TENTATIVE DEFINING OF "KNOT"

[Dan_Lehman]

... 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  bend, "Eskimo" a loopknot (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 ...

[nautile]

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 ! :-)
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

[nautile]

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

[nautile]

"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

[Dan_Lehman]

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 anatomy vs. physiology/function, 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)

(-;

[nautile]

So, yes, but WHY ... ?
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!?  
(-;

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 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...

[nautile]

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.

[nautile]

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. :-)

[Dan_Lehman]

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.  

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!)

Structure is left "unchanged".

--my bolding.  Is it pure structure 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*
====

[nautile]

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 structure 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.

[Dan_Lehman]

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"

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 LOADING!  
(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 tangled
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 I was thinking of structure, 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*
====

[merickson]

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.

[KnotNow!]

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?

[KnotNow!]

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.
 

[KnotNow!]

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.