TENTATIVE DEFINING OF "KNOT"

General Discussion
21
I may have missed Charles original point, you know I often do... but I think it was not to define "knot" but how to define a specific knot in hand.
Well, one need only read the Subject, really; but, beyond that, do consider his post:
    • DEFINITION beginning : a lure? a bait?

" A knot is a spatialy defined structure of crossings (to be “defined” under)
that are made using one or several RoTaCa (to be defined) and that obey
AT LEAST these following rules :

In short, yep, you missed it.
And there are various aspects to this: what a “knot” is, in general; what should one call
some unit to be considered (e.g., what does one call the general structure common
to the Bwl (3 ends loaded), Becket H. (3 ends loaded), Sheet Bend (2 ends loaded), mesh knot (all 4
loaded), Eskimo Bwl, Lapp Bend, T knot? Is the general, topologically identical
structure “A knot” which can be given hitch/loop/bend/mesh loadings, or … ?

or mybe I had too much Yorkshire tea (which I deduce is the "Spirits Up" that keeps my bones from grinding too badly). Please read back over and see if you don't think we are trying to define each knot.. not the word "knot".
Or not enough--take it literally, not, ah, [i]Spirits-ually[/i]. Cf. www.yorkshiretea.co.uk (or www.barrystea.ie) --though I recommend a tea w/keemun in it, quite distinctive! Now, speaking of tea, I think it's about tea time here (got the weather for it).

(-;

22

Let me add a further confusion to the question:
It has been said that two knots with a topological difference are different knots. The main question has been whether loading is a factor in what makes knots “different”.

But, topological considerations are not a sufficiant criteria.

A 3 stranded Matthew Walker Knot is topologicaly differnt from a 4 stranded MWK, but is that enough to be call them different knots? Isn’t it more useful to recognize them as the same knot?

Another example is a coil. I consider a coil a knot. (a stopper knot actualy). Yet, two figure eight coils are not the same or different depending on the number of turns taken around the neck of the coil.

Perhaps a defintion of would read:
Given two “complications of cord” A and B.
If every person who is taught how to tie A immediatly knows how to tie B, then A and B are the “same knot”.

23
It has been said that two knots with a topological difference are different knots. The main question has been whether loading is a factor in what makes knots "different".
This is what I tried to articulate near above: that there can be a need to refer to the general knot-structure w/o regard to loading, and the Meshknot/Bwl/BecketH. /SheetBend/T-bend/LappBend/EskimoBwl is a nice paradigm to consider. Although for this structure, there can be some sharp differences in the [i]geometry[/i] between the various enumerated "knots"--the SPart of the Bwl being sharply bent in the Eskimo Bwl. as the end.

Dick Chisholm, e.g., has defined a notion of abnormal loading which is to be
attached to each particular-knot structure (to the Bowline, e.g.); but note that
for an Overhand loopknot the abnormal loading named “ring-loading” (where the
eye alone is loaded, making the knot effectively a bend), the knot is loaded just
as the Offset Overhand Bend (OOB, aka “Thumb Bend”, “EDK”, “Overhand Bend”)
is normally loaded! Were one to step a level back from this “particular-knot”
perspective, to be considering the doubled Oh. knot indepent of loadings, one might
then have no basis for “abnormal/normal” and talk of the knot in any/all of the
possible loadings. (Being a symmetric knot, unlike the Bwl///etc./, there are fewer
differences for the Oh. structure.) There should be a name–maybe not “knot”–
to denote this level of consideration, this sort of general entity.

<general_entity>

  • particular loadings => <particular_entity_1>, <p_e_2>, … <p_e_N>
But, topological considerations are not a sufficiant criteria.
Not sufficient, nor even [i]necessary[/i]! At least in some sense of "knot", one much wants to discriminate between the Sheet & Lapp bends. Also, consider the case of the Bwl & capsized Bwl--something I've seen (the latter phys.entity, i.e.) pretty often, almost as though it is the desired result!?
A 3 stranded Matthew Walker Knot is topologicaly differnt from a 4 stranded MWK, but is that enough to be call them different knots? Isn't it more useful to recognize them as the same knot?
--good example; also the multiple Oh. series, and knots built with them (e.g. the Grapevine bend & Triple Fisherman's knot; or the "Fig.N" series of stoppers & loopknots ("Fig.8" begetting "Fig.9"--a half-twist more--and thus "Fig.10" (which, btw, all have TWO symmetric forms, of which for the Fig.9 the stopper is Ashley's Tweenie (#525) [nb: ABOK error--left & right images are of opp.handedness!])). Here I think I'd say, yes, different knots but definable from a construction rule that can be [i]scaled[/i].
Another example is a coil. I consider a coil a knot. (a stopper knot actualy). Yet, two figure eight coils are not the same or different depending on the number of turns taken around the neck of the coil.
Hmmm, not a multi-eye loopknot? At some point, I think that some of what are presented as "knots" should be seen as compound structures--the Trucker's H. seems an obvious case; the Sheepshank and Twin (X = Bwl.s, Overhands, ...) bends seem problematic. In these, the actual [i]knotted[/i]/entangled parts are disjoint/separated by indefinite amounts of material. (Chisholm also has a notion of [i]nub[/i], but what's the nub of the Sheepshank?!)
If every person who is taught how to tie A immediatly knows how to tie B, then A and B are the "same knot".
I'm leery of invovling human [i]intent[/i] or other external aspects. (And certainly not everybody will be able to do anything!)

–dl*

24
I consider a coil a knot. (a stopper knot actualy).
Uh...

Isn’t that actually a loose 1L x 1B Turk’s Head Knot with an inordinate number of Doublings? ???

I only guessed this because I like that particular 1L x 1B THK (ABOK# 1313) for “Flashlight Service”, wrapping “oh-snot” handles in trucks, etc.

Hey, don’t look at me! I’m paraphrasing CWA!

;D (Ain’t I a stinker?)

25

I’ve had further thoughts about the figure 8 coil. It looks like a Sheer Lashing with the poles removed and extra frapping turns. Or like a seizing. In either case, it seems that it would be in the Binding Knot family.

On the main topic, I think that the desicion of whether two knots are similar enough to be “the same” depends on what aspect of the knots the decider considers.

Each branch of knotting looks at knots differently, leading to different criteria for deciding “sameness”. All of those are equally valid. I am not sure that there is much value in choosing one canonical system. Each branch of knotting should evaluate knots (including “sameness”) in the way that serves that branch the best.

26

I think that each knot can have a numerical definer to it, in addition to its name and describtion, for the variations.

Like a overhand knot, (1)
Double overhand knot (2)
Multiple overhand knot (7)

Can be simplefied into ‘overhand knot (N)’

Or Crown knot 3 ends, tucked under 1.
Crown knot 12 end, tucked under 5.
(Yes I do make knots like that and I do have to make notes like that at times.)

This is the scientifical aproach and not everyday language unless you are into tying a lot of different versions of a knot.

I hope I make sense here.

Willeke

27

Hi all around !

Yes Roy I had in mind to define the knot structure in a general manner.( go back to different “mind map” in different languages)
I was not addressing this or that knot or bend or hitch ( those 2 last words are not “sense-bringer” in French for exemple).

But I understand what could have misled you, just like in English foxhunting ( you being the Fox of course) instead of the dogs taking it, it was the fox that followed that red herring ( to the confusion of the Hun): the repeated apparition of specific names.

My part in that was my proposing a method of “sequencing” with H&L and to examplify I had to specificaly evokes particular knots ( understand that in my French mind I can only use noeud/knot = knots + bend + hitches ), since it is to be applied to “real” knotS and not to “an ideal knot”.

So you were not so much erring as having been mislead by, at least, some of the “how” it was argumented here and there.

But your “confusion” is to me less that the “constant” return of “loading, use/usage of knot so and so” in this particular topic.

I thought that I had made clear the following points :frowning: must have over-estimated my capacity to explain my thinking in another language than my own, so I will try one again. Sorry to be so repetitive, but I will try to keep it "short and to the point " at the risk of appearing curt and abrupt, and will not come at it again if I do not succedd this time, since I do not knos how to re-formulated it).)

  • My main intention was structure - construction - anatomy and not function - usage - physiology

  • reasons for that were :

          - arbitrary : my own inclination and mind map.
      I tend to perceived "structure" well before I am sure of "function"
      My "mind map" make me rather think that defining some "materialized" thing is rather [B]WHAT[/B] this thing is [I]first and foremost[/I] and only after ascertaining that, then I go to "what can I do with it" and "how I can" and "how does it works". 
      See, in French : only "knot" : structure, whereas as in English "knots, bend, hitch"....this already imply a "function"point of view as well as some aspect of structure.
      
      - wanting to be reasonable : 
            
            
            - structure is usually more "apparent" and/or "evident" than function. (See history of "sciences of Life" : anatomy was knwon well before physiology, and usage of bodies in specialized tasks were in action without any physiological knowledge, just "imagined" 'how it works')
            
            - structure is more "discriminating than "function". I mean : seing a structure you can infere more easily a function than stating a function and after infering a structure. 
            Or in other words : given a structure it will be easier to get several people to aggree to a function ( one among others posssible), whereas stating a function you will be more often hard put to get people to agree on one structure. 
            Preferences, opinions, preconceptions and so forth would be let loose, while they are "coralled" when you start with the structure. 
            Don't know if that comes out "clear"?
            
            - structure being what you "get at first" is more helpfull, more discriminative, than the quite empirical"to what use it is put" which in turn is much more easier to know than the more difficult attempt at being "experimental and rigorous"[B]"how it works"[/B] as classification criterion
            
            - Structure was to be only [B]one of many things[/B] ,not even the main heading. 
            That(heading) was to be something like an  "identification number"to be put in what was imagined as the "personnal identification file for a knot".
            That was "in the body" of the file that the "how it works" would be attended to.
            
            - about, knots specifically, you have to "MAKE" it before "USING" it, and also you can put it to use ( not "advisededly" may be) without "KNOWING its inner working".
            
            The time sequence of using a "materialized knot" begin with structure ; I understand that the "immaterial" part of the time sequence could very well be thinking about "function". 
            But in the phenomenal world the "structure" is the first to be made manifest. Or so I think.

I think ( yeah! bringing down open doors) that in “knowing a knot” there are at least two folds :

  • may be a third that I put first : knowing “of” or “about” a knot

  • First fold ,structural: knowing how to lay the knot without any mistake, even dressing it properly. without fail, even under stress, as when in military training with dismantling a gun in the dark and putting it back to working order in the shortest time possible.
    That small part of knowledge is what opens the door to “danger” since you can “materialize” the knot and put it to use.

  • that lead me to the second fold ,functional : knowing how, why, when, to use, not to use a knot, and in which sort of rope to cast or not to cast itand so on.

  • uses, tests versus opinions or lore, internal working, how to cast the knot, different methods, different naming, indication, not-an-indication, contra-indication, in which rope to do or not to do it, remaining strenght in a rope ( to be clearly stated in nature, sizes…) with it… were all conceived to be in the file not in the defining.

I quite understand that this individual file would be of no use if left at the defining of the structure.

But I would like the “logical planes” (structure - functionning - uses …) be respected ( differentiated clearly) and not “opposed” one to the other(s) in “defining” THE knot.

…to be continued in next post…

28

…continuing above post

Already two threads are intertwining or entangling (?) not to distinctly : “defining knot” and “can of worms”. A third one, may be in order : " internal functioning of knots" with a bit of “uses of…”.
It would not add too much confusion.
Those three threads being "at the end " compacted and synthetized ( by common working) in a template for individual file.

I would like for all our collective thinking effort, not to go down the drain. Hope that it is “kept in archives” by some of us in case that, one big bright day ( the one pigs will fly or as they say in France “hens will have teeth”), the powers that be at IGKT will really hear, (as in “understand and act upon” , not as in : "giving the silent treatment " or the “pooh-pooh”, or the victorian “quiet and not to be seen and heard” ), what we say on this forum.
( yes I know I should not levy judgment at my betters. “Most sorry! Beg your pardon, will do it again though”)

That necessity “doing a specific work at Igkt” is already, since a long time, in clear and no uncertain terms, expressed by Dan_Lehman in KM66 ( march 2000) “Knot Slops”.

Must say it rather pull the rug under me to see that much more than 5 years later, nothing, that I know of, has been done, by the “Wold Authority On Knots” WAOK , if not Igkt’s acronym it seems to me it was implied in the declaration of intent at founding.

To jest with a silly politician sentence " it is more than urgent to powerfully apply the brake on the immobilism that drives us at full speed into the abyss where we will attain summits of despair".
At this moment in time,I am suffering a bout of “sub-chronic motivation loss”.
Condition can ail but can just as easily go : “terminal” :slight_smile: and I will go just cast my knots and renounce thinking about them.

Suppose that part of the problem is : Igkt is an “entity”, and only administrative at that, and not a “being”.

Now to quote : “3S and 4S are MW are topologically different” .
Certainly they are not topologicaly equivalent , and that answer itself : they are not the same knot.

I propose some silliness just to be amusing :
Obviously, a lion and a panther, though different, are “intrinsicaly” the same animal .
Yes do not doubt it : they are mammals, carnivorous,felines both, just as 3S or 4S it is still a MW.
Saying they are different and give them the same specific “label” is “?” ( let you choose the value to be put here.)
Said like that it is a “no-no” from where I stand.

To me saying MW /S and MW/4S are not different knots while saying they are the same is a logical “no-no”( without the topo in it this time) .

They are indeed MW ( or felines) so they can go in a “file” MW", that well known criminal using many aliases and disguise, so in his file, disguises ( 3S, 4S, 5S…lion, panther, tiger…) would be recorded.

Just the same for the Turkshead group, or the Crown and the Wall with their hybrids siblings, or the Tack and Manrope, just to name the ones that come to my mind: recognize that they are “family” ( there ,going back to FCB - Hi Frank !- seems to me a good idea ).

Now to what Merickson" wrote :

  • I like a lot the tolerance of “different point of view” or of “oulook” that it imply. So I keep it, in the interest of being “open and tolerant” ( a “structured” work need not be to be “dogmatic and closed” ).
    In the interest-of-saving-ethnographic-data I would say that it will ( should have said “would”, but I want to be optimistic or irrealistic as you want) be a good thing to put that notion as a paragraph" in the individual file.

I am a bit stranded at the moment with the H&L : have something like 50 Mo worth of writing and drawings with sequencing.

Drawings are all right , tabulation of sequencing are all right, but what is still a much less that preliminary draft is the text and conclusions. I am aiming at “generalization” and not " 4 or 5 set of different rules" as it looks like to be now.

I am ready to take the risk ( and the time - lower estimation : 3 to 4 hours - to put it in line on my site ( in zip format, eventually .html,;doc (as it is) and .pdf) for those interested to “work” on it. Would be quicker to put it not on site but in “web space” and I would give access, and to do zip of course but only one format .doc or .pdf or .html. I will not loose time ( now, since I considered the “product has not passed quality control” so I am waiting for ordering if any one is sufficiently interested.

But please that is under the understanding that you will not -yet- judge the written part, but only the drawing and sequencing part.

   A formal but not very useful ( for us ) defining 
   [B]A polygonal curve in 3D[/B]

Cannot be shorter! Cannot be much less useful to us.
Just to satify the “functionnalists” party I will amend that to

   A material polygonal curve in 3D which can be put to some uses depending on factors pertaining to its internal functioning.

PS:

Is a kink a knot ?

How many angels can dance on the head of a pin ? ( long medieval debate was “What is/are the sexe(s) of angels”
What is the opposite of my cat ? ( HE asked me to go for that one)
What is the sound of a one hand clapping , ( Zen this one)

29

Help! I’m swamped beneath another Nautilevanche of ideas!! :o
:wink:

Nautile, how do you view the Lapp Bend and the Sheet Bend?
(Consider the Sheet Bend oriented so that the bight tip is up (N =north, 12:00),
its legs thus South; the looPart ties to this by entering the tip crossing Under,
turning leftwards (West) and crossing Over the left leg and then goes back around
Under the bight legs, to continue then in anti-clockwise turning to cross Over the
bight leg, Under the earlier set part of itself, and Over the left bight leg (pointing
thus NW) ?
Call the four ends, starting at the top (N) and moving anti-clockwise as A-B-C-D.
The Sheet Bend would be defined as tensioning A & D (ends being B&C); the Lapp
Bend … B & C.
Do you consider these to be the same knot, anatomically?

–dl*

ps: What size pin? ::slight_smile:

30

Hi Dan_Lehman

Was a bit “Da Vinci Code” like.
Had a bit of a problem with naming nomenclature since what I have seen give as true the following statement :

Lapp = eskimo/esquimo bwl = dutch bwl = left-handed bowline ( equality A )

some even add to this above equality = Asian or Turkish bowstring knot !? in http://groups.yahoo.com/group/knottyers/message/2933?viscount=100
and even Honda knot !? this one in http://www.scoutxing.com/knots/honda_knot/honda_knot.htm

I do not see all that as “true”

eskimo = lapp (?) suppose that “True”
dutch bwl = left-handed bowline “True”

eskimo = dutch “False” plus eskimo = Asian Bowstring is “False” and Eskimo = Honda is False

so Equality A is “False”

Worded instructions instead of “traced instructions” are always a bit dicey for me to follow.
Thank you for adding orienting and vectors.

eskimo bowline in http://eskimo-bowline.wikiverse.org/media/8/80/eskimobowline.jpg
Bowstring knot in http://www.realknots.com/knots/sloops.htm#bowstring

There is no problem comparing : sheet and eskimo or bowstring as shown in the above links so no interesting point in the “quizz” it is rather evident that no equivalence is there.

Just as bowline right-handed is based on sheet-bend right-handed
Dutch or left-handed bwl is based in left-hand sheet bend as I understand it.
So :

Dan_Lehman quizz as I undestand it :

compared to

See the one I did following (or rather thinking that I was following) dl instructions at http://tinyurl.com/7loan

Anyway I do not feel it is all that important in this particular set.

I fell this particular one can be reasonned about, in the “abstract”

To be a “real tease” it must be one of these cases so as to offer as many red herrings as possible in aspect:

  • First case -NOT same number of crossings : if that is the case :topologicaly non equivalent

  • Second case - same number of crossings : then number of crossings is not discriminating so seek elsewhere:

          - if same number + NOT same sequencing : then topologicaly non-equivalent ( for these controled points, there are other to be controlled but too mathematical to be easy)
      
          - if same number AND same sequencing then not discriminating  seek elsewhere :
                      - - it is a given that it is a "bowline" compared to a bend.
                        Hence with a loop in the first and not in the second.
                              Hence one more "hole" than in the bend : not topologicaly equivalent

Seems to me there was a post about “naming” the “emptiness” enclosed between the “line joingning the crossings”.
Left it here at “hole” though “lagon” with its bordering coral has a lot of appeal for me.

I do not hold those 2 structures as equivalent due to the number of holes discriminating them , but there are clearly sharing an important part of the same “genetic” background so to speak.

Do I pass? or do I fall flat on my face ? :slight_smile:

I would like to see the following hypothesis be examined and if retained, then ‘researched’ for examplifications :

    • if structures not equivalent, the more ‘non-equivalent’ they are ( what IS more non-equivalent ? I don’t know at the moment), the more 'functionaly" different they will be found , it would then follow that the uses/usages are different in a direct function of the 2 preceding, but not in equal part.
      Or is that a tautology so not worth thinking about.

Cheers

  Nautile

PS
Pin size ?
Try the one you used trying to pin me on the corkboard like a hapless insect with this “quizz” lapp/Left-Sheet :slight_smile:

PPS
“swamped” you are dl ?
Did not intended to mired you.
Was neither able nor inclined to make it shorter.
Thanks to Guardian Angel in Chief for longanimity in fellows knotters.:slight_smile:

Well! in my psychitry training what I did in my last posts, depending upon the fraction of victorian era, in the background of the speaker , was labelled" “verbal incontinence” or “verbal diarrhoea” though I am sure it is better in literary fashion : “logorrhea”. Shameful.

31
... since what I have seen give as true the following statement : Lapp = eskimo/esquimo bwl = dutch bwl = left-handed bowline ( equality A )
No, "Lapp" is [i]bend[/i], "Eskimo" a [i]loopknot[/i] (related as are Sheet & Bwl).

eskimo = dutch “False” …
it is rather evident that no equivalence is there.

Although we can shift the question to the loopknots field, if that catches onto
something. Now, why do you say “False”, for anatomy? How is this evident,
as I was getting the sense that by excluding function at this stage of analysis,
you wanted to exclude considerations of loading (and thus more knots would be the
same, such as I’ve suggested for one sense of “knot” for the SheetBend-Meshknot
structure)!?

See the one I did following (or rather thinking that I was following) dl instructions at http://tinyurl.com/7loan
Good, but upside-down--same order, so "A" in your pic is at bottom, and then go around anti-clockwise for B-C-D.

number of crossings

Frankly, I’m often put off at trying to assess this, which works with a 2-dimensional
perspective that must be (somewhat arbitrarily) forced upon the knot of 3-D space.
How do you see this for Sheet/Lapp? I guess one is forced somewhat into the area
I’d seen as “functional” if that is what positions one for determining the crossings
structure (begin at THIS not that end, and proceed)?!

PS Pin size ? Try the one you used trying to pin me on the corkboard like a hapless insect with this "quizz" lapp/Left-Sheet :-)

Of course, it might depend on the particular dance …

:stuck_out_tongue:

32

Hi
I think , with the dutch bwl and the eskimo bwl in the links I sent, that they are , to my eyesight, at first sight, different knots.

Sorry, not trying to dodge the question, but where can I find the Lapp bend you are speaking of ?
Can you sent drawings ( plane projection ) or the two structures you are speaking about so that I get a chance to follow.
Sorry about my misunderstanding of your question.
Which difference(s) do you see between this left-hand sheet bend and the “lapp bend” ?
I only found ref to “lapp bowline” with all the “discrepancies” I put in my last post.
Google pictures "lapp bend " = zero result. Same thing with Alltheweb.
There is a limit to my ability to follow in English, the more so without the “images”; am at my limit and going into “massive incompetence” level here. Remember I have not your shared background in language and in knot naming.

If “Lapp bend” is “exactly” done as the “sheet” bend I do not understand the question about their difference. That would be only on name or in “mirroring”. If differently tied then it answer itself : not same knot.
Or I am coumponding misunderstanding with misunderstanding?
You got me totaly lost and erring here.
.
Crossings : may be going back to my set of rules would clarify. I cannot do it in a clearer manner. Short : no hidden crossings and no “not necessary” crossing" or “collapsable one” in the “flat” projection of knot. Without that convention crossings and holes counting is useless as it has become arbitrary. ( crossings and holes are used by topology just in that manner, except that knot is “closed” for the “math”). But doing “right” you get the mean to “tie” the knot by following slavisly the diagram drawn. After that of course much dressing may be in order.

I do not know how to count the crossings in a 3D representation .
If plane projection rejected , then I do not know how to do it, not having the competence for higher dimensions topology and may be not even really for the plane one.

Added : came to my mind this morning! can be lightening quick if I really want ! :slight_smile:
I will do an eskimo bowline, cut the loop and : lapp or eskimo bend should be there. Will go and see

You can download my H&L drawings (no text ) 10 Mo so long time on dial-up and less than 1mn with high speed at :

http://tinyurl.com/7ajer

click on the lonely file and it should propose download

33

Hi!
complication

I have a problem here.

Is it to mean : more intricate, more confused.
If so I can suscribe, even a simple overhand certainly, in that perspective, “complicate” the curve of the rope or the way to describe it. Sort of complicate its structure.

Can or may or must I take it to mean as in medecine : an unfavorable evolution ?
Then “à propos” of casting a knot in a rope I do not see quite well if I can suscribe since you casted it to have “more” than with the rope unknotted.
Unless if one take on account the weakening of the rope by the knot.
I can find that interesting to consider. Sort of complicate its function. But somehow I doubt that it is what it was meant to mean

Does it means, the same that the horloger denote with this word, as in saying “this is a watch mechanism with complication(s)”, for telling something has been "added to the “basic” needed to be used as a watch ( hours/minutes and seconds).

Then I am not sure I can suscribe :
A watch with the complication, say date, is still a basic watch, it nature of “basic watch” is not altered, it has just been “added to” it and it still function very much like the “basic” watch it was, its giving performance in hour/minute/second measuring is unchanged.

But I am not so sure that a rope with a knot in it does not have its nature changed and can be said : It stay a “basic rope” ( for example the knot leave “a memory” in the strands and fibers and there is now a “weakened” point in it.

I will, for the time being, choose to stay with first : complicate its curve, making it polygonal.
"
Or I am trying to understand more that I can ?

And I have more of a problem with " know how to A AND know how to…B then A equal B"
I know how to catch a rabbit so I infer how to catch a cat, then cat and rabbit are the same ?
I learn how to write “PA” then I know how to write “PAPA” (then PAPA = PA. Hard for me to believe they are the same.

Cheers

34
"A knot is a deliberate complication induced into a piece of rope, line or cord, in such a manner that it may be later undone, or not, as may be required." Nick

Hi Nick

Given : (single) Overhand knot , Double Overhand Knot , Triple Overhand knot

Conclusions :
Single oH is a “complication” of the rope
Double is a complication of Single oH then it is complication squared of the rope ?
Triple is a complication of Double oH then it is a complication of the double, a complication squared of the oH, a complication power 3 of the rope ?

?? as use in chess notation.

See where “complication” can lead.

Why “complication” rather than “complexifi-cation” ?

I am ready to learn that I am “erring in error country” but I rather think that some knot are more complexifying the rope than they are complicating it.
( my caricatural mind map here is : complicated : usually numerous parts and low level of intrication of relations between the parts and complex : not necessarilly a very high number of parts but highly sophisticated integration of the parts)

Let me add a further confusion to the question: Perhaps a defintion of would read: Given two "complications of cord" A and B. If every person who is taught how to tie A immediatly knows how to tie B, then A and B are the "same knot".

Hi Merickson

I have some clarification to ask.

Firts
I teach someone the underhand crossing loop ( L1) [ in the nomenclature I pout in precedent posts : H is as above and L is as Under ] then she/he knows how to add 2 “half twist” and get an underhand knot ( L1 H2 L3 )ABOK#519 in underhand
Knowing Underhandt he/she know OverHand
Knowing that she/he immediatly know how to add an half twist and get (L1 H2 L3 H4 ) a Fig-8 like ABOK#516 with a begining as underhand
Then knowing that he/she immediatly know how to add another half twist and get (L1 H2 L3 H4 L5) a stopper like ABOK#520 with a begining as underhand
Then knowing that she/he immediatly know how to add another half twist and get (L1 H2 L3 H4 L5 H6) like ABOK"522 stevedore with a begining as underhand
When one know the Overhand one can get the Fisherman’s and the Overhand Loop too.

Are you prepared to say, abiding by what you wrote that :
crossing loop = underhand = overhand = fig-8 = stopper = stevedore = fisherman’s = overhand loop = underhand loop
Me I am not prepared to endorse that long equality, false from where I stand now.

I could have begun with : "you know how to handle a rope so easy to go to “underhand loop” "
That would have given
rope without knot = crossing loop…underhand loop.
To get the above “surprisig statement” I just appliedyour statement in a step by step manner.

All I am prepare to say is “they are related” but not they are “same knots”. Kno-Kno!

Second
Crown learned then you immediatly know Wall or double crown or double wall or crown and wall or wall and crow, or tack or manrope or…

Following your rule then all are the same knot ? Or do I misunderstand your rule?

Third
Overhand knot
Having learned to cast it you immediatly know how to “combined” some of them : getting just a few exemples : Zeppelin/Rosendahl- ABOK#501 - ABOK#1408 -ABOK#1408-9 - ABOK#1409 - ABOK#1425 - Fisherman’s

So following rule you stated I can state

Zeppelin/Rosendahl is same as ABOK#501 which is same as ABOK#1408 which is same as ABOK#1408-9 which is same as ABOK#1409 hich is same as ABOK#1425 which is ame as Fisherman’s
I could add the thief knot or the granny since if you knwo the oH you know how to do them or ABOK#1412 ( ring knot) plus ABOK#1414 plus ABOK#1426.

Really ?

Why so much different names and so much different “instructions to cast them” if they are indeed “the same knot” ?

Fourth
Overhand knot if learned then you know immediatly the Underhand knot
Following rule stated by you then it means you are ready to say Overhand is the same as Underhand.

Me I am not, since they are not the same knot just as your right hand is not the same as your left one.
Just try to put on the left glove ( without putting it inside out first ) on your right hand.
If you have a “machine” geared for making overhand you will have to change the algorithm to get an underhand. If they were the same there would be no need to. ( Note : chirality is not “an abstract” mathematical view : in human biology there is a strong bias towards the levogyre ( turning polarized ligt to the left) and the chemical synthesis give dextregyre and levogyre in 50-50, meaning that half the molecules of, say chemicaly synthetized C vitamine, are not “used” by your body ( unless things changed since I learned)

Sorry but decidedly I will not stamp this rule as “importable” into my mind map.
Either it leads to “bizarre” conclusion, or it leads to misinterpretation of it just like the one I may have commit and just exposed applying a reductio ad absurdum

Cheers.
Nautile / Charles

35
Hi I think , with the dutch bwl and the eskimo bwl in the links I sent, that they are , to my eyesight, at first sight, different knots.
So, yes, but WHY ... ? I'm trying to understand [i]anatomy[/i] vs. [i]physiology/function[/i], which I took to be something of a distinction between form w/o loading and that WITH loading!? (If one makes a circle around the compared knots above so that all "ends" ("limbs"?) run outside of the circle and one cannot know their existence beyond, what is that ?!)
Sorry, not trying to dodge the question, but where can I find the Lapp bend you are speaking of ?
I described this above. Tie a Sheet Bend; now load the ENDS: that is the Lapp Bend. (that's a same-side (ends & SParts) SB, btw)

(-;

36
So, yes, but WHY ... ? I'm trying to understand [i]anatomy[/i] vs. [i]physiology/function[/i], which I took to be something of a distinction between form w/o loading and that WITH loading!? (-;

It is rather visualy “evident” that they are not the same.
But I suppose you want something “articulated”.

Please use http://tinyurl.com/869ly : I used Peterson’s notation system in animal description : Arrow only on distinctive points.

1_
Crossings are at different level (red arrows) . That alone make them apart, without any reasoning just looking.
No real need to go further.

I will try to give more “articulated” arguments

2_
I found no way, using only sliding, and putting more length in play ( no cutting, no flipping, no “redoing” of crossing by re-threading the WE) of starting with one and finishing with the other.
Only that equal “are not same”. Agreed I could have miss a trick with the Reidemeister’s moves, so…

3_
Crossings sequencing (just following the “imaginary” WE along the diagram, ) are different.

4_
I even “signed” the crossings ? ( http://tinyurl.com/d926f to see the convention )

I hold that topology is necessary to analyze a structure, be it a knot.
Just try learning anatomy without using it!
First bone ( one of the simplest : clavicule / collar-bone) I learned, without having those tools, kept me more than 8 hours.
After mastering the topology used, even the most complex one was not even 1/4 of that in learning time):

Note : neither numbers of “holes” , nor Drawing Sequence of crossings can discriminate here ( The “GSC” would discriminate since in the left bowline H3 & H4 can be “one H3-4” crossing H1 in High position.

I think I have shown them to be different in structure".

My sense ( mind-map) of structure - usage - internal functionning is based :

  • on my French culture - on my training in anatomy ( animal - vegetable ), in physiology of thereof - on a non negligible training in chemistry ( mineral of course, but organic and biochemy too, all domains where “structure” , “orientation” & so forth are most important).
    It may not be congruent with an english culture mind-map.
    I feel unable here to use any more of my feeble english mind-map and language knowledge.

Structure : anatomy, how it is “built”, static inter-relations.

For a “knot” : laid diagram-like.
No superfluous crossing, no missing crossing, no crossing hiding another.
After setting it in close conformation, dressing it, tightening it , using it : if you reverse what you did and lay it flat again you get the diagram you begin with.

I understand that with “structure/form/shape” I did a mistake.
“forme” in French is “shape”, not what the way it act as in “form” for english language ( “that is bad form” as in “bad behaviour”).
So discount my precedent use of “form”.

Usage : what you do with it, what it is applied to. What “this knot , here” can be use to . In negative: what it cannot be used to.

Internal functionning ( physiology ; dynamic inter-relations, the activity inside ) : what happen inside the knot, slidding there, pinching here, torque here, strangling elsewhere, inner curve compression or outer curve elongation, less strain in the inner fiber than on the outer ones in a laid rope, friction between fibers…
The internal moves and what is happening in the knot being tightened by hand first and then by load.( I suppose that it is during this transition hand to load that the “correct dressing” is much important )

Reformulation :

Structure : my right upper limb ( bones, muscles, sinew…IN A STATIC state, just as you can look at it on a dissection table)
My anatomy does noes change when I use it in life, unless I have an accident that “breaks” or “strains” something.

Usage : what my upper arm may be applied to: throwing a javeline, writing, holding a load in static position…
That is the “imagined”, “conceptualized” upper limb as tool.
In my view it very much depend on the structure :
An articulation like the human ankle is quite different in mobilities from shoulder and that is [B]just because of the anatomical disposition & construction of parts/B]. Just seeing one I can tell you what it can do and what it cannot do mobility/stability-wise. ( I can infer the pressure zones too).

Internal working : which angulation between bones segments change, how it change and how much ; muscles put in action in an agonist and in an antagonist way ; which part of which muscle it put to contribution ; modification of blood circulation, nerves impulses, hormonal discharges and many other things..My limb in action this time.
Of course though done the same shoulder anatomy a move in external rotation-abduction imply something quite different from a move in, say, antepulsion, or internal rotation-abduction.

Of course my real limb is all that and more, simultaneously.

I am sorry not to be able to express it in a better fashion.

Last try:

Would “morphology” be better than structure

structure : that is the carpentry skeleton.“drawing of architect”
usage : garden shed or house
function : how the shed allow me to “pack” my things in an orderly and safe manner
If house : how it goes from daylight to artificial light, air circulation, heat repartition, noise repartition, circulation ways between the rooms, loss of heating from bad isolation, heating from the sun in summer, reaction to a high wind…

37
I described this above. Tie a Sheet Bend; now load the ENDS: that is the Lapp Bend. (that's a same-side (ends & SParts) SB, btw)(-;

I still have the feeling I do not understand you question, that I keep missing some important point.( first time I already misunderstood it : mind block about the whole notion)
I know it must be frustating for you, sorry.

I will try to answer though I do not really understand how, for the only reason you load it ( I understand :loading is pulling strain applied ) you change its name.

To me it is a bit like :empty in the hands of the cowx-boy it is a lariat and around the neck of the straining bull it is now another knot ?

Whether you write it C6 H12 O6 or C6 (H20)6, it does not change neither that it is still sugar nor how it is used by your cells.
It only denote your “mental attitude” in conceiving of it. As a “not special coumpound” or in the other as a carbon hydrate clearly flagged as such.

Quite mystifying to me that a knot can be evoked by another name just because it is in use.
I can barely think that a “knot structure” put to 2 different usages will have 2 different names.
Intellectually I conceive this but I don’t feel it inside my brain, it stay “alien”.

Now I am asked to push it further : name changing with loading pattern.
I cannot understand how Sheet Bend can become Lapp Bend just by virtue of different loading.
Am i misunderstanding gravely some fine point?

I am feeling like the complete moron.

I do know that you are stating some important point, I know that I do not hold silly notions about what I am saying about structure/usage/inner working, but I cannot begin to get your point,and I cannot see how to “synthetize” both our outlooks ( not as in “making” but as opposed to “analyse”, as in "making it a non-contradictory whole)

Anyone think she/he understand without any misty areas, the finer point of what I try to state, he/she is quite welcome to state it better than I did.
I will see if I recognize it “in depth”.

Or is it a case changing appelations just to differentiate the different way “pulling” ( loading) can be applied ?
Then I do not see the need for a second name, to me source of confusion: saying sheet bend in a lapp loading pattern would have been quite enough.
I cannot envision calling my upper limb one name when it is pulling and another name when it is pushing.
Well I learned something today, so a day not wasted.

Structure to me is what you get back if you “undo” gently the knot so has to lay it flat on a plane with all the crossings there, not one missing, not one too much.
I do not see, since loading cannot change what the crossing are ,how I will not get the same “laying flat” knot I had before loading.

If after loading the sheet bend ( and calling it lapp bend) I can get , by laying it flat again the same disposition with which I begin with : then in my view it is the same knot, unchanged.
To be another “structure”, another knot, at least one crossing would have to be “changed”. Frankly I cannot see how that can happen.

See here http://tinyurl.com/7djrb (nomenclature of the extremities )
I do not see the “structure” changing whether I pull on :
A & C or A & D or B & C or B & D or AB & C or AB & D or CD & A or CD & B or ABCD

I am quite ready to say that the “pressure points” , the “happening” inside the bend , are quite different in each of these configuration of “pulling on the extremities”.
They are the same knot structure, working differently under different loadings

Whether you are lying quietly in bed or running full tilt in the woods does not change your structure on iota ( unless accident !).
it only change what your struccture is doing, your inner functionning,( rest versus effort , base cardiac and respiratory rythm, tachypnea, hearth beating faster, glycogen and hormons being released…
Internal functionning is momentarily modified. Structure is left “unchanged”.

A metaphore : structure / inner functionning === genotype / phenotype
genotype : the entire genetic library contained in the cells
phenotype : the “observable” result of the genotype being “externalized”, being made manifest in the outside world.

With same genotype some quite different phenotypes can get expressed :

  • thermal shock on drosophila and you get some queer wings
  • temperature gradient on reptilian egs and you get a different repartition of sexes
  • age or demographic modification and some fishes change sex

Same genetic structure , different inner functionning.
Say that the driver, different driving styles.

Structure === say “a watch” ( not ticking yet)
Usage : as in reading the time, measuring time intervals, using as compass, using as reflecting surface to send “sun signals”…
Inner functionning as in “this watch” how it ticks, what move, how, in which order, what happen if you modify this part…" say a mecanical watch non self-winding , a self-winding one and an electric one with hands : same usages but not same structures and not same inner functionning.

If you use it"in the manner of a good family man" as goes the judiciary saying, the structure of the house is not changed by how you use it .It is not change in “its building” because you put the lights out early or late, or because you leave it “empty” during your vacation, or invite some friends to stay for a few days.

In my world “naming” is rather for structure and then you “qualify” it for function, or for usage.

house : maison ( M. as of here )
M. de retraite : house for the retired
M. de santé : house for the ailing
M. d’arrêt : a house to put under arrest ; a jail, a prison.

Sorry if it “read” confused, I feel confused and making an ass of myself.

38

Usage and meaning again ( Hi Brian_Grimley)

Just to insist on how quickly misunderstanding can happen when “comparison of knots are done”, particularily when having “strangers” like me coming in.

EQUIVALENT ( Webster Thesaurus : equal, duplicate, identical, indistinguishable ) :
What I find i my Cambridge dictionnary do not reaaly satisfy me : “having the same value , purposes, qualities”

I do not think that “having the same value” “having the same purposes” and “having the same qualities” are interchangeable statements.
And as far as “phenomenal” as opposed to “ideal” is concerned with knots , the more so.

Just saying “these 2 knots are equivalent to each other” is to open the door to confusion, in my view.
equivalent “in/on which comparison plane” must be stated to alleviate a bit this confusion.

SIMILAR ( Webster Thesaurus : akin, alike, analogous, comparable, corresponding ): looking or being almost but B]NOT EXACTLY[/B] the same.
looking and being are quite different concept to me ( just as what you look and your sibblings looks, and what genetics you each have are quite a different things).
To me it is not at all the same thing to say “they ARE the same” and “they LOOK the same” ( and much less they works/fucntions the same")

SAME ( Webster Thesaurus : identical, selfsame, equal, equivalent, comparable):
Not different

SUPERPOSABLE ( in French if you say : this is superposable to that then : this = that , point to point correspondance)

ANALOG / ANALOGOUS ( Webster Thesaurus : akin, alike, comparable, similar, undifferentiated, ) :
Something which is similar OR which can be use instead of something else

IDENTICAL ( Webster Thesaurus : selfsame, equal, duplicate, identic, indistinguishable ):
exactly the same OR very similar
To me since [similar = not exactly the same] that statement above is non-sense.

I will keep only [exactly the same]

COMPARABLE ( Webster Thesaurus : like, alike, corresponding, parallele, similar, undifferenced, uniforme):
As good as, similar
Shed nothing more that “similar” then.

ASSIMILABLE TO ( Webster Thesaurus : identification ): in French is A is “assimilable” to B it means you can indifferently use one for the other
Assimilate : to make similar.

All this to show that precision and absence of ambiguity is not the forte of these words, doing like the snake biting its own tail!

If someone believe the above they can use anyone of these words in place of any of the others ! Not so in my mind map.

Not reassuring at all for clear interaction.
Better not go the short way : not one word but the lenghty way : a full expression of the meaning to be transmited, I think.

One day I will learn to limit myself with just casting knots and not trying to understand anything, beyond how to throw them, sort of keep the hands and leave the brain well enough alone!
Just about to go and make some splices, to soothe my nerves. :slight_smile:

39
I still have the feeling I do not understand you question, ...
Yes, well, your image referred to below shows that!
I cannot understand how Sheet Bend can become Lapp Bend just by virtue of different loading. Am i misunderstanding gravely some fine point?

I am feeling like the complete moron.


Finally, we agree. ;D

I asked: I’m trying to understand anatomy vs. physiology/function, which I took
to be something of a distinction between form w/o loading and that WITH loading!?

If after loading the sheet bend ( and calling it lapp bend) I can get , by laying it flat again the same disposition with which I begin with : then in my view it is the same knot, unchanged. To be another "structure", another knot, at least one crossing would have to be "changed". Frankly I cannot see how that can happen.

See here http://tinyurl.com/7djrb (nomenclature of the extremities )
I do not see the “structure” changing whether I pull on :
A & C or A & D or B & C or B & D or AB & C or AB & D or CD & A or CD & B or ABCD


Hmmm. Firstly, for some reason you have added a black image here, when in fact
my words clearly say ONE image, with different ends to be loaded. (Why show a
“Left” (Opposite)-Sided Sheet bend? I expressly say “Same-side”. How is the bend
derived from Eskimo Bwl? --wrong orientation (by 90deg. angle): rotate clockwise, …)

It is very simple: I want to know how you regard the structure/thing you show in
red & blue, a Sheet Bend (maybe!) all of whose ends/“limbs” (we need a neutral term)
run out of sight, loading unknown, CONNECTION unknown (eye legs of a loopknot
e.g. connect themselves). Well, I guess we need ONE color (else there is the implication
of connections/non-connections).

How does this quite general, unspecific entity fit into your scheme?
It becomes the Same-Side Sheet Bend loading AD, the Lapp Bend BC, the Bwl A-BD,
the Dutch Bwl A-BC, the Meshknot ABCD, the Becket Hitch A-CD,
and so on (w/needed material dis-/connections).
And in the Lapp Bend case, the actual geometry is markedly different in that A will be
drawn sharply back, folded. (Though one can dress & set a Bwl somewhat like this.)
(As you can see, this General-Meshknot form if fertile with possibilities!)

[b]Structure[/b] is left "unchanged".
--my bolding. Is it pure [i]structure[/i] that one has in the situation above, where the connections & loading of "limbs" are unknown/irrelevant? This is what I'm asking, for I see some need or desire to want to talk about knots at this general stage--which we might decide is at some level removed from our locus of "knot".

–dl*

40

This is for me hopeless, I think I cannot conceive of where you are trying to lead my thinking. I feel I am falling ( and failling) from thing misunderstood to thing totaly un-understood

your image referred to below shows that!

http://tinyurl.com/869ly was answering why left Bwl and Eskimo Bwl are not the same, just as I understood you asked.

to understand anatomy vs. physiology/function,...distinction between form w/o loading and that WITH loading!?

In my mind:
structure imply without loading : laid flat on an horizontal plane , no dressing, no setting

As soon loading is ( or even dressing and setting ) at play that is “physiology” not anymore basic “anatomy”

you have added a black image here, when in fact my words clearly say ONE image, with different ends to be loaded. (Why show a "Left" (Opposite)-Sided Sheet bend? I expressly say "Same-side". How is the bend derived from Eskimo Bwl? --wrong orientation (by 90deg. angle): rotate clockwise,

Black image was for me as I did the drawing like that and did not feel like doing it again so discard the left, black image.

Why an opposite sheet bend : your first post ( under as quote) did not specify and you agreed on the picture I sent.
.
Yes the derived bend is being “derived” so not in same orientation as in the eskimo Bwl. That is why I prefer “images” to words in such case.

(Consider the Sheet Bend oriented so that the bight tip is up (N =north, 12:00), its legs thus South; the looPart ties to this by entering the tip crossing Under, turning leftwards (West) and crossing Over the left leg and then goes back around Under the bight legs, to continue then in anti-clockwise turning to cross Over the bight leg, Under the earlier set part of itself, and Over the left bight leg (pointing thus NW) ? Call the four ends, starting at the top (N) and moving anti-clockwise as A-B-C-D. The Sheet Bend would be defined as tensioning A & D (ends being B&C); the Lapp Bend ... B & C. Do you consider these to be the same knot, anatomically?
Where do you specify "the short leg, side, of the bight ?
the structure/thing you show in red & blue, a Sheet Bend (maybe!) all of whose ends/"limbs" (we need a neutral term) run out of sight, loading unknown, CONNECTION unknown (eye legs of a loopknot e.g. connect themselves). Well, I guess we need ONE color (else there is the implication of connections/non-connections).

Yes it is a sheet bend, the same one you “accepted” in a precedent posts, only remarking it was upside down.

…run out of sight… : it is a sheet bend so only the tails are important and are shown.
I was not speaking here of it as "a component " of a larger stucture, say a BWL, where connection ( loop for example and no change of colour since same rope ) would have to be shown.

How does this quite general, unspecific entity fit into your scheme? ...Lapp Bend case, the actual geometry is markedly different in that A will be drawn sharply back, folded...this General-Meshknot form if fertile with possibilities!)

geometry is markedly different : not to my mind which equate structure = static geometry.

drawn sharply back : yes : inner working, dynamic geometry, physiology to my mind.
I did say that the inner working is different from one loading pattern to the other. I just pulled on the different “extermities”.
When I wrote “loading” it was in THIS sheet bend not on some other structure with it as “component”.

Is it pure [i]structure[/i] that one has in the situation above, where the connections & loading of "limbs" are unknown/irrelevant? This is what I'm asking, for I see some need or desire to want to talk about knots at this general stage--which we might decide is at some level removed from our locus of "knot"

Yes pure structure of sheet bend as whole entity and not as some component.
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.

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. ( only moves accepted are “continuous” ( math sense) as in a very fine and elastic rope . No “discrete” ( math) move : cutting, joigning, flipping as flippping a page in a book to turn it.

My structure is purely staticly descriptive and for “classification”, “discrimination”, purposes only, not for “analysing a knot behavior under loading” or only as a theorical play, trying to see if the suencing of crossing can shed any predictive light upon the “comportement” of the knot ( I tried that with the whole serie of carrick : see here http://tinyurl.com/7ajer if you want to download L&H-Carrick comparisons.zip 660Ko )

Sorry? But I feel that I am at the end of my tether and cannot make my conception clearer to you.
Not trying to change the world of knots, just airing my thoughts, no proselytism here, just seeking to test them.
Laying down my king, board is yours. Cheers.