TENTATIVE DEFINING OF "KNOT"

General Discussion
41
In my mind: structure imply without loading : [i]laid flat on an horizontal plane , no dressing, no setting[/i] As soon loading is ( or even dressing and setting ) at play that is "physiology" not anymore basic "anatomy"
But this really isn't quite so, for you implicitly involve loading.
Why an opposite sheet bend : your first post ( under as quote) did not specify and you agreed on the picture I sent. Where do you specify "the short leg, side, of the bight ?
I specified the labelling of knot-limbs, and the loading (A-D) for the Sheet bend. Now, what is "the short leg of the bight"? IT IS AN IMPLICIT INDICATION OF [I]LOADING[/I]! ::) (Knots aren't really defined by relative lengths: one can easily join two ropes with a Sheet Bend such that the SParts are shorter than the ends.)

This is the distinction I’ve been driving at, that there is a general view of the knot in
which loading is removed and so equivalences at this generalized level can be found
with other knots–how we can say that the Sheet Bend & Bwl have the same structure,
or maybe we need some other term. But I believe that we DO want to at times view
knots at this level of generalization.

If you put that same "tangle" (math) in one rope instead of in two as in sheet bend then you get the bowline and that is another structure. "one hole" more, which is a decidedly important topological criterion and "real life" difference for using.
Hmmm, I'm unsure about how the legs of a loopknot (or the span between the [i]tangled[/i] parts of the Sheepshank) fit in the scheme of things. Dick Chisholm has defined "nub" to denote the tangled part of a knot, but this has seemed redundant of "knot", to me, who I guess must view "extremities" as beyond the "knot" proper.
sheet/bwl are not same structure : no way you can , using only Reidemester's move ( contrary to what can be done with you pet ABOK#525 and Fig-Nine), you cannot go from one to the other.
But you see, in the way [b]I[/b] was thinking of [i]structure[/i], there is no "move" needed, just a change of what is regarded as loaded (and in what degree, or how things are externally connected). (And, as for moving the Tweenie into the asymmetric form similar to the Stevedore, I see much less likeness of "structure" there; I've not tried to figure out crossings profiles of them.) One will hear people utter that the Sheet Bend and Bwl have the same structure, or same ... --well, what should it be called?
Laying down my king, board is yours. Cheers.
Can I accept this, with only a knight?

–dl*

42

I’m not going to defend that statement for two reasons. First, I advanced it as the starting point of a different way to look at “sameness” more than a studied conclusion.
Secondly, after reading this thread and thinking more about it, I don’t think it is a good definition.

To answer your question, at the time I would have said that an OH knot is the same as an UH knot. (Actualy I was thinking of the Sheet Bend and Becket Bends at the time.)

My current thinking starts from the point that “sameness” in knots depends on how one thinks about them. When working back stage, I frequently run into the situation where THIS knot holds up the back drop and THAT knot holds up the lights. But even though both this and that knot would have the same ABOK number, it is important that I recognize them as “not the same”.

On a different level, as I mentioned before, seeing a 3-strand Matthew Walker and a 4-strand MWK as the same is valuable at times.

My current thinking is that, given two knots A and B, consider the set {A,B}. The various relationships that {A,B} has to the rest of knotting are more important that how many elements there are in {A,B}. Those relationships change with the interests of the knotter. I realize that this sounds very stilted and incomplete. Which reflects the state of my current thinking.

If one is to tell someone “Oh no, those are different knots”, it is important to include how the knots are different and why the difference is significant. In many cases, the difference can be ignored for the use to which the knots are to be put.

43

Hi Merickson,
You have me wondering. Are the two knots, as used “back stage”, the same knot but holding up two different parts of the theater, hence different to you or are they different knots in the structure? Help me out. The belaying knot that holds the “lights” is a different structure than the one that holds the “backdrop”? I’ll bet they are not. Nor do I think they are on the ships of old. I think (and many fine sailors will jump to the fore to correct me) that “knowing the ropes” had to do with where the rope was belayed on the pin rail or other.. and that you could tell in the dark and cold, not by the structure… but by the location on the rail… am I not correct? So, when you are back stage… isn’t the backdrop always belayed on the same “pin” or cleat and aren’t the lights always on the same location.. not by the structure but by location?

44

I think this has gotten “off thread” from the second posting. I think Charles wanted to start a classification of knots.. not a defining. Animals/mamals/hoofed/ungulant/horned = cows. line/end/loop/fixed = bowlines. Now cows can be Brown Swiss or Gurnsey or whatever and bowlines (If I can believe the 87 bolines or so proposed in Knotting Matters) can also be diverse… so maybe Charles needs more levels beyond “bowlines”… but it seems to me that what Charles was headed for was a classification.. genus, species, and all the stuff that I missed in school. I think he intended to ask us to help develope a classification of knots. I am sorry that it got so easily derailed. Is it a bend? Class it as such. Is it a fixed Loop? Class it as such. And I am ashamed that a fine mind as Chas should be browbeaten to resign.. tip his king.

45

I may be wrong and often am but I thought that Charles was not trying to name specific knots but develope a vocabulary to help classify knots.. not define to the word “knot”. or even define a particular knot… but open the vocabulary of knotting to classify any complecation in a cord by the form, use, method, configuraion… or for all I care the color.. but lets not get tangled in our own cords and throw away the original idea… “Tentative Classification of “Knot””.. yes I know that is not what he said but I think it is what he ment.
My point is simple: This thread went off on a “naming” tack and not on “classification”. Naming knots is an almost impossible task. However classifying is not. Bends, loops, binding, nooses, etc.. with standardized moves such as underhand, overhand, backhand and so on. With some further effort the “common” names could become standardized, if we could come to an agreement. After all we could agree that in the USA the “square knot” is for all others the “reef knot” and that the world wide square knot is the “good luck” knot in USA . Under some univerasal system.. it could be “left over right/right over left binding knot” for the reef and “four crowns” for the other “square” knot.
I think this will never happen if we argue about eskimo bowlines. Of course I may have missunderstood the whole post.

46

About the stage work example, I was giving an example where two physical instances of the same knot had to be considered as different knots. I mostly work outdoor festivals, so the regularity found on sailing ships is lacking. (Hanging banners makes outdoor festivals similar to sailing ships in other ways.)
An indoor stage, with more lines and more demands on the rigging, is a very good example of how identically tied knots cannot be thought of as the same knot. Whether they are mentally tagged by location or by function, they have to be thought of as different from each other.

47

HI!
H.L. MENCKEN : “The average man does not get pleasure out of an idea because he thinks it is true ; he thinks it is true because he gets pleasure out of it”

PABPRES is absolutely right in the reading of my fundamental intent : classification.
Instead of, like the rest of us, losing sight of the forest to look only one tree, he took the “integrated view”, and that allowed him to see the broad perspective.

When I answer “knot in general” it was about the very precise starting point of this topic we are inside just now, not about my deep intent.

Defining “in abstracto” what a knot can be is in my mind only a tool to be smithed. If it were not to make a tool it would be useless words juggling.
The real objective, the work, is “classification”

PABPRES took the larger view and rightly integrated 2 topics that are not really “separated”.

Thanks Roy, you put me on the right track again : I was so occupied looking at where I was putting my foot that I lost the way, with a bit of help here and there.:slight_smile:

A bit of history : in fact 2 topics are on “classification”

I started “can of worms : naming knots”. In it is evoked the probleme of a “knot individual file” (KIF here after - I think it was another acronym I used previuosly, will have to “clean” that) to make a sort of database.
inside this topic Dan_Lehman asked about what is a knot ?

That made me start this topic : defining knot .

Not a new thread in fact, only a paragraph following the first one, in the general topic : classifying knots. They should be read, as PABPRES seems to have done as two paragraphs in the same chapter.
I then met, thanks to Fairlead with FCB who shared his ideas which much precede mine. ( see his documentation on my web space :http://tinyurl.com/cwf3f

While trying to precise my thought I found the H & L , again only a possible tool.
That sent me on further “things to be put” in the so-called “knot individual file”

Thanks to PABPRES, I now recall what experience taught me : when one stopped “thinking” about the perfect way to do something, and actually “begin to do it”, things have a way to clarify themselves.

So I will work with a method I used with success quite a few times : "consider all problems solved and start!
If only for my amusement, I will go on, this time drafting a form for the KIF. May be I will propose it one of these days.

My current thinking starts from the point that "sameness" in knots depends on how one thinks about them. When working back stage, I frequently run into the situation where THIS knot holds up the back drop and THAT knot holds up the lights. But even though both this and that knot would have the same ABOK number, it is important that I recognize them as "not the same".

In my view you are not speaking here of what the knots “are” but what they are “used for”.
This distinction of function is more important than the difference in nature/name/whatever in the situation you speak about.
Nothing to do with the knots which here are only an “epi-phenomena” to the "rope needing to be used in view of getting “that effect”

On a different level, as I mentioned before, seeing a 3-strand Matthew Walker and a 4-strand MWK as the same is valuable at times.
They are not the same, I insist. But I aggree that one can "view" them , momentarily and knowing it is in error, on a "practical" plane as : "they have the same recipe" Sure that is a useful "tool" to see them as such. ( See Jimbo)
My current thinking is that, given two knots A and B, consider the set {A,B}. The various relationships that {A,B} has to the rest of knotting are more important that how many elements there are in {A,B}. Those relationships change with the interests of the knotter. I realize that this sounds very stilted and incomplete. Which reflects the state of my current thinking. If one is to tell someone "Oh no, those are different knots", it is important to include how the knots are different and why the difference is significant. In many cases, the difference can be ignored for the use to which the knots are to be put.

That was why, while FCB is thinking, (and did a real start), along the lines of a linear hierarchical classification akin to the one Linneaus created and that was used for so long, I would rather think more along the lines of “cladistic” classifying.
Allow for “fuzzyness” and “emptiness” that the linear do not allow.

About cladistics ( not heavy reading if really interested in subject):

http://www.ucmp.berkeley.edu/clad/clad1.html
…Cladistics is a particular method of hypothesizing relationships among organisms. Like other methods, it has its own set of assumptions, procedures, and limitations. Cladistics is now accepted as the best method available for phylogenetic analysis, for it provides an explicit and testable hypothesis of organismal relationships.

The basic idea behind cladistics is that members of a group share a common evolutionary history, and are “closely related,” more so to members of the same group than to other organisms. These groups are recognized by sharing unique features which were not present in distant ancestors. …

http://www.ucmp.berkeley.edu/clad/clad5.html

http://www.gwu.edu/~clade/faculty/lipscomb/Cladistics.pdf

http://www.med.nyu.edu/rcr/rcr/course/phylo-cladistic.html

http://en.wikipedia.org/wiki/Cladistics

I will NOT discuss the merits/demerits of cladistics. At this stage my thinking is not “practical”, only “theorical, on principles”.

48

Hello Charles !!! :smiley:

Je viens de tomber sur ton sujet et de le lire, du moins d’essayer de le lire dans ces grandes largeurs. Il me manque trop de vocabulaire hélas pour tout saisir. :-/
Mais j’ai compris en gros les gandes lignes ! :slight_smile:
Je suis sincèrement désolé de répondre en français mais là encore, il me manque trop de vocabulaires pour être compréhensible par nos amis “anglois”.
Tu as parfaitement raison de dire, qu’une classification un peu plus scientifique s’impose en matière de noeuds.
Certes le AKB par Ashley en fait une mais par usages ou type de noeuds, mais sans plus.
Je suis assez fasciné par ce débat dont j’ai essayé de comprendre le sens et les interventions de chacuns.
Je regrette d’avoir été si longtemps “coupé” du net car je prends le train en route avec beaucoup de lacunes.
Pourrais tu si te plait me ressituer le débat ?
Je serais moins idiot !
Par le biais de quelques uns de tes liens, j’ai vu le fabuleux travail que tu as fait. Fantastique !
Je dois t’avouer avec sincérité mon admiration.
Une chose cependant, je crois que cette classification doit être comprise de n’importe qui, dans sa langue maternelle par le biais de shémas explicites et par des mots simples.
L’aide des traducteurs, du moins dans le détail, n’est d’aucuns secours car le vocabulaire est trop technique parfois.
Peux tu s’il te plait, sans que cela ne te demande trop d’efforts traduire mon propos, celui d’un simple noueur parfois béat d’admiration devant le travail de certains sans qu’il ne puisse comprendre, le comment du pourquoi, de certains noeuds. :o
Cela est parfois très frustrant ! >:(
Transmet également à la communauté anglo-saxonne toutes mes amitiés et mes salutations. ;D

Avec amitiés à tous et à toi en particulier,

Al

My Text translate by Nautile.
Thank’s very much to you Charles.

Hello Charles !!!

I just came and read this topic, at least, the main lines of it. I am
missing too much vocabulary. But I understood the main lines.
I am truly sorry to answer in French, but then again I do not master
enough of the specialized vocabulary to be able to make me understood by
our anglophone friends.
You are right to say that a classification, more structured in a sort
of scientific way,is “a must have” in knots.

BOK by Ashley do a classification, but by uses or by types of knots,
and no more.

I am fascinated by this debate in which I tried to follow the meaning
of each of the posters.

I regret to have been out of the Net loop for so many months and I am
now “jumping on board the moving train” with many “missing parts”.
Can you give me a good resume ?
I will feel less of an idiot !
Thanks to some the links you gave, I saw the work done.
I must confess…

One thing though, I think that this classification must be made
understandable by anybody, whatever her/his mother-tongue background, by
making much use or many quite clear schematics and simples words.
On-line translators are of no use for the finer points and details with
a very technical vocabulary such as the one used at times.
Can you please, without overstretching yourself translate this post,
one by a simple knotter sometime admirative of the work of others, even
if he do not get in detail the “why and how” of some knots.
That can be quite frustrating !
Convey to the anglo-saxon community all my friendly salutations.
With “mes amitiés” to all and everyone, and to you in particular.

Al

49
Tu as parfaitement raison de dire, qu'une classification un peu plus scientifique s'impose en matière de noeuds. [...] Cela est parfois très frustrant ! [...] Transmet également à la communauté anglo-saxonne toutes mes amitiés et mes salutations.

Bonjour et bonne santé, Al!

I agree completely! Any knot language needs to be easy to understand in any spoken language! Like math, but knot.

And, on behalf of the “Anglo-Saxon community”, thank you! ;D

Jimbo

OR…
Hello and Good Health, Al!

Je conviens complètement! Il doit être facile comprendre n’importe quelle langue de noeud en n’importe quelle langue parlée! Comme les maths, mais “knot”.

Et, au nom “de la communauté anglo-saxonne”, merci! 8)

Jimbo

50

Hi Jimbo !!! ;D

Many Thank’s to you for your response in french ! :wink:

Very best regards,

Al

51

Hi
Glad you are back Alain.
Hey Jimbo, when are you going to post only in French?

See here http://tinyurl.com/bmt5a
clarifying : structure ( topology) versus geometry

52

Hi!

Still pounding at the coconut…
Going again at structure versus geometry leaning on these knotting diagrams .

Topology/structure = the very foundation of a “materialized knot”.Without it no knotting is possible.
Without geometry/fairing it is not a finished thing but only a careful arrangement of crossings in cordage that you get.
Simply this is usually “implicitly hidden” in the verbal instructions given to thrown a knot.

Because topology is “very visual” it is better shown by “picture/drawing/photo” than by words.
But once the structure is correctly laid the words take power again in that they are more performant for the geometrical instruction of the fairing of the knot.

Just try to get hold of a ROUVIERE if you are French or a GRAY’s Anatomy if you are Anglo-saxon and try :

  • to learn the anatomy of the upper limb without looking at even one part of a drawing
    then
  • try to learn the anatomy of the lower limb, without looking at the text but only at the detailed illustrations

and see which is easier to do! Of course, in the end you will need both PLUS to see a real anatomical piece.

As for me I will say that the only sure way to some give instruction about a knot"over the phone"is to be “topological and diagrammatic to give simili-visual drawing instruction” : (e.g) :

Start at the south of a sheet of paper , middle of the width.
Go straight North on a 360° course for 2 inches
Turn westward on a 330° course for 1/2 inch
Turn eastward on a 30° course for 1/2 inch
Turn westward again on a 330° bearing for 1/2 inch.
Then due west on a 270° bearing for 1 inch
Then south on a 180° bearing for 1.5 inch
Then est on a 90° course for 11/10 of an inch (or as long as necessary to be able to cross in a straight line bearing 360° or due North the 3 zig-zag previously drawn.)
Then due north for 3 inches : first crossing is High/over, second in Low/under third is High/over
Done.

I have known apprentice-surgeons able to recite backwards the “words of a procedure” but absolutely unable to find their way on a real anatomical piece at the morgue!
So uniquely powerful is the “image” that only with it can “the picture be complete”!!!.

I can draw the way to throw a knot for someone with which I have no language in common and she/he will get it.
It is not so sure with words, or blind persons would be wonderfully swift tyers of complex knots with just verbal instruction!

For reference see these knotting diagrams

Granted the Moebius diagram has no immediately perceptible “rapport” to this Moebius Turk’s head but it is the simplest way to get this conversation piece “done”. The Moebius strip outward appearance will come with doubling and tripling! Yet seeing the diagram you are hard put at “imaging” the final result. Try doing this Moebius turk’s head with this “structural” diagram and try another one with the " usual sort of illustration mixing structure with geometry with what when it is explained to me, appear to my mind when as “revelation of an insider secret” and “alleged global perception and knowledge”!

Still in doubt about difference of structure and geometry ?
…then try this ABOK#2272 to get something like that

Laying the topological structure is child play with this diagram and need only 2 or 3 minutes at the most.

BUT fairing the geometry is the Devil’s own job! Do you FEEL it now ?

That was with only 6 to 9 feet of 1/10" of polypropylene not 99 feet of 1/2" of hemp or manila!

IMO the sequence is : intent, structure, geometry,use, re-evaluation. and not some “global perception/knowledge of a knot” even if the fast ( real slow in fact ) neuronal work in our brain make it appear so.

Try to make this Oval mat using the traditional “global instruction” and then again with this analytical structure diagram .

A topological structural diagram is the “resume” of a knotting,on this resume one can apply the geometrical manoeuvers destined to give it its “faired” final aspect.

53

I apologize in advance for this definition. :wink:

While teaching a few children some basic knots last week I had one 8yo child who kept tangling her cords randomly and I made the mistake of saying, “That’s not really a knot”.

Of course one of the brighter children immediately asked, “What makes a knot a knot?”

I replied that a knot is something you make in rope for a specific purpose, which you remember how to make, and which you know how to untie your own darn self.

54

First thing : thanks for rekindling this thread.

Witty and swift answer you gave,
and absolutely pragmatically tailored for 8 years old
children who like Nature " abhor the void" and will never
let you off the hook if you do not answer one of their queries.

With it they got an immediate operational 'handle' on the notion
that cannot be faulted outright and cannot be rejected as 'in error'.

Of course "they are arrangement of crossings in a malleable
material that give it a 'relatively continued existence'...."
would have been a silly answer for them and more than likely
I would have fall for it!

But ...


What make a hammer a hammer ?
It is something made in a heavy and hard matter with the intent
of hitting something and that I know how to wield so as to do
the job in mind without crushed some parts of myself...

…
Now I am not anymore, by leaps and bounds, 8 years old, and when
I were still 8y I had already been quite finicky for some years
on definitions and things never amended themselves I am sorry to say
( “cannot you stop with your endless questioning, even of books!”
was a sentence I heard many time everywhere except in
my parent’s mouths :frowning: ) so I will say that :

- it begs Berkeley's question : does a tree falling in a wood
with no 'consciousness' to hear it make a noise ?

So if I give you a knot that you cannot tye or cannot untie it is not a knot? ...

Are knots only those you can throw AND untie yourself?
while those I can do and not you are not knots ?

Take an  absentmindedly thrown knot
( knotters do their 'dwindles twiddles scribblings' with cordage as other make doodles with a pencil )
so with out 'intent : is it a knot or not ? ... ( by your definition absence of intent = no knot)

    In a way it is as right as to say that someone who
    do not believe in tiger cannot be eaten by one.
    Even if someone else witness the ' tiger's meal'
    and say that it was indeed a tiger the "meal and first guest" 
    will go to the other side believing rightly he never was eaten by a tiger.

So if one person do not remember how to make a 67B x 57L turk's head it is not a knot?  ...

A knot set so hard it cannot be untied then become a a-knot
The Gordian knot was not a knot ( could not be untied ) ,big historical enigma solved ! ;-)

"Specific purpose" : the spontaneous overhand ( a knot you will agree)
that happened in proteins or in vines or in blades of grass
or in a bunch thin chains left dangling then are not knots.
Well you may be right they are 'accidents'.


Still... putting 'intent' and 'purpose' in a definition
of a 'material' thing is leading fast onto the path to become
a disciple of this French philosopher who wrote that :
" a melon has 'ribs' because it is meant to be eaten at the family table."
A bit too much of a leaning towards teleology, at least IMO.
But still teleology give you hard and fast answers if what you are
after is only "some sort of answer".  :-))

Kind regards.

PS I am still working in this topic...one day...i will...I hope...may be...  >:(
55
First thing : thanks for rekindling this thread.
I love definitions.
So if I give you a knot that you cannot tye or cannot untie it is not a knot? ...
It is a "conundrum". 8-)

Of course, I had no intention of defending that definition beyond its humor value… but I begin to wonder if we might not be having a problem that is fully caused by not allowing different usages for different situations.

Many of us will allow that there can be one shape which around a spar is a ‘hitch’, around a larger cord is a ‘bend’ and around a bundle of twigs is a ‘binder’. In one sense, none of these is a “knot” (they are a “hitch” etc.), in another sense they are all the same “knot”, in yet another they are all different and distinct “knots”.

So, to avoid having to defend a rope thrown into the air and falling down tied in a “knot”, I assert that the word “knot”, while used in a ropework class, adheres to my spurious definition, while other definitions apply in other situations.

56

Once again it seems that we are at Brian_Grimley’s usage and meaning!

I will not repeat what I wrore at length about “mind map” names, structure and geometry,
my theorical answers to your practical remarks
even in the guise of fun are already in this thread or in “can of worms”.

Sorry to have missed the connotated conundrum,
I had the mistaken feeling you were writing seriously;
Babel effect! :wink:
Though paradoxes do tend to appear when two ‘logical’ planes are mixed. ???
Cheers

57
I will not repeat what I wrore at length
I have to admit that at many points in reading this thread, my eyes came unfocused. I plead unfamiliarity with the many terms and a calcified brain. I just went back and tried to read it again, but had to stop long enough to restore blood flow to my cerebrum. 8)

That said, I noticed that there was a discussion about classification and I wonder if something I ran into might be of some help.

The folk who solve Rubik’s Cube have notation for their turns. Most use a combination of letters and symbols such as T’B2R (meaning "Top counterclockwise 90º, Bottom 180º, Right clockwise 90º). Another guy uses what (to me) seems easier to learn and remember, TaBiRo (Top Anti, bottom twIce, Right Once).

I, needing something even easier to remember, immediately translate the latter into “Take a bight in a Rope”.

Perhaps if clever people develop a notation for knots which could be made pronouncable, even knots which have well established, historical names could be equiped with subtitles which not only describe their form, but which concantate into phrases which illustrate their purpose.

Off topic, I am sure.

58

Hi !
I was not trying to be stern or demeaning or disparaging, it is just that I fear that I am unable to write things really differently. It would only “feed up” the rare readers still somewhat interested. Your post certainly does not show any symptoms of failing neurons and I should know!
By nature I tend to avoid being disparaging since it is not what I put in the category or “intellectual arguments”, sorry if the wording used ( but then I am French! :wink: ) came out somewhat stern or rude.

Here is a ‘natural’ knot :
http://www.keef.net/tanner/archives/photos/vine-knot.jpg

See other ‘natural’ knots here:
http://www.igkt.net/cgi-bin/yabb/YaBB.cgi?board=news;action=display;num=1130521042;start=0

Thanks for the interaction.

59
Hi ! I was not trying to be stern or demeaning or disparaging,

I never imagined that you were, I hope I didn’t give the impression that I was somehow offended!

I use a somewhat formal writing style which might easily be mistaken for testiness. Nothing could be further from the truth, instead, “jocular and easy going” better describe me.

(Learning to make Pineapple knots)

60

Let’s take the new query by Derek into the extant thread on this very topic.

or - 'When is a knot not a knot?'

Charles (Nautile) holds that a knot must be a self contained entity and cannot rely on any external help for the maintenance of its function or existence. Yet this seems wrong to me.
…
Is this then the essence which defines a ‘clever kink’ as a knot? If the kink performs the function of holding - is it a knot?
…
This brings me to the root of my post.

Is the object around which the hitch is made in fact part of the knot? I believe that there is good reason to argue that it is indeed part of the knot and that this has significant implications in Defining and Indexing Knots.


I concur in your sense of involving the object. I’ll excerpt & reiterate my thinking
on “knot”:

My conception for most simple things is of six classes:

| ON DEFINITIONS of RELEVANT TERMS FOR KNOTTING
|
| knot ::= A curvilinear structure that can be realized
| in one or more pieces of some flexible material(s)
| of uniform crosSection, incorporating or not some object(s),
| under tension, and independent of torsion
|
| hitch ::= A knot that joins a piece of flexible material
| to an object and is dependent upon the object for its
| structural integrity, for its shape
| or
| ::= a knot of a single PofM with an object where one
| end is tensioned
| or
| ::= A knot that joins a PofM to an object which gives
| it structural integrity, shape, where one end is tensioned
|
| loop ::= A knot that creates one or more eyes of any size,
| with one end tensioned in opposition to the eye(s)
|
| bend ::= A knot that joins two pieces of flexible material(s),
| tensioned on one end of each
|
| binder ::= a knot in a single PofM with an object where both
| ends are untensioned
|
|stopper ::= a knot of a single PofM with one end tensioned
| through an object against which the knot body is stopped

Let’s assume (keep in mind) that we are here trying to “come to terms” by
analysis & defining-as-per-needs, NOT looking for the Trvth of some What Is.

Further, I’m coming to regard such structures as nooses–fixed or sliding–and
trucker’s hitches as rope structures that involve knots, but not as knots
themselves. And I’ve wondered about cases where tension is necessary for
the integrity of the knot–say, for some fixed loopknot.

We should not be terribly bothered if we find there are fuzzy boundaries,
esp. if such boundaries are rarely touched.

–dl*