International Guild of Knot Tyers Forum

General => Chit Chat => Topic started by: DerekSmith on July 02, 2006, 05:01:14 PM

Title: Overs Index - First example
Post by: DerekSmith 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 --

(http://igkt.pbwiki.com/f/Bk-Blt03-sml.gif)

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 (http://igkt.pbwiki.com/Table) (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.

(http://igkt.pbwiki.com/f/Bk-Blt01-sml.gif)

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;

(http://igkt.pbwiki.com/f/Bk-Blt04-sml.gif)

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
Title: Re: Overs Index - First example
Post by: Dan_Lehman 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*
====
Title: Re: Overs Index - First example
Post by: DaveRoot 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
Title: Re: Overs Index - First example
Post by: Dan_Lehman 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*
====
Title: Re: Overs Index - First example
Post by: DaveRoot 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
Title: Re: Overs Index - First example
Post by: knudeNoggin 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?

 :)
Title: Re: Overs Index - First example
Post by: DerekSmith 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.
Title: Re: Overs Index - First example
Post by: DerekSmith 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"
Title: Re: Overs Index - First example
Post by: Dan_Lehman 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*
====
Title: Re: Overs Index - First example
Post by: DerekSmith 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 :

(http://igkt.pbwiki.com/f/M-Spike-sml.gif)

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}

(http://igkt.pbwiki.com/f/Granny-sml.gif)

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

(http://igkt.pbwiki.com/f/Clove-H-sml.gif)

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.
Title: Re: Overs Index - First example
Post by: DerekSmith 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.
Title: Re: Overs Index - First example
Post by: DaveRoot 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.

(http://www.layhands.com/knots/forum1.jpg)

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:

(http://www.layhands.com/knots/forum2.jpg)

-- 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
Title: Re: Overs Index - First example
Post by: Dan_Lehman on July 07, 2006, 05:27:08 PM
Treated the same way, take the Granny, {OI-6:12}

(http://igkt.pbwiki.com/f/Granny-sml.gif)

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*
====
Title: Re: Overs Index - First example
Post by: DerekSmith 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.
Title: Re: Overs Index - First example
Post by: DerekSmith 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.

Title: Re: Overs Index - First example
Post by: Dan_Lehman on July 08, 2006, 07:01:02 AM
... 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*
====
Title: Re: Overs Index - First example
Post by: DerekSmith on July 09, 2006, 04:47:40 PM
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:-

(http://igkt.pbwiki.com/f/Jug-hitch-edge.gif)

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

(http://igkt.pbwiki.com/f/Jug-hitch-overs.gif)

The big issue looming is - should a knot be counted in its 'in use' configuration?  The next example really brings this home.
Title: Re: Overs Index - First example
Post by: DerekSmith on July 09, 2006, 05:27:46 PM

(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.
Title: Re: Overs Index - First example
Post by: DaveRoot on July 09, 2006, 06:29:17 PM
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
Title: Re: Overs Index - First example
Post by: DerekSmith on July 09, 2006, 07:43:52 PM
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.
Title: Re: Overs Index - First example
Post by: DaveRoot on July 10, 2006, 04:10:16 AM
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
Title: Re: Overs Index - First example
Post by: DaveRoot on July 10, 2006, 02:31:59 PM
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
Title: Re: Overs Index - First example
Post by: squarerigger on July 10, 2006, 03:32:44 PM
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... ;D

SR
Title: Re: Overs Index - First example
Post by: DerekSmith on July 11, 2006, 10:36:27 AM
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... ;D

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.
Title: Re: Overs Index - First example
Post by: DerekSmith on July 11, 2006, 01:21:17 PM
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.

(http://igkt.pbwiki.com/f/Bwl%20on%20Bght%20sml.jpg)

'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.

(http://igkt.pbwiki.com/f/Bwl-on-Bght-free-sml.gif)

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.
Title: Re: Overs Index - First example
Post by: DaveRoot on July 11, 2006, 05:56:55 PM
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:

(http://www.layhands.com/knots/forum2.jpg)

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
Title: Re: Overs Index - First example
Post by: DaveRoot on July 12, 2006, 05:24:44 PM
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

Title: Re: Overs Index - First example
Post by: DerekSmith on July 12, 2006, 07:07:23 PM
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.