the 'end of the knot' means that as the ends B and D come out of the knot they cross over two cords and account for four crossings.  But the rule says that because the second crossings are the same priority, then we have to go back one cord  and discard the second crossings.  Exactly the same happens as ends E and F come out under two cords.  Using the new rule the OI for this knot is 12:15.  The rule has made us dismiss a cord which is clearly part of the knot and therefore MUST be included.  A rule designed to help us distinguish between components integral and extraneous to the knot has in this case failed.

When I relaxed out the Bowline on the Bight, the "rabbit around the tree" part was in the same configuration as in this picture:



Therefore, yesterday when I cut off the loops I didn't run into the same issue that you did.  The 'end of the knot' rule didn't come into play (edit: referring to ends B and D in your picture.  I didn't catch that for E and F!).

we cannot keep the rule as it would fail in situations such as this one.  Any thoughts on how to rephrase it so that it does not cause such problems or must we approach this problem from a new direction?

Clearly it makes a significant difference how we relax out a knot, so perhaps if we focus on standardizing the procedure for relaxing out a knot then hopefully some of these other issues will go away!

As for counting in from every end, each cord will have two ends.  I doesn't matter which end we start the count from, the count will be the same, so if we count it from both ends, we have just counted it twice, so counting in from every end simply doubles the counts we would have made by simply counting each cord once.  I do not see haw that will add clarity to counting the OI.  Following the KISS principle we should only count each cord once.

It could be argued that the "Keep It Simple" principle is best served by treating each cut end as a separate Working End (even though this doubles the count for some or all cords), because this allows our imaginary neighbor to follow one single procedure without the added complexity of having to determine which ends actually belong to the same cord.  Conceivably there are certain knots in which it might be cumbersome to try to identify and keep track of individual cords as they weave throughout the knot.  Incidentally, I arrived at {OI-16:34} by treating each cut end as a separate Working End, thus counting the same cords from both ends.

I don't really have a preference either way yet (counting a cord only once vs treating each cut end as a Working End)....more playing is needed!

Dave

[DaveRoot]

As I'm trying to get a better feel for how to calculate the Saturation of various knots, I find myself coming back to the question of the purpose for calculating the Saturation.  Here is Derek's description (emphasis mine):

When I first started to make some Crossing Point assessments, I was not too surprised to find the 80:20 rule hard at work.  That is, 80% of our knots are going to be found in the most popular counts of Crossing Points.  That’s why I started to look for a further means of differentiating between the knots that were collecting within a single Crossing Point group.  The Saturation perspective sprang out from Charles Hamels work on H and L sequence analysis. ...
However, having read the replies, I see that not only is Saturation valuable as a means to sub categorise knots,  but I now realise from Dan's observation, that Saturation is in fact a vital part of being able to correctly define the Crossings Count.  It is essential to consider Saturation in order count Crossings, even if you do not need Saturation to refine the search for the knot in question.

So the Saturation at the ends of the cords will help identify where to begin counting the Crossing Points, but the primary purpose of finding the Saturation count is for sub-categorizing knots.

From that perspective, can the WIK be useful if we cast aside the idea of calculating Saturation counts?  Absolutely.  In fact, the WIK will be simpler and more user-friendly without the added time and effort involved in calculating the Saturation.  However, I'm all for continuing to study and test options and alternatives in order to see what fruit it bears.  Eliminating the Saturation concept is just one of a number of options.

Now, based on the above quote, let's try renaming "saturation count" as "sub-category number" for the moment.  Just for fun, let's also rename "priority" as "altitude" for the moment, because "priority" doesn't quite capture the essence of what we're doing (IMHO).

Using these new terms, first we calculate the Crossings count in order to get the primary category number, and then we calculate the sub-category number by counting each time the cord changes altitude (from over to under, or from under to over).

Notice that all we are trying to accomplish is to develop a procedure for consistently finding the correct primary category number and sub-category number.  From this perspective, it really doesn't matter if our "end of knot" test bypasses critical strands of cord.  All we're after is a sub-category number.

On the other hand, if the intention of the Saturation count goes deeper than that, e.g. to assist in the scientific study of knots, then we should make sure that we properly define the goal of the Saturation concept so that we have a better idea of what we're shooting for.

Dave

[DerekSmith]

As I'm trying to get a better feel for how to calculate the Saturation of various knots, I find myself coming back to the question of the purpose for calculating the Saturation.

From that perspective, can the WIK be useful if we cast aside the idea of calculating Saturation counts?  Absolutely.  In fact, the WIK will be simpler and more user-friendly without the added time and effort involved in calculating the Saturation.  However, I'm all for continuing to study and test options and alternatives in order to see what fruit it bears.  Eliminating the Saturation concept is just one of a number of options.

Dave

Without question, the Wiki Index of Knots (WIK), does not need a subcategory to be useful.  If someone has a knot and has established that it  has a crossing count of say 24, then with that information alone, they could type OI-24 into the Wiki search box and be presented with a list of every reference to OI-24 on the Wiki (including of course all those including a sub-category or even a sub-sub-category or D/L variation).  They can then simply compare their knot with those on record for OI-24.

We may not need a sub-category at all, and for certain, it does not have to be saturation, that just seemed like a handy differentiation having already laid out the knot in order to count the crossings.  Indeed, Frank Brown has a load of classification parameters that could double for a sub-category - should we even need one that is!

The observation I had made that the Saturation was important in order to determine the true begining and end of the knot ( necessary to be able to correctly count the knot crossings ) is now wrong - see the Topic on Lessons Learnt.

Finally, are we determining Saturation for something deeper than simply fixing a sub-category?

When I read Charles Hamel's work on H/L sequences, I was 'romanced' by the thought that Saturation somehow imbued a sense of 'knottiness'.  After all, a fully saturated knot could not possibly be more wrapped around itself, it should therefore behave with the ultimate level of knottiness.

But !! Take the Granny knot - fully saturated at 6:12, yet it is a nasty knot.  Then the Carrick at 8:16, again fully saturated yet it shape changes something terrible when put under load (see OI Example 2 - coming soon).

By contrast take the Myrtle only partially saturated at 7:10 yet it is a dream of a knot, pull it any way you like - two ways, three ways or four ways, it stays rock solid.  Or take the new knot I posted a few days ago (no name yet) weighing in at 12:18, yet bend, or loop on any of the ends and it retains its shape wonderfully.

So, although Saturation indicates a level of knottiness, it doesn't indicate or reflect the structural stabilities which we seek in our quality knots.  Probably, then saturation then will turn out to be little more than an easy method of sub-classifying an unknown knot, and some other - as yet unidefined parameter will feature in our assessment and prediction of a knots stability.