Overs Index - review of Lessons Learned from Example 1

General Discussion
1

While the issues raised in OI Example 1 continue to be chewed over in ever increasing detail, it is perhaps appropriate to consider a review what we have potentially learned from that example.

Rationalisation

The initial terminology used was “Rationalise the knot to remove extraneous crossings and to achieve the lowest crossings count”. Dan demonstrated that this can be taken to absurdity, because many knots can be transmuted between different knot forms. The intention of the initial statement was to eliminate obvious ‘non knot’ crossings in our attempts to create an 2D layout from a 3D knot. The result we observed was that if you under rationalised you finished up with extraneous crossings - nothing to do with the knot, simply artifacts of our 3D to 2D manipulations. Alternatively, if we over rationalised we could finish up either transmuting the knot into some other knot or distorting the geometry away from the working geometry of the knot. While it is simplicity itself to transmute the Bwl. into the MS hitch, these are clearly totally different knots with abjectly different functionality.

Conclusion:- We have shown that rationalisation requires an understanding of the function of the knot and a perception of the role of individual elements within a knot. We have not been able to encapsulate this understanding and perception into a simple rule or guide. We will need to continue to work through examples to develop a consensus approach.

Using Knot Zero

This concept was established in an attempt to clean away the numerous variants that can be created by loading / connecting a knots inputs in different ways. It was assumed that by establishing the ‘essential knot’ the user could identify rapidly the basic family of knots they were dealing with. This has turned into a significant distraction, loosing sight of the purpose of the Overs Index, which is to enable a user to identify a knot found ‘in the field’. In reality, the ‘Zero knot’ will never be found ‘in the field’ because it is a knot without function.

In use, most knots change their internal structures in response to the forces applied. Only a few knots stubbornly resist changing their shape when required to ship forces through different inputs. The Zero knot does not reflect this restructuring in use and is therefore of little value in identifying the knot of interest, which will likely have transmuted its internal structure to reflect its use.

Conclusion:- We will need to consider cataloguing knots based on their structure IN USE as the primary categorisation. The theoretical ‘Zero knot’ is secondary to this category.

Ends Rule / Multistrand knots

In an attempt to formalise and simplify the identification of where a knot starts and ends, the observation was made that when a cord exits past multiple strands of the same priority, that only the first cord has any function. The ‘Ends Rule’ was based on that observation. The examples considered in the exercise have shown that all parallel, multi-cord knots violate that observation and a few single cord knots likewise do not comply. It is self evident that in a knot tied with a double cord, both cords are functional and that the ‘Ends Rule’ in its current form is wrong.

Conclusion:- We do not have a simple definition of the end of a knot for counting purposes. The ‘Ends Rule’ can be used as a guide but it does not apply to double/treble etc. cords and the final determination of the ends of the knot must be based on a rational assessment of the functionality of the cords in question.

Man in the Street

It was felt that the method for counting the Overs Index should be clear and unambiguous. To this end it was targeted that the method should be usable by the man in the street with no specific knot knowledge of knots or training. It has been demonstrated that even amongst individuals with considerable experience tying, using and analysing knots, there is the opportunity for disparity in calculating the Overs Index and that with our current state of understanding of the field of classification, it is expected that at least until the index has been created, there is little chance of assessments being carried out meaningfully by an untrained ‘person in the street’.

Conclusion:- The IGKT, through this forum, should continue to assess a number of examples until consensus has been reached on the method and the results. The Overs Index should be built using values which have been posted onto the IGKT forum for scrutiny by members - i.e. Peer Review. Finally, it should be a long term goal to establish an OI Assessment Training Package which can be trailed on key knot user groups such as scouts etc. before being made available to the public, schools etc.

Participation

The first example has been worked through by just three people. It would make the process more robust if additional members could be encouraged to participate in the formation of a voluntary Peer Review Group. Ideas on how to promote such a group from the active members of the forum could be progressed via the forum.

It all feels a bit like three steps forward, two steps back, but at least its progress ??

2

Progress is often achieved by finding and eliminating the wrong paths in order to discern the right path, so we’re definitely making progress!

Dave

3

If you want the man next door to understand the system you will need to simplify it.
I have been reading all the post in this forum, and I still have great difficulty understanding what is ment.
If I read things like fully saturated, cutting ends, opening up, nub of the knot and fully saturated at 6:12, I think that it is not likely going to be the man next door who will be able to use the system to find which knot he holds in his hands.
As it is now it looks like it is going to be a system for the specialists. If that is your aim it is not bad at all.

Willeke

4

That’s your take on it: mine is that I showed that counting crossings
even for seemingly simple structures is not so simple, and that forcing a
2D perspective on a 3D object in problematic. I’m skeptical that this crossings
counting can lead to productive classification. Topology does this, by some
means; there are tables of knots given by crossings. In History & Science
of Knots, p.274, Fig.3 shows “Part of Tait’s Table of the Ten-crossing
Alternating Knots (1885)”–“part”, in that the full count was 166 such knots!!
But, then, in “1979, nearly a century later, … using modern topological
invariants, [it was shown] that two of these knots are the same …” !!

Do you want the Eskimo Bwl & Lapp Bend & Sheet Bend & Becket Hitch
& Bowline & “T-bend” to all be found together by the classification method?
There is some significant difference in geometry among these, but then
there is some subjective assessment re that, too. And they cover the classes
of bends & loopknots.

Conclusion:- We have shown that rationalisation requires an understanding of the function of the knot and a perception of the role of individual elements within a knot. We have not been able to encapsulate this understanding and perception into a simple rule or guide. ... Conclusion:- We will need to consider cataloguing knots based on their structure IN USE as the primary categorisation.

For the purposes more of the EveryOne, my judgement is that crossing-counting
will be overly problematic; it will be more easy to assess geometry and component
features (such as the “gooseneck” of the Bowline, or an Overhand component of the
Overhand loopknot or Shakehands loopknot), and maybe also overall knot aspects
(such as trace knots–such as the Overhand & Fig.8 & Fig.9 “re-woven”/“in the
bight” families). Topologically, I can finagle a Fig.8 to look much bowlinesque, with
a nice loopy nipper, & collar. Crossings-wise, who knows where that ends up;
geometry-wise, well, there is some matter to debate, but maybe some principles
to be established for that–more in line wtih WhatYouSeeIsWhatYouGet.

–dl*

5

Dan,

It’s taken me a little while to fathom your writing style.

I now read your posts three times before allowing myself to consider a reply.

First read - .!!$&* - I see you as a grumpy old bugger with nothing better to do than wind me up.

Second read - I see that you are agreeing with me, just putting your reply in tormentative, wind up manner.

Third read - now I start to get a glimpse of where you might be leading me.
As a consequence of this little bit of self control, I have to say that I agree with most of the points you make.

I'm skeptical that this crossings counting can lead to productive classification.

I even feel this way occasionally as well. As for:-

Do you want the Eskimo Bwl & Lapp Bend & Sheet Bend & Becket Hitch & Bowline & "T-bend" to all be found together by the classification method?

Well, I find that I cannot answer that question, because I do not know what a T-bend is. If however it is a Bk,Blt then yes, if the Overs Index could reliably put these knots into the same classification, I would be well happy - they are after all simply different utilisations of the same knot – so where else would you expect to find them but snugged up next to one another.

Even -

There is some significant difference in geometry among these
It triggered an initial Bol****s, but by the time of the third read through, again I am in agreement that the Bk,Blt is a nasty knot for shape changing under tension and that different usage configurations lead to different usage geometries.

Likewise, I also do not think the OI will be a tool for the EveryOne, but even if we do not succeed in making a tool to service the needs of the EveryOne, at least we can strive for a tool that knottists can use which will be better than the miasma we have today.

And then you catch my attention !!

it will be more easy to assess geometry and component
features (such as the “gooseneck” of the Bowline,

OK, Show me !! Take the Bk,Blt of the first OI example. Show me how to catalogue its 30 odd variants using geometry and component features. I don’t understand what your subsequent words mean so please show me more clearly in a manner that I can apply. If you can help me understand, then we can put this method of cataloguing into the WIK together with a method of how to do the assessment so that perhaps the EveryOne can find her knot (or maybe even geometry won’t be ‘that’ good)

The Wiki can use any criterion you index under, to find a match - Ashley name, number, AKA names, OI, Usage group (bend, loop etc), Used for, used by, geometry - etc. etc. If you can quantify it and have recorded it, then the Wiki will let you search for it.

So, how about you post a First example of - geometric classification of a knot. A knot wears its name in its geometry - how do you say its name?

6

It’s a supposed attachment of a line to another, mid-span, so to speak; the attached line makes
the bight part and the other line forms the gooseneck mid-line to receive that bight.
(It is more stable if one forms a bight collar on both sides of the mid-line loop.)
–have only seen this mentioned in CWarner’s A Fresh Approach to Knotting & Ropework.

There is some significant difference in geometry among these
It triggered an initial Bol****s, but by the time of the third read through, again I am in agreement that the Bk,Blt is a nasty knot for shape changing under tension and that different usage configurations lead to different usage geometries.
Odd reaction, and to what you must have known, anyway. What most bothers me, of the changes, is the Lapp Bend's hauling of what would be one of the Sheet Bend's SParts back sharply (as here it's an end). And yet even this is less distortion to the [i]nub/knot[/i] than what topological manipulation will do to a Bowline--though for that, it's required to connect the knot's ends in some way. Ashley's Stopper is one knot that can be topo-fiddled from the Bwl.
And then you catch my attention !!
it will be more easy to assess geometry and component features (such as the "gooseneck" of the Bowline,

OK, Show me !! Take the Bk,Blt of the first OI example. Show me how to catalogue its 30 odd variants using geometry and component features. I don’t understand what your subsequent words mean so please show me more clearly in a manner that I can apply.

But this geometry (shape)-based method will give a different sort of classification.
I.e., it won’t take the bight-loop knot-nub (I’m thinking that maybe the term tangle
might work well for this afunctional view of the structure?!) and unite all manner of functional
knots that arise from it, but rather will group together those knots that resemble it geometrically,
which implies functionally, and which shows that more than the tangle is the classification guide.

A paradigm for my thinking is the Bowline, whose essence I regard as its central nipping loop
–the so-called “gooseneck”. That DoubleCross loopknot from Dave also has such a structure,
and the end reenters this loop on the same side as for the Bowline, so I might put them together.
“Anti-Bowline” knots I see (in the sense of “anticyclone” “anti”) as similar but with the end entering
from the opposite side, as for the “Bollard loop” of issue a few KMs ago. And all these (loopknots)
stand in contrast to e.g. the trace knots Overhand & Fig.8 loopknots, and various Overhand-based
knots, among others. Although for the bowlines & antibowlines there is some issue with the very
loop that characterizes them: by degrees of dressing/setting and tension, it can deform into
more of a spiral (the Bowline can e.g. capsize into a sort of dog-leg S & Pile Hitch’d end).

And, yes, there is much subjectivity in such discriminations. --much like biological classification!?
And there are all sorts of challenging combinations of knot characteristics to sort out.
(What does one do with the feathered animal with mammary glands and an exoskeleton?
–besides send it back to Australia! ;D )

–dl*

7

Thanks Dan, if I understand the explanation correctly then is it this knot with the attached line on either C or D.

http://igkt.pbwiki.com/f/T-bend-sml.gif

If this is indeed the T-Bend, then to answer your question, yes I would be happy when the OI put this knot into the Bk,Blt category. Then as the method points out, the actual function of the attached lines is then used to identify the specific knot. In this case, it would lead the searcher to the bends table. I had made the point that load could be applied to any of the unallocated ends, but as I was not aware of the T-Bend, I had not included it in the table ( it’s in the table now).

There is a tendency for this knot to spill into this when the tension on A B is great against the tension on C or D.

http://igkt.pbwiki.com/f/T-bend-tension-sml.gif

How would the geometry system describe these new shapes?

As an asside, the ‘Clamp-Bowline’ I posted here makes a good inline attachment and it looks like the strength might be quite good too.

Derek

8

Yes, that’s it (you’ve Cowboy’d/Dutch’d/Left-hand’d the orientation). And
one could make a 2nd collar with the end around the other end of the red
line, to thwart the capsizing you go on to show (which is something possible
for the Bowline, too). I’m not sure about the heritage of this knot, any uses, etc..

There is a tendency for this knot to spill into this ...
No, "[i]capsize[/i]"; "spill" and it's unknotted rope(s) (or unjoined formerly knotted-together ropes for some knots that might leave a reminder knot). "[i]capsize and spill[/i]" is to be a useful, not redundant, expression, you see.
How would the geometry system describe these new shapes?
This transformation of the Bowline has bothered me re classifying. You see my idea of what [i]a **bowline**[/i] is depends upon there being a nipping loop in the SPart. This loop I once saw as a half-hitch, but even if dressed and set to be, in some materials under tension it can shift into a round turn, and even further, into a [i]spiral[/i]!? --what to do? And there might be the case that the last form is exactly what's intended (I have designed such knots, thinking that the spiraling part would be strong, gradually off-loading force w/o any sudden/hard turn). Another bowline transformation arises where setting can change the loop into more of a Crossing-knot shape--e.g., #1033, a so-named "Carrick Loop" is this way, with the eye leg on the left as drawn being able to be pulled sharply back if the end's snugged). And there's really no obvious line between having the loop and going beyond that into a spiral!

So, it’s a problem to be addressed somehow. (Another case: one can
push the double turn of the Dbl.Bwl (aka “Round-turn Bwl”) into a nice
spiral–it can change geometry a lot, yielding a quite mild spiral
(tested this ages back in 0.25" laid nylon to 67%?, break apparently
coming amid spiral part). Obviously, topologically but not, er,
topographically, they’re identical.

I think one might just recognize the connection between the two,
but have the extreme forms in presumably separate groups.

A bit father in transformation of that loop → spiral → line (straight) and
you have a (white) Pile Hitch locked onto your (red) line.

–dl*

9

Hi 3D (Derek, Dan and Dave),

You have all been struggling with “what-ifs” to the extent that you now are trying deliberately to rationalise something in a radically different form by cutting off parts, rearranging loops and twists and generally changing a 3D object into a Klein bottle. For a moment, consider the octopus - it always has eight arms, unless one or more have been lost in combat - even so it is still an octopus, because it originally had eight. Yet the octopus is able to change shape and move into seemingly impossibly small volumes simply by manipulating its body, and yet it is still an octopus. Now, that IS a different thing than you are struggling with, but to the MND (Man Next Door) the octopus and the knot (whichever one is being considered) can be described by considering it in it’s “normal” form, the form inwhich it is most readily recognized. How does that observation help? By recognizing that, as clever manipulators of manila, we are able to make all kinds of weird shapes and forms of the familiar bowline, half hitch or whatever, but when we come to use it in its “normal” form, we should be able to describe its essential form in words and pictures, be they drafted or photographed and then manipulated. I recognize that recognizing the essential form is no revelation for you all, but for the MND it is so obvious that we may be flogging a dead horse for him. If we as clever curlers of cord can make awkward and weird shapes with our knots, so be it. We are definitely cleverer than the average Joe in that respect, but so what? We are no closer to describing the simple functional “normal” shape of such a knot for the MND. How does it look when it is in use - unloaded, but ready for action, tightened, but not strangled?

The OI has some dreaded weirdness to it and may be eventually solved for the clever kinker of cords, but it will never catch on with the MND because it is too darn complex! You are all right that, with some cords the bwl can capsize or wriggle into a different shape. How does that help to solve the OI complex? If it has changed I would respectfully submit that it is now different and should be returned to its “normal” shape before trying to classify it. We do not consider frappe’d worm as a viable organism for anything other than garden mulch or Fear Factor fodder (TV show - sorry). Is it still a worm when it is tied into a knot? Yes, but that is not its “normal” appearance, although somewhat entertaining, depending on your point of view. In the same way, a knot that has been frappe’d or twisted into unrecognizable form is no longer viable as a knot, but has taken a form perhaps radically different than its own and therefore no longer functional as an original knot. You can no more use the frappe’d version of the worm to describe it as an earthworm than you can use the frappe’d version of a bwl or any other knot to describe that knot in the frappe’d version. We have to have the knot in its “normal” functional form.

I know that you will likely take issue with this line of reasoning, so have at it and I will attempt to clarify. For me, gentlemen, you are flogging a dead horse and your efforts could be used more usefully elsewhere. Just my two cents’ worth…

SR

10

Jeez SR, you’re damn right I will take issue. I have a hard enough time as it is trying to justify my “meaningless” - “worthless” - “unproductive” - “time wasting” hobby, but if my good lady sees a fellow knotter (yes, she occasionally reads this forum) saying that my efforts could be used more usefully elsewhere, then I will be stuck on decorating duty for the foreseeable future. Remember, ‘Idle words cost lives’ - or at least in this case - my liberty !!!

As for the rest of your post, well I have to agree with most of it. We are splashing around in a large muddy place with little idea of any reference points. We are exploring certain aspects seemingly to absurdity. We know what we want to achieve, yet each time we explore a ‘simple’ solution it gets crazy complex the moment you test it with the real world of knots.

The goal is to be given a knot and to be able to ‘read’ its various signatures, then look these up in the Wiki Index of Knots (WIK) and hopefully find a single knot or at worst a small handful of knots, from which we can match the one we were given. Behind this of course, once we have found our knot, would be a feast of information relating to the use, formation, history, strengths, weaknesses etc. etc. of the knot. As I have said before, I think that we have probably set our sights too high by going for the MND as our target audience. To begin with, while we find out where the sensible edges are to this swamp, I believe we will have to limit the usage to ourselves - though even that is a big challenge.

One thing is for sure though, we can all too easily make the problem harder than it needs be.

We can distort a knot until it is transmuted into a totally different beast, yet still try to call it by its tied name.
We can confuse ourselves by taking into consideration what a knot is being used for or even by how we have tied it.
We can even add confusion by worrying over the material (thickness, stiffness, substance) that the knot has been made with.

Yes we seem to be going round in circles, but hopefully each circuit brings perception and offers the chance of nailing a little bit of clarity into place. Early chemists will have wondered at the seeming infinite complexity of ‘stuff’, but they stuck at it and we can now read the name that every compound carries within itself. I am sure the same must be possible for knots and I am reasonably sure that reading a knot will be a lot easier than reading a chemical compound (a knot after all is much much bigger than a molecule).

You may well be right and there might not be a means of attaining this goal - but please - for the sake of my obsessive, compulsive disorder - please don’t utter those terrible words again.

Derek

11

Hi Derek,

Duly noted (with a wry chuckle!) and I’ll try to hold it in better check ;D. Thanks!

SR

12

Ah, but in fact what is before us (say) to classify is exactly one of these “abnormal” versions
of the Bwl–what then, where does IT go?! My sense of the OI is that it purported to be a sort
of hashing that would objectively slot a knot; one would though often find the slotting not
to a unique position but amongst others, for which some sort of further sorting out is needed.
The geometric approach I’ve sketched is more in line with your WhatYouSeeIsWhatYouGot
feelings; but it depends on quite subjective assessments from the start, and one can see
some cases that are problematic.

The OI will group things that are not normally associated, I think; the Geometric classifying
will struggle to define such associations, using some kind of Group Think to discriminate
various classes & subgroupings (possibly to be revised over time & reconsideration), which
I think is not so unlike biological classification (whether some bird represents a truely new,
distinct species, e.g.).

The case I put of #1033 is quite to the point: it’s reasonable IMO to see groups of loopknots
based on resp. central nipping Bowlinesque loop, overhand, or Crossing-knot, among other
structures. But #1033 can, depending upon dressing/setting, fall into either of the first/last
groups here. What to do? This isn’t a case of deliberate distortion for the sake of testing
some classification method for strength, etc., but an example of the sorts of real cases
a good system must anticipate.

Derek adds:

We can distort a knot until it is transmuted into a totally different beast, yet still try to call it by its tied name.

This discussion has led me to like the term “tangle” for denoting the set of things
a “knot” can be manipulated into, perhaps with the constraint that all “ends” are to be
considered tied off at some remove from the structure–which distinguishes such
manipulations from topological ones, which would require that first the structure
be made into an endless loop (or couple?).

–dl*

ps: As for “manipulaters of manila”, that is “sooooo yesterday” !! --have just liberated
some play ropes of polycombo & coex from recording (holding) “new” knots, myself.

13

Hi Dan,

Your response was as thoughtful as ever and coming not a moment too soon. It seems to me that you speak of the OI as being the Holy Grail in some respects, thereby attempting some kind of “force-fit” into a classification system, just to see if it would work. You are correct that there may be some problem areas of WYSIWYG but life is like that - sometimes you get one or two curve balls and it is up to the system devised to be robust enough to either withstand and classify those oddballs or you make one or two special cases or the system does not work for many more cases and must be rejected - the search would go on unabated. I would not attempt to challenge you to come up with as many objections on the grounds of WYSIWYG as have been seen by you and others for the OI, but I believe that you can see there appear to be many, many more cases of “how does this fit?” with the OI, than there have been of “this is (simply) how to do it and this is what it looks like.” How about looking at simple structures (such as a loop, a knotted loop, a tuck, turn, etc) for a signpost to where classification may be simplified and then work through the myriad different postures that involve putting a “knot” (i.e. a tangle) into different thicknesses, types of line, line construction forms, wet/dry, open/closed loops, etc. may give? Maybe the same energy level could address such a system and then compare the two (OI & WYSIWYG or any other system) to see which is most readily understood, by democratic fiat if necessary (I don’t mean democratic fiat, so ignore it).

Maybe manipulators of manila is sooooo yeaterday, but it too has its place - and one of these days, the oil will give out and where will we be then? That’s another day… Perhaps victors of vectran, or knotters of kevlar or whatever… I think I could come up with a list of structures that would start the ball rolling, provided you all thought it worthwhile. However, if you are he-double-hockey-sticks-bent on the OI, then I shall merely sit back and try not to encourage it. I could be wrong, but I’m willing to take that chance. ;D

SR

14

I (and no doubt Derek!) would very much like for you to quote me where I in any even subtle
way spoke thusly! ??? --or have you confused your "D"s? Re the OI, I think that
even D-erek has some d-oubt about its efficacy, and he’s given it much effort to work.

You are correct that there may be some problem areas of WYSIWYG ...

Another situation that sometimes bothers me is that an aspect of a knot such as having
an Overhand base can seem merely incidental to its essence–that one might seek
to improve it by making a slight re-positioning of a part (to soften the SPart’s curve, e.g.),
and get a quite lookalike derivative, but, by golly, having lost the Overhand in the process
(and now have a Marlinespike H. form instead)! --and this cognate knot gets sent out
of this class down the hall to another, by that measure. Maybe it’s no big deal–shrug.

A term I came across recently led me to wonder at its worth in considerations of
knot classification: “derivational paradigm”–linguistics term (which at times I think
should be “derivation” but that’s another issue of meaning(s) for "-al’ adjectives).
That certain types of knots will lend themselves to certain derivations, to ways of
e.g. “doubling”. A Bwl is doubled by repeating the loop part; an Overhand
is doubled by (in one tying method) making an overwrap before tucking the
end–and tripled by making another. !? And whether a knot shares such
derivational paradigms might be a qualifier for class membership?!

–dl*

15

Yay Dan!

Thanks for the response.

I (and no doubt Derek!) would very much like for you to quote me where I in any even subtle way spoke thusly! --or have you confused your "D"s? Re the OI, I think that even D-erek has some d-oubt about its efficacy, and he's given it much effort to work.

Well, I know I can’t and you know I can’t, which is why I said it seems to me - it is an illusion, based on no factual front (otherwise I could have quoted it) other than a feeling (hence it seems). No matter - it raises questions in an ongoing conversation, which hopefully will enlighten all eventually.

Re: the overhand knot - I’m wondering, what about the OH being used as the base for the Barrel sling or used as the base for the Ocean Plait? I would maintain that, once it has changed from its original form, it is a different knot. The MND sees that and the kid down the street sees it, so why would we worry? It is good for teachers to recognize that different forms exist, because that can be used to free the student from worrying about remembering all the knots, if they can only remember a few structures. We seem to be (careful with that one SR!) in agreement that knots need a description that will fit many forms - by starting with simple structures and a defined appearance when finished, taut but not so overtight that it appears to be a person struggling to get into a corset Yes, the OI is ONE signpost but not the ONLY signpost, so let’s not worry ourselves silly about its shortcomings (why don’t all people named Dan look the same?) but rather revel in its abilities and let another measure allow for further description (Dan who ties knots and has an amazing mind), even if it is incomplete? In the English language we enjoy many different words for what is described in some other languages by one or two words. That is the richness of our language. I suspect that the language of knots is equally diverse and interesting, made up over thousands of years to arrive at today’s miasma of “descriptions,” their names.

Do please explain some more about how derivation(al) paradigm fits in here? I know nothing of the subject of DP and would like to understand what you interpret here? Thanks again Dan!

SR