Author Topic: TENTATIVE DEFINING OF "KNOT"  (Read 33605 times)

Jimbo

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #15 on: September 20, 2005, 10:29:51 PM »
Quote
I found how to highlight your text ...
Code: [Select]
[glow=yellow,2,300]TEXT[/glow]
TEXT

Willeke,

Thank you for sharing "style points" for dressing up posts!

However...

If your computer (and/or browser) is "secure" and you block nasty things like ActiveX, this trick won't work.  The TEXTstill shows, but the effect is gone.

Ditto (i.e. same results) for the [shadow=red,left,300]SHADOW[/shadow] code (That's the button to the Right of G[/b]low).

Another oddity I couldn't work around:  Both the 'GLOW' and the 'SHADOW' codes apparently trigger a LF (Line Feed) before and after they do their business.  Ah, ActiveX!  :-/  That means, even when it did work for me, I have been completely unsuccessful in getting the glowing or shadowed text to appear interleaved with the rest of the text.  YABBC insists on sticking the glowing or shadowed part on its own line.  And of course the posts I made showing that have long since been flushed.

:(

YMMV, of course.

But please don't let that stop anyone from using them!!

Jimbo
(PS: OTOH, the col or codes seem to work (although word wrap will wreck multicolored word tricks like <- that one), and if you add bold it looks a little "pretty"... EG:
Code: [Select]
[color=Orange]Your Orange (and [b]bold[/b]) Text Here[/color]Your Orange (and bold) Text Here.)
(PPS:If you see a "trick" you like in a post, use the "Quote" button instead of "Reply".  Then are all the secrets revealed!)
« Last Edit: September 20, 2005, 10:58:38 PM by Jimbo_The_Kinky »
Thank you all, for everything.  As of 6/6/6, I have changed my password to a random string (which I forgot), thereby assuring that anyone posting as "Jimbo" in the future will NOT be me.  Good luck!!!

Jimbo

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Off-Topic But (Hopefully) Helpful...
« Reply #16 on: September 20, 2005, 11:28:30 PM »
Quote

Yes it is common sense to "begin" with the English language

Bonjour et bonne santé, nautile!

One of the nice things about English is its efficiency.  Eg: "Adjustable Loop Knot" vis-a-vis "Noeud Réglable De Boucle".  Also its adaptability.  Eg: "vis-a-vis" vis-a-vis "compared face-to-face to" and "eg:" vs. "Exempli Gratia"!

But before you accuse me of being an arrogant American, let me assure you I studied Latin, Greek, French, Spanish, German, Sign (both both "deaf-mute" styles and Native American), some Mandarin, and a double-handful of computer languages as well, so I'm trying to reach out here.

In that spirit, and in hopes of being helpful to All, here's Yet Another Jimbo Trick:

If you want to write in almost any language, but post to a forum based on another language, there are a lot of WWWeb pages that'll help.  Here's the one I like best (so far): BabelFish.

I hope this helps.  (I also hope I didn't offend Jacques when I used this site to translate a whole paragraph of Jimbonics!)

Going to Google & clicking on Language Tools may be useful too.

;D

Jimbo
Thank you all, for everything.  As of 6/6/6, I have changed my password to a random string (which I forgot), thereby assuring that anyone posting as "Jimbo" in the future will NOT be me.  Good luck!!!

Nick Wilde

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #17 on: November 30, 2005, 03:08:41 AM »
Such learned submisions, I am loath to lighten the tone with my offering, but being a Yorkshireman I am going to anyway.

"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."

Sorry!  I'm feeling frivolous.

Nick

Dan_Lehman

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #18 on: December 01, 2005, 04:05:19 AM »
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but being a Yorkshireman

Does that include drinking "Yorkshire" tea?  :P

Quote

"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."

What counts as a complication,
and how does one discern deliberateness?
Say that in your pleasant stroll along some beach--maybe as Dee's companion--,
you come upon a grand tangle of cordage:  how will you sort out knots?
Is a kink a knot?

(-;

KnotNow!

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #19 on: December 01, 2005, 06:46:39 AM »
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.  A bend?  A hitch?  A binder?  A lashing?  A knob?.... and then I think he was hoping to get further reductions for "functional yet decorative" "purely functional" and so on.. 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".
ROY S. CHAPMAN, IGKT-PAB BOARD.

Dan_Lehman

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #20 on: December 02, 2005, 01:07:17 AM »
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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 ... ?

Quote
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, Spirits-ually.  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).

(-;

merickson

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #21 on: December 02, 2005, 06:01:37 AM »
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".  

Dan_Lehman

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #22 on: December 02, 2005, 09:39:52 PM »
Quote
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 geometry
between the various enumerated <other_sense> "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>

Quote
But, topological considerations are not a sufficiant criteria.

Not sufficient, nor even necessary!  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!?

Quote
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 scaled.

Quote
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> (X = Bwl.s, Overhands, ...) bends seem problematic.  In these,
the actual knotted/entangled parts are disjoint/separated by indefinite amounts
of material.  (Chisholm also has a notion of nub, but what's the nub of the
Sheepshank?!)

Quote
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 intent or other external aspects.  (And certainly
not everybody will be able to do anything!)

--dl*
====
« Last Edit: December 02, 2005, 09:57:19 PM by Dan_Lehman »

Jimbo

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #23 on: December 03, 2005, 11:34:08 PM »
Quote
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?)
Thank you all, for everything.  As of 6/6/6, I have changed my password to a random string (which I forgot), thereby assuring that anyone posting as "Jimbo" in the future will NOT be me.  Good luck!!!

merickson

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #24 on: December 05, 2005, 02:33:22 AM »
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.

Willeke

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #25 on: December 05, 2005, 01:41:22 PM »
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

« Last Edit: December 05, 2005, 01:42:41 PM by Willeke »
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nor what a clever person can do with simple tools." - Ian Fieggen

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nautile

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #26 on: December 06, 2005, 01:07:42 PM »
  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 :( 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 WHAT this thing is first and foremost 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""how it works" as classification criterion
                  
                  - Structure was to be only one of many things ,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...

nautile

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #27 on: December 06, 2005, 01:13:52 PM »
...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" :-) 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
      A polygonal curve in 3D
 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)

Dan_Lehman

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #28 on: December 07, 2005, 03:53:10 AM »
Help!  I'm swamped beneath another Nautilevanche of ideas!!   :o
;)

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?  ::)

nautile

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Re: TENTATIVE DEFINING OF "KNOT"
« Reply #29 on: December 07, 2005, 07:28:27 PM »
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 :

- - Dutch bowline : http://www.realknots.com/knots/sloops.htm
left hand bowline     in   http://www.layhands.com/Knots/LeftHandBowline.jpg  or in budworth "the book of knot" Fig 13Bowline p 49  

compared to

- - Sheet bend ( left-handed) as you say  : not same lay as ABOK#1432   and   http://www.videos.sailingcourse.com/images/sheet_bend_left_hand_X.jpg  

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 ?  :-)

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 :-)

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.:-)

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.