Author Topic: Overs Index - First example  (Read 12945 times)

DerekSmith

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Overs Index - First example
« on: July 02, 2006, 05:01:14 PM »
snip…..
Then I thought I'd try my hand at counting some Crossing Points so that I can help fill out the Overs Index.  I tied a Bowline and followed the Standing Part as it entered the knot, and the first Crossing Point is where the "rabbit" goes around the "tree."  But I found that when I laid the loose Bowline flat on the table, I ended up with two Crossing Points due to the angle at which the Standing Part was entering the knot.  In addition, if the Working End is long enough, it can create different numbers of Crossing Points depending on the angle at which it exits the main loop.

So it seems that there will need to be a set of "rules" to help ensure that people are able to calculate the proper number of Crossing Points for a knot.  But is this turning out to be so complicated that people are not realistically likely to go through this process?

Dave


In order to start developing the guidelines for the 'Method for Counting the Overs Index for a Knot' lets follow Dave's start and put a few examples to the test.  In doing so we should soon uncover the rules needed to count the Overs Index.

Lets start with a nice simple knot with no name --



Interestingly, some knots have a name outside of their use, this one however seems to depend totally on its application for a name.  The knot has many configurations and many names, but if I don't tell you what each of the four ends are connected to, then you cannot tell me which knot this is - interesting.  This 'unassigned' knot has two parts.  The white part is a loop or a bight or a Becket, so I will call it Bk for short.  The second part (red part)  clamps itself against the two white strands a bit like the tang of a belts buckle so I will call it Blt for short.  For want of a better name then, this little knot is now a "Bk,Blt".  It has two strands and four ends.  If we now start to assign function to these ends we start to create working knots from the basic functional knot.

Possible setups for this knot include :-

One cord,
Two cords,
No loops,
One loop,
Two loops.

To assign the possible variations, I will use the following annotation :-

W = working part, i.e. it will be under tension and transferring force to or from the knot.
L = loop, i.e. one of two working parts sharing  similar forces in the same direction.
E = free (or tying) end.  In operation this end has no forces on it.

To view the tables see here (I couldn't make tables work in this new forum yet)

The tables show that (at least) seventeen possible configurations exist, unless you consider that any of the free ends could also be loaded, which bumps up the variations to 37, and of course, every one of these knots can be tied in its mirror configuration giving an available mix of at least 74 configurations.

[Of note, easily half of these knots are dangerous.  If opposing tension exists on C-D and the tension on A drops, then the C-D loop can pull the A leg through the A-B loop, converting it to an overhand slip knot and allowing the C-D cord to pass through unobstructed.]

Half a dozen of these configurations, which are reasonably safe, have fallen into common use and have attracted names dependant upon that use, except perhaps for the "Manx" (my naming), only one variant of which seems to have been taken up in the form of the Eskimo Bwl.

So ….  one knot - the "Bk,Blt" and a number of named uses.  The point here is that it is just one knot.  The uses may define or influence the working shape of the dressed knot. but they are all still one knot.  The OI cannot record or tell us anything about the loading or use of a knot, so I feel the first step in defining the OI Method is to stipulate that the knot is assessed in isolation from any use.  That is, you assess the "Bk,Blt" -not the Bowline or the Sheetbend or the "Manx".

STEP 1 :- Make a note of the function of each cord entering/leaving the knot for later refinement of the knot identification, then 'cut off' the extraneous connections leaving the knot in a forceless configuration.

STEP 2 :-  Open up and rationalise the knot into a two dimensional plane (special note for cylindrical knots).  Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count.  Attempt to achieve a situation where there is no more than two thicknesses of cord at any one point.



STEP 3 :-  Count the Crossings being careful not to include extraneous Crossings where ends leave the knot.  For example, if an end leaves the knot from the center and has no further function within the knot, then do not count this end as it crosses over other parts of the knot (physically or mentally shorten the cord to its last point of function within the knot).  Consider - any end could be wound back and forth over the knot.  Clearly, this cord laying on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.

STEP 4 :- Count the Saturation by following  the cord into and through the knot and counting every time the cord changes 'priority' from above to below or from below to above.  If the knot has multiple cords, count each of these separately  and total the counts for the final knot.  Start the count as the cord enters the knot, counting as one the very first time it goes over or under another cord.

STEP 5 :- Record the Overs Index for the knot in the format {OI-X:Y-Z}  Where X is the Crossings count and Y is the Saturation count.  Use the {OI-X:Y} to identify the family of knots in the Index and then use the detailed function of each cord recorded in STEP 1 to identify the exact knot from the Index (The WKI).  This will give the final designation for Z and access to specific information on the particular variant being identified.

In this particular example;



There are seven crossings i.e. X=7.  The red cord has a saturation of 6 and the white cord a saturation of 5, so Y= 6+5 = 11.  This makes the Overs Index {OI-7:11-Z} and because this is the forceless knot "Bk,Blt", I have arbitrarily assigned it position 0 in the table i.e. {OI-7:11-0}


Will those five steps do? or is there a need to clarify or refine them?

Derek

Dan_Lehman

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Re: Overs Index - First example
« Reply #1 on: July 02, 2006, 06:34:36 PM »
In order to start developing the guidelines for the 'Method for Counting the Overs Index for a Knot' lets follow Dave's start and put a few examples to the test.  In doing so we should soon uncover the rules needed to count the Overs Index.
Much thanks for explaning this in slow motion to help us understand!

Quote
The white part is a loop or a bight or a Becket, so I will call it ...
A rose by any name ... ; but "BiLo"/"LoBi" fit best the simple nature of the knot
as you have presented it, based on the traditional defined terms most knots
books give (then often transgress them later.   :P ).  But, by any name, ... .

Quote
If we now start to assign function to these ends we start to create working knots from the basic functional knot.
... The point here is that it is just one knot.  That is, you assess the "Bk,Blt" -not the Bowline or the Sheetbend or the "Manx".
So, here we take the knot at a most general state.  Okay.

Quote
STEP 2 :-  Open up and rationalise the knot into a two dimensional plane (special note for cylindrical knots).  Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count.  Attempt to achieve a situation where there is no more than two thicknesses of cord at any one point.
This is the difficult step, at least for more complex knots, for the least-number-of-crossings
form is often going to have a starkly different appearance from the functional knot subject
to examination; finding this form can be difficult (as I think I show below, for even THIS simple case!).

Quote
STEP 3 :-  Count the Crossings being careful not to include extraneous Crossings where ends leave the knot.  For example, if an end leaves the knot from the center and has no further function within the knot, then do not count this end as it crosses over other parts of the knot (physically or mentally shorten the cord to its last point of function within the knot).  Consider - any end could be wound back and forth over the knot.  Clearly, this cord laying on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.
Here I think some of the trouble begins to show:  "no further function" sounds odd,
for a knot rendered devoid of functionality for this examination.  I think I've the sense
of what is wanted--that some layouts will be unable to have ends nicely going off the
edge of the planar view--; but, still, assessing functionality might prove problematic!?

Quote
STEP 4 :- Count the Saturation by following  the cord into and through the knot and counting every time the cord changes 'priority' from above to below or from below to above.  If the knot has multiple cords, count each of these separately  and total the counts for the final knot.  Start the count as the cord enters the knot, counting as one the very first time it goes over or under another cord.
Ahhh, I wondered how this was done!  It might be helpful to point out that,
unlike for the Crossings count, one counts each crossing twice (potentially).
Why begin with a count at the first crossing, though?
--won't it necessarily be the case that the first two crossings must
be 1 (i.e., how could they not?) ?  Well, begining with the first crossing
enables one to have the potential fully saturated ratio of X:2X.

Quote
STEP 5 :- Record the Overs Index for the knot in the format {OI-X:Y-Z}  Where X is the Crossings count and Y is the Saturation count.  Use the {OI-X:Y} to identify the family of knots in the Index and then use the detailed function of each cord recorded in STEP 1 to identify the exact knot from the Index (The WKI).  This will give the final designation for Z and access to specific information on the particular variant being identified.
So, Z is dependent for meaning upon a predefined table.

Quote
In this particular example; There are seven crossings i.e. X=7. 
Here I take issue:  as you've presented the knot, this is how it appears; but I submit
that the least-number-of-crossings form hasn't been given--it's the C-D tucked
through A-B qua Marlinespike Hitch form, which has but 6 crossings, and a saturation
index of 12 (!). (I.e., pull C-D ends apart to get this form.)

--dl*
====

DaveRoot

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Re: Overs Index - First example
« Reply #2 on: July 03, 2006, 03:35:26 PM »
Derek,

I agree with your statement (in the other "Overs Index" topic) that somewhere down the road we might see benefits of the Overs Index, etc., which we would not have recognized if we hadn't put forth the effort.  Or we might put forth the effort and then discover that it hasn't helped much.  Such is life! 

Either way, something is usually learned through the effort, and I'm willing to contribute.

Thanks for developing some guidelines for counting the Overs Index!  There might be a few refinements needed, but that's how progress is achieved.


STEP 2 :-  Open up and rationalise the knot into a two dimensional plane (special note for cylindrical knots).  Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count.  Attempt to achieve a situation where there is no more than two thicknesses of cord at any one point.
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.

Also, when I had previously tried "relaxing out" a Bowline, I didn't achieve the configuration in your pictures.  Instead, I ended up with something like the "relaxed out" Cowboy Bowline shown here: http://www.Layhands.com/Knots/Knots_KnotsIndex.htm#1034.5.  If I'm counting correctly, the relaxed out Cowboy Bowline has an OI of 7, just like your pictures do.  However, is it possible that different people will calculate a different OI for the same knot simply because they relaxed out the knots in different ways?


STEP 3 :-  Count the Crossings being careful not to include extraneous Crossings where ends leave the knot.  For example, if an end leaves the knot from the center and has no further function within the knot, then do not count this end as it crosses over other parts of the knot (physically or mentally shorten the cord to its last point of function within the knot).  Consider - any end could be wound back and forth over the knot.  Clearly, this cord laying on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.
As Dan said, I've got the sense of what you're describing, but I think that in practice it's not going to be very clear-cut as to whether or not the final crossing(s) should be ignored.  Using your pictures as an example, one might assume that ends A and B are simply exiting the loop, so their final crossings (pink and blue respectively) might be "external" or "extraneous" crossings.  Do those crossings have any function in the knot?  We won't always know unless we dress up the knot with the appropriate form of loading and so on.

I think you're on the right track with the idea of excluding extraneous crossings, but somehow we need to refine this concept in order to make it more foolproof.


Consider - any end could be wound back and forth over the knot.  Clearly, this cord laying on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.
That's a good point, because any end can have an arbitrary number of windings around another strand, and those windings don't usually contribute to the functionality of the knot in any of its loaded forms.  But now I'm curious what the OI should be for the Timber Hitch!


Start the [saturation] count as the cord enters the knot, counting as one the very first time it goes over or under another cord.
This makes sense to me, because before the cord reaches the knot it has a "priority" of nothing/null.  Therefore, when the cord reaches its first Crossing Point then it changes priority from "nothing" to "over" or "under."


STEP 4 :- Count the Saturation by following  the cord into and through the knot and counting every time the cord changes 'priority' from above to below or from below to above.  If the knot has multiple cords, count each of these separately  and total the counts for the final knot.
I still need a little clarification here.  I can see how you arrived at a saturation of 11 based on your picture, because your picture has multiple cords which are counted separately.  So if two separate ropes are joined with a Sheet Bend then the saturation of that bend would be 11.  But if we imagine A as being the Standing Part, and we imagine that B curves around and becomes C, then we have a form of the Bowline.  In this case, the saturation would be 10, right?  Similarly, a Carrick Bend which joins two separate ropes would have a saturation of 16, but a Carrick Bend which creates a sling in a single rope would have a saturation of 15, right?

In Step 1 you said to "cut off the extraneous connections leaving the knot in a forceless configuration," which I guess would resolve my confusion.  I'll play with that idea some more, and perhaps it will prove to be a clear-cut or foolproof method of calculating the correct saturation every time.  I'm just wondering if in practice it might be possible that people will "cut off" the knot at the wrong places and arrive at the wrong values.

Just to throw another idea into the mix here, is the saturation really very useful?  It is more complicated or cumbersome than counting the Crossing Points (in my opinion, anyway), while providing only a limited benefit.  For example, if we simply say that the knot in your pictures is OI-7 then we have a very simple index value which follows the "Keep It Simple" model.  If a person has a knot and calculates the OI as being 7, then he can go to the WIK OI-7 page and scroll through the pictures of OI-7 knots until he finds his particular knot.  He has drastically narrowed down the field by calculating the number of Crossing Points, and there was no need to spend the extra time calculating the saturation.  This would make the Overs Index simpler and more user-friendly.  Just a thought!

Thanks for the effort you've put into documenting the method of calculating the OI....progress is being made!

Dave

Dan_Lehman

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Re: Overs Index - First example
« Reply #3 on: July 03, 2006, 04:55:48 PM »
Also, when I had previously tried "relaxing out" a Bowline, I didn't achieve the configuration in your pictures.
...  However, is it possible that different people will calculate a different OI for the same knot
 simply because they relaxed out the knots in different ways?
Dave, clearly you didn't make to the end of my post--go read the final prg.!

Quote
but I think that in practice it's not going to be very clear-cut as to whether or not the final crossing(s) should be ignored.
Unless, as I suggested, it comes down to ignoring crossings not producing a Saturation count
--for how can a crossing be useful if it's the same as the next one, at the exit from the knot?!


Quote
Consider - any end could be wound back and forth over the knot.  Clearly, this cord [lying] on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.
That's a good point, because any end can have an arbitrary number of windings around another strand, and those windings don't usually contribute to the functionality of the knot in any of its loaded forms.  But now I'm curious what the OI should be for the Timber Hitch!
Different numbers of such tucks simply must be counted as part of the definition
of the Timber Hitch, just as number of wraps are counted (in arborist nomeclature, at least)
for friction hitches ("3 over 2" and so on)--and they DO affect functionality for the
Timber Hitch, depending upon the materials (more = more secure).  (What is also
needed for the TH is indication of how the first crossing of the end with itself is
made--taken over than tucked/dogged (which I prefer--easier, of course, and
puts the binding crossing point farther back around the object), or under, as in
a Half-hitch.)

Quote
Start the [saturation] count as the cord enters the knot, counting as one the very first time it goes over or under another cord.
This makes sense to me, because before the cord reaches the knot it has a "priority" of nothing/null.  Therefore, when the cord reaches its first Crossing Point then it changes priority from "nothing" to "over" or "under."
Well, that is a rationalization that might find acceptance, but I think the real
point is a matter of yielding a maximum SI of double the CI; otherwise, I
think it would not be so easily known how close to fully saturated some
knot was.  (point:  we're simply making rules here, not matching some
fundamental reality; so, What point have these rules?, is a valid question.)


Quote
In Step 1 you said to "cut off the extraneous connections leaving the knot in a forceless configuration,"
 which I guess would resolve my confusion.
Exactly.  And you can see how this removes the problems that arise otherwise.

Quote
Just to throw another idea into the mix here, is the saturation really very useful?
It is more complicated or cumbersome than counting the Crossing Points (in my opinion, anyway), ...
As you suggest, it can further assist discrimination among knots (although from this
beginning example, we can see that a bunch of knots (Bwl, SheetBend,LappBend,...)
will share an OI#; perhaps we'll find out something about SI# as an indicator of knot
behavior (although, given the above-indicated set of this example, we can find in
that quite a variety of behaviors).  But for discrimination alone, it is useful, as being
indexed to a set of, say, 75 possible functional knots starts to look like
missing the boat on helpful locator functionality!

--dl*
====
« Last Edit: July 03, 2006, 05:46:13 PM by Dan_Lehman »

DaveRoot

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Re: Overs Index - First example
« Reply #4 on: July 03, 2006, 09:38:45 PM »
Different numbers of such tucks simply must be counted as part of the definition of the Timber Hitch, just as number of wraps are counted (in arborist nomeclature, at least) for friction hitches ("3 over 2" and so on)--and they DO affect functionality for the Timber Hitch, depending upon the materials (more = more secure).
I agree.  However, I'm thinking about all of the "everypersons" out there (e.g. our neighbors) whose knot knowledge essentially consists of the Shoelace Knot and the Reef Knot.  We'll all need a standard method which consistently provides the correct OI values.


This makes sense to me, because before the cord reaches the knot it has a "priority" of nothing/null.  Therefore, when the cord reaches its first Crossing Point then it changes priority from "nothing" to "over" or "under."

Well, that is a rationalization that might find acceptance,
Not so much a rationalization, rather it's my "memory device" for recalling the rule.  Works quite well for me!   ;D


In Step 1 you said to "cut off the extraneous connections leaving the knot in a forceless configuration," which I guess would resolve my confusion.

Exactly.  And you can see how this removes the problems that arise otherwise.
I agree.  It standardizes the methodology, which is a good thing.  But again, I'm thinking of the "everypersons" out there, and whether or not they will "cut off the extraneous connections" in the same way that any of us knot-nuts would.  Perhaps it is always completely obvious where the extraneous connections should mentally be cut off, but I haven't yet played with the idea enough to determine that...

Dave

knudeNoggin

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Re: Overs Index - First example
« Reply #5 on: July 04, 2006, 12:13:56 AM »
And another simple example or couple might further help:
how goes the procedure for a Clove hitch?

 :)

DerekSmith

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Re: Overs Index - First example
« Reply #6 on: July 05, 2006, 11:54:25 AM »
Well, that's quite a batch of issues drawn out from just the first example.  Low fruit perhaps.  At this rate we should have the bones sorted out by the time we have worked over just a half dozen or so examples.

One issue which seems to be present in the background is the general fear that the OI will not be 100% accurate.  I see the OI as little more than the Dewey Decimal equivalent for knots with the added advantage that every knot carries with it its own 'signature' so to speak.  I don't feel too worried at this stage that it will be possible to 'count' certain knots differently, simply by relaxing them into different popular shapes.  Perhaps until we manage to rigorise the method a little more, we simply need to note that knot 'abc' is often counted as {OI-X,Y} but is also sometimes counted as {OI-X1,Y1}.  This way, whenever someone is looking for it with either of the possible OI's they would be able to find it in the WKI.

The OI is not Science, it is really nothing more than a signature by which to catalogue the knots.  Hopefully though, one day when we have catalogued the knots and we have some idea of the organisation of the beasts, we can start on the Science of knots.  What makes each one work and why.  What makes and destroys strength and by how much.  At least when we start on the Science, we will have a catalogue within which to record our findings.  Today though, our task is little more than that of a dusty librarian, finding all the knots and sorting them all out into their place in the library so that we, and others, will know where to find them.

This brings me to the issue of Crossings vs. Crossings plus Saturation.  The KISS principle will argue that if Crossings alone will do, then stop there, and I would have to agree with that argument.  However, there are a couple of BUT's we need to consider.

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.  H-L analysis is very promising but was in itself too complex as an indexing aid.  Nonetheless, it highlighted the essence that knots often varied in their 'saturation' and moreover, saturation was very easy to count once the knot had been laid out to count the Crossing Points.

If we see the world as 'All Possible Knots', then the categorisation of knots into working functionality such as Bends, Hitches, Loops etc., can be visualised as taking us to one of the continents.  In contrast, the Crossings Index could take us to a specific County and in conjunction with the Saturation we could be directed to a specific Town or City.  Then, final rationalisation by function could take us to the street, or family of knots, to which our knot belonged.

The 'Tree of Knots' then would be:-

Crossings Count
     Saturation
          Functionality
               Isomer (i.e. right 'D' or left 'L' mirror view)

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.

Dan made the point that the last change in priority a cord makes is in fact the last point that the cord makes any further contribution to the knot.  The last change in priority is the point at which the cord has left the knot and therefore this defines the last crossing point to be counted.  We can utilise this test for all of the ends simply by following the cord OUT of the knot for each end, then either physically or mentally 'cutting off' the cord beyond the last crossing point defined by the Saturation test.  The knot is now ready to be assessed for Crossing Points.

Any ambiguity with step 3  (STEP 3 :-  Count the Crossings being careful not to include extraneous Crossings where ends leave the knot.) can now be cleared up by writing in this test for the end of the knot.

Something like:-

Step 3.  Count the Crossings, using the "Saturation Endpoint Test" to accurately define the beginning and end of the knot.

"Saturation Endpoint Test"
This test is used to define the beginning and end of a knot for the purposes of counting the Crossing Index and the Saturation Index.

Repeat this test for every end entering/leaving the knot

Trace the end into the knot until the saturation count is 2.  Now retrace along the cord until the count goes back to 1.  This crossing point is defined as an end point.

or

Follow the cord into the knot.  If it maintains the saturation count of 1 over more than one crossing then these were 'extraneous crossings'.  Continue to follow the cord into the knot until the saturation count goes to 2.  The last crossing PRIOR to the count 2 crossing is then defined as the end of the knot and is the first/last crossing for that end.  Disregard the other crossings as extraneous.


The test is important, but I am not happy with either of these descriptions.  Can anyone offer clearer pros please.

DerekSmith

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Re: Overs Index - First example
« Reply #7 on: July 05, 2006, 02:13:04 PM »
......snip
Here I take issue:  as you've presented the knot, this is how it appears; but I submit
that the least-number-of-crossings form hasn't been given--it's the C-D tucked
through A-B qua Marlinespike Hitch form, which has but 6 crossings, and a saturation
index of 12 (!). (I.e., pull C-D ends apart to get this form.)

--dl*
====

Dan, I see your issue here as critical and as yet we have failed to address it on any of the levels in which it influences the generation of the OI.

The next example I am working on is the Carrick and in it I cover an equally important transformational issue, however, the example you make is one not so much of transformation, more, it is a case of DISLOCATION.

Make CD rigid in the undressed knot and the knot dislocates into the Marlinspike hitch which you interestingly categorised as {OI-6:12}  (I will hold you to that when we get to the MS hitch example).   Make AB rigid and the knot dislocates into a strange little slip/grip hitch (9:13 or 8:10).

Many other knots will of course dislocate under this treatment:-

Myrtle will decompose to the Constrictor, the Reef to the Larks Head and the Granny to the Clovehitch.  (I surmise that you 'play' with your knots much as I do).

First reaction to this brutalisation of a knot is that this is not relevant because you no longer have the knot of interest anymore.  However, before dismissing dislocation in this manner, we should perhaps consider any Pros that arise from the exercise.


Of significance, it could be argued that reducing the knot in this manner has the potential to minimise the risk of laying out the knot into a not fully rationalised form.  Indeed, perhaps two cord knots could better be catalogued by the pair of knots they reduce to when they are dislocated by making each cord rigid in turn.  Of course, this technique is also a useful to establish alternative methods of tying the knot.  Finally, we should consider the opportunity to use the dislocated form as a means of testing our knot identification (If you have knot XYZ, then it will dislocate into knot abc along cord XY etc.)

The Con for doing this however, is that not all knots dislocate into something simple, and laying out the resultant muddle can be even more uncertain than handling the parent knot - imagine doing this to a Fiador !!

The fact that we cannot apply this approach with any degree of constancy suggests to me that we should not adopt this rationalisation method as part of calculating the OI, rather, we should retain the knot in its 'essential form' - in this case the Bk,Blt in order to perform the OI calculation.

Having said this, we should not ignore the opportunities to use this additional means of assessment, nor should we ignore the warning that it is very easy to over rationalise a knot and that we perhaps need guidelines for this step a little more meaningful than "rationalise the knot into two dimensions"

Dan_Lehman

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Re: Overs Index - First example
« Reply #8 on: July 05, 2006, 07:17:20 PM »
Dan, I see your issue here as critical and as yet we have failed to address it
on any of the levels in which it influences the generation of the OI.
... the example you make is one not so much of transformation,
more, it is a case of DISLOCATION.
Well, dislocation sounds too subjective to me.  Going for the least number
of crossings will move one to distance the structure some measure from the
source; in the case of more complex, more thick knots, I think that this
will be overly problematic--i.e., where there might be a knot-depth of say 4
diameters, one could see apparent crossings well removed from actual
in-use contact, but hard to remove from a 2-D perspective w/o pushing
the affected strand(s) well away from their view-crossing.  Take a Dble.
Overhand stopper, e.g.:  one natural arrangement of that hides some
extra crossings; one has to rearrange it to get to the minimum.

Quote
Make CD rigid in the undressed knot and the knot dislocates into the Marlinspike hitch
which you interestingly categorised as {OI-6:12}  (I will hold you to that when we
get to the MS hitch example).
Make AB rigid and the knot dislocates into a strange little slip/grip hitch (9:13 or 8:10).
My emphasis:  I tried to apply the procedure; if I went wrong, can we discuss it now,
prior to any further example, as this is about a simple as it can get.  (And that MS H.
can be taken as a workable (bulk) stopper, a valid in rope knot, nothing rigid.)

Quote
First reaction to this brutalisation of a knot is that this is not relevant
because you no longer have the knot of interest anymore.
Again, this seems subjective to the point of rendering the process pointless.
As you have noted, the various things that can arise from the Sheet Bend/Bwl
orientation presented can quite alter the apparent physique of those two
knots (Eskimo Bwl, Lapp Bend, e.g.).  And somehow there is supposed to be
a judgement about this on the basis of excessive rearrangement?  That then
would seem to cast question on the initial layout--for that entails some particular
perspective/angle-of-view on the knot (which wouldn't concern us if the rules
demanded minimal representation re crossings, which I think is equal no matter
the start)!

--dl*
====

DerekSmith

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Re: Overs Index - First example
« Reply #9 on: July 06, 2006, 12:01:33 PM »

I tried to apply the procedure; if I went wrong, can we discuss it now,
prior to any further example, as this is about a simple as it can get.  (And that MS H.
can be taken as a workable (bulk) stopper, a valid in rope knot, nothing rigid.)

--dl*
====

No contention, we are in full agreement.

Take the Bk,Blt.  Apply tension to CD and allow the knot to dislocate, capsize, transform (- whatever word pleases) into the structure permitted with CD straight and you have :



The Marlinspike knot on CD.

Without question this has a crossings count of 6 and is fully saturated so {OI-6:12}

Quote from: knudgeNoggin
And another simple example or couple might further help:
how goes the procedure for a Clove hitch?

Treated the same way, take the Granny, {OI-6:12}



Tension CD and the knot will transform to create the Clove Hitch



There are four red/white crossings and two red/red crossings, total crossings = 6.
Saturation count for AB is 8 and the count for CD is four, total saturation count = 12

This makes the Clove hitch another 6:12 (it looks like it is going to be a popular group)

Doing the assessment this way (with CD as a tensioned cord instead of a stick or spar) makes it easier to see that both cords are part of the knot.  Without CD there is no knot, without AB there is no knot.  The knot only exists when both parts work one against the other, together they are the knot.  This is of course true even when CD is more rigid than a cord under tension - i.e. when it is a stick or spar etc.

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.

DerekSmith

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Re: Overs Index - First example
« Reply #10 on: July 07, 2006, 12:48:46 AM »
snip.....

Also, when I had previously tried "relaxing out" a Bowline, I didn't achieve the configuration in your pictures.  Instead, I ended up with something like the "relaxed out" Cowboy Bowline shown here: http://www.Layhands.com/Knots/Knots_KnotsIndex.htm#1034.5.  If I'm counting correctly, the relaxed out Cowboy Bowline has an OI of 7, just like your pictures do.  However, is it possible that different people will calculate a different OI for the same knot simply because they relaxed out the knots in different ways?

Dave


Dave,

I think this is definately going to be the case - as in Dans example of rationalising the Bk,Blt down to an MS Hitch on the cord CD.  However, if it is going to be possible to resolve such issues, then getting as many folks as possible to follow a number of examples, and for them to really try to 'get it wrong', then posting how their attempts went wrong, is going to be a fast track to at least finding all the warts.

Only when we have identified the warts do we stand a chance of developing a robust system.

DaveRoot

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Re: Overs Index - First example
« Reply #11 on: July 07, 2006, 03:52:58 PM »
STEP 1 :- Make a note of the function of each cord entering/leaving the knot for later refinement of the knot identification, then 'cut off' the extraneous connections leaving the knot in a forceless configuration.

STEP 2 :-  Open up and rationalise the knot into a two dimensional plane (special note for cylindrical knots).  Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count.  Attempt to achieve a situation where there is no more than two thicknesses of cord at any one point.

...

Step 3.  Count the Crossings, using the "Saturation Endpoint Test" to accurately define the beginning and end of the knot.

"Saturation Endpoint Test"
This test is used to define the beginning and end of a knot for the purposes of counting the Crossing Index and the Saturation Index. ...
The test is important, but I am not happy with either of these descriptions.  Can anyone offer clearer pros please.

It occurs to me that there are several categories of people who might make use of the WIK.  Based on the number of people who tend to contribute to various knots forums, the smallest category consists of those who enjoy studying, dissecting, testing, exploring (etc.) knots.  A larger category consists of those who frequently use knots in their professions or hobbies, and who would like to know the best knots for various applications, but who have neither the time nor the desire to study, dissect, test, explore (etc.) knots.  But by far the largest category consists of all of the "everypersons" out there who perhaps have learned a knot or two along the way, such as the Shoelace Knot and the Reef (Square) Knot.  So when I think about the Overs Index and the WIK in general, I occasionally try to step back and put myself into the mind of some next-door-neighbor.  If he knows nothing about knots, but he is looking for some information, how will he react to the Overs Index?  Will it be user-friendly or will it put him off by its complexity and vocabulary and so on?

Okay, so trying to apply the "neighbor test" to some of the good ideas which have been posted so far, here are some thoughts:

Step 1 (from Derek's quote above) - I'll get to this in a moment.

Step 2 - I would suggest that we remove the statement, "Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count."  For one thing, a knot aficionado might recognize some "meaningless twists," but our next-door-neighbor is not likely to know which twists are meaningful and which are meaningless.  In addition, finding the "simplest form giving the lowest Crossings count" might cause problems for our neighbor because he doesn't have much experience with knots to be able to recognize the simplest form, plus at this point he has not yet read Step 3 and doesn't know how to determine the lowest Crossings count.

Step 3 - Imagine that our neighbor has relaxed out a Bowline as in the picture below, and the Standing Part (end #1 in the picture) has fallen across the open loop marked A.  To us it seems fairly obvious that the Standing Part does not "belong" in that configuration because it "should" exit the knot and continue heading due north, but to our neighbor any configuration seems just as valid as any other configuration.



My purpose for draping the Standing Part across loop A is to illustrate a possible way of describing how to find the first true Crossing Point:

-- Starting with one end of the rope, follow the rope into the knot and record the sequence of "overs" and "unders" (i.e. where the rope goes over or under another strand of rope) until you no longer have any duplicates.  For example, following end #1 gives us this sequence: over-over-over-under.  We have 3 duplicates of "over," and we stop when we reach a non-duplicate (the "under").

-- Do the same with the other end of the rope (end #2), which gives us this sequence: under-under-over.

-- Cross out the initial duplicates for both ends:
   end #1: over-over over-under
   end #2: under under-over

-- Adjust the knot in order to get rid of the crossed-out Crossing Points:



-- Now the knot is ready for the Crossing Points and saturation to be calculated.  It should be noted that any remaining duplicate Crossing Points (i.e. within the knot), such as over-over-under, are acceptable.


This procedure appears to be a simple, step-by-step method for eliminating extraneous Crossing Points, and if it passes scrutiny then it can be word-smithed in order to make it as clear and generalized as possible.

Now let's look at Derek's Step 1, using my second picture (above) for illustration.  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.  Sure, they can probably recognize that the Bowline's loop needs to be mentally cut off (loop C in the above picture), but the picture also shows a loop A and a loop B after the Bowline was relaxed out.  I can just hear people thinking, "If this loop (C) needs to be cut off, then I guess I'm supposed to cut off the other 2 loops as well (A and B)."  Knot aficionados can "see" where forces and nipping and gripping and binding and friction will come into play in my second picture above, but most people will just see 3 loops.  It's likely that some people will treat all 3 loops identically, and will mentally cut off all 3 loops and end up with a very inaccurate saturation.

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?

Dave

Dan_Lehman

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Re: Overs Index - First example
« Reply #12 on: July 07, 2006, 05:27:08 PM »
Treated the same way, take the Granny, {OI-6:12}



Tension CD and the knot will transform to create the Clove Hitch
Hmmm, but if one orients end D to exit parallel & between ends A/B, one
has preserved the OI but diminished the SI (OI 6:10).

--dl*
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DerekSmith

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Re: Overs Index - First example
« Reply #13 on: July 07, 2006, 11:58:14 PM »

Hmmm, but if one orients end D to exit parallel & between ends A/B, one
has preserved the OI but diminished the SI (OI 6:10).

--dl*
====

Hmmmm --

I start to feel the will to live  --  sapping away.

DerekSmith

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Re: Overs Index - First example
« Reply #14 on: July 08, 2006, 12:13:39 AM »

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?

Dave


Dave, I like your rationalisation for determining the begining and end of the knot.  We need to include this in the method.

I do not feel so inclined towards leaving components external to the knot in place during counting.  However, the second example from me is going to be the Carrick which has some new issues and leans heavily towards counting the knot 'In Use' rather in its 'purist' form.

One thing we should remember though, is that if someone is using the OI to find info on a knot, then they already have an example of the knot to hand, including the external parts.  This means that there will be no reason for them to confuse these external parts with loops from within the knot.  They can put a tape on the external parts to simulate an end, then open out the knot for counting and safely treat real ends and pretend ends in the correct manner.