The shape of a knot after dressing-before loading : does it determine the knot ?

[Tex]

WHAT "that one" ?  I think that this is a fragment of another post of another thread, which fell here by accident... Off topic, and off everything, as far as I can tell from those fragments...

No xarax, that was not from another thread, it was a direct response to your own post two posts up.

[Mobius]

The Munter hitch / crossing knot is an interesting form that can be loaded on one strand of the other, transforming itself in the process, but nevertheless remain stable.

Indeed. It took me ages to see it, however the Bowline I have bee working on does have a Munter hitch shape to it's turNip. It was hard to see since the tying method doesn't use a Munter hitch and depending on how the loose knot sits it can look like a 'pretzel'. I have done quite a few trials on it and will share with everyone in due course.

Cheers,

mobius

[Tex]

   Please, elaborate a little more... I confess I had not understood a thing !  I thought it was a comment about the Munter hitch !

You mentioned the Scott and ampersand bowlines as an example of topologocial equivalents.  My post was a tangent, and I probably should have quoted yours, but it was a tangent related to the discussion, and this is a tangent of that.  Anyway, it was a fun and certainly not obvious (to me) thing to see, so thanks for sharing that.

[alpineer]

1)  If two knots are topologically equivalent then both knots are 'the same', especially if one knot is deemed to easily capsize to the other. Therefore there is not a good reason to use the name "Mobius Loop" when it is the same topological knot as a Butterfly Loop, and it can be capsized to Butterfly Loop. The same viewpoint was expressed about the Farmer's Loop and the Plait Loop recently, so this idea is not without supporters.

No, I have never expressed the opinion that, because the Farmer's loop and the Plait loop can be transformed topologically one into the other, they are the same . That's a misinterpretation of my statement "Probably better used in it's ABoK #1054 Farmer's Loop form". I made that statement for two reasons. 1) to see if anyone, including xarax, had noticed the relationship between the two forms, and 2) suggest that IMO the Plait loop has no advantage over the Farmer's loop.

[alpineer]

Even now, your language is NOT precise, to my knowledge of this language... What does this " solely " means ? I can read it as " They ARE the same, but not only because..." ( meaning that this is not the sole / only reason, there are also other reasons for this "same-ness" ). The sentence I would had understood, is : "The Farmer s loop and the Plait loop are not the same, although they can be transformed topologically the one into the other ".

I see your point and have edited above.

I have a hard time reading the page-long writings of Dan Lehman

You and me both.

   I understand that you have not understood anything of my long post, with the MANY advantages, IMO, I had described / explained, a few days ago - and I will not repeat my arguments.
   Simply I have to point out that you should not compare two different things, an in-line loop to an end-of-line loop.
   If you want an in-line loop, stick to the great Butterfly loop. I wanted something else...

Not true. I've read, and understood, all of your arguments and thanks for not repeating them. Who says the Farmer's loop is only a inline[sic] loop and not an end-of-line loop? The Parrot parroting the parroters?
 

[Tex]

Not true. I've read, and understood, all of your arguments and thanks for not repeating them. Who says the Farmer's loop is only a inline[sic] loop and not an end-of-line loop? The Parrot parroting the parroters?

I have trouble seeing how any loop can be an called an inline loop and not an end-of line loop.  Maybe I misunderstand the use of the word "in-line", but to me, any loop that gets a habit of being tied in the middle of a rope is VERY likely to end up loaded by the two eye legs and one parent leg, with the 4th leg left slack and having no effect on the knot, just as a tail would be.  This is not different than how an end-of line loop is loaded.

I can certainly understand an end of line loop that cannot tolerate end-to-end loading and thus wouldn't be very robust as an in-line loop, but the other way around doesn't make much sense to me.

[xarax]

Who says the Farmer's loop is only a inline[sic] loop and not an end-of-line loop? The Parrot parroting the parroters?

  Perhaps I was parroting parrots, indeed, in this matter. I have never seen a picture of an end-of-line Farmer s loop, with both ends adjacent and pointing to the same direction - and the same was true for the Butterfly loop.
   To me, the Farmers loop was always an example of an amorphous structure - what you had described as "an octopus", but with tangled legs !  And what I describe as looking like the farmer s, or the farmer cow s, you know what !  And the tying method shown by Ashley was an example of a BAD tying method, which conceals, and not reveals, the structure of the final knot. A "magic trick", which tends to persuade people that knot tying is such an advanced rocket science, so the only thing they are allowed to do, is to parrot the biblical script of Ashley...
   Now, if you want to call the Plait loop as " end-of-line Farmer s loop", do it ! You just make the mistake of using the same name for two altogether different, geometrically, structures - but do not bother ! You would nt be the first one, you know !  We have so many knots named by so misleading and wrong names...

[xarax]

  For another example of an "in-line loop", and a topologically equivalent, but geometrically / structurally, very different "end-of-line" loop, see :
   http://igkt.net/sm/index.php?topic=4680

[alpineer]

The Munter hitch / crossing knot is an interesting form that can be loaded on one strand of the other, transforming itself in the process, but nevertheless remain stable.

Indeed. It took me ages to see it, however the Bowline I have bee working on does have a Munter hitch shape to it's turNip. It was hard to see since the tying method doesn't use a Munter hitch and depending on how the loose knot sits it can look like a 'pretzel'. I have done quite a few trials on it and will share with everyone in due course.

Cheers,

mobius

Mobius, the knot you're describing is the singular form of the Karash Double Loop, aka the Fusion Knot.   http://en.wikipedia.org/wiki/Karash_double_loop

[Dan_Lehman]

I have a hard time reading the page-long writings of Dan Lehman

You and me both.

Firstly, I'm amused that my posts are regarded
as "page-long" by none other than the keystroke king
(who provides examples in this very thread!).  And re
'trouble reading" (which I take to be "understanding"),
you can try asking questions --the absence of which
makes redress quite difficult, from my side.

Meanwhile, I will now entertain myself by thinking of
y'awl being "you & me both" --conjoined in confusion !!


 

[Dan_Lehman]

DL I think you read my comment on point 1 in the reverse of how I meant it.

??!
Mobius asserted:

1)  If two knots are topologically equivalent then both knots are 'the same',
especially if one knot is deemed to easily capsize to the other.

to which you said that this should be uncontroversial.
How else is this to be understood?

I am not amused by saying that TIB knots are equivalent to the unknot,
a tired and useless argument, even as a straw argument to be countered,
in my opinion.   The mathematical notions of knots, knots should  have no
free ends either.

Yes.  And how to you go about assessing topology?
I put the ends out of play --and not having them is one
way to do this(!), but leads to issues of how ..., e.g.,
with the bowline and how one would fuse ends
to get mathematical purety (it matters how the tail
gets outside of the eye).

If you can untie a knot then ...

... you're doing something outside rules of assessing
topological equivalence, no?!  But I think I'm seeing
a/the problem with TIB, in that my "loaded tangle"
idea of *knot* would not equate such things, but have
the 4 ends of end-2-end/eye-knots running outside
of the "cookie cutter" boundary and inaccessible to
manipulations to see about equivalence.


--dl*
====

[Dan_Lehman]

But, wait, we are past the fundamental question :
What is a *knot*?
IMO, its an entanglement of cordage WITH specific loading.
(So, a bowline/(a/b/c/d) / sheet bend-a / sheet bend-b/ net knot / becket hitch
though looking --by helping hand of artist-- identical in the
cookie-cutter/all-ends-run-out-of-image-circle view (of the
"entanglement"), they are differentiated per loading (which
has greater & lesser effects on respective geometries).


--dl* (Who thought he had VERY "same" URLs, elsewhere ... !!)
====

If I understand you correctly,

I think that you don't.

I don't mind the a/b/c/d idea as it makes naming knots based on shape
 and load a much more useful approach.

I was quickly tossing in placeholders for common
names of bowline variations "left-handed/cowboy",
"Eskimo", and so on.  But they would have a loading
profile of an *eye knot* (nb : it might be part of this
system of understanding that there is no "eye" in the
system (though that might be a good way to explain
the equal loading of (nearly) parallel ends! (Think of
joining a short mooring line from the port cleat to a
like-sized tow line that is tied to the starboard cleat,
of a barge, and the joint has the structure of a
bowline.  (Well, one can regard the barge as
effectively completing an *eye*, but ... .) )

EBDB Bowline - implies the normal standing part (SPart) and eye loading of the knot only
EBDB (T) Bowline - implies the same knot shape as above, however someone has looked at loading the tail
EBDB (R) Bowline - ring loaded version
EBDB (E) Bowline - end to end loaded version
EBDB (4) Bowline - end to end and eye loaded (could be 3 instead of 4 I suppose) version
.
etc if there are more ways to load.

And here I'll say that one isn't really dealing, in *knot*
terms, with a "bowline" : there is this entanglement,
and some loadings are consistent w/eyeknots, some
are ... with end-2-end knots.  (Hmmm, Ashley's stopper
is a bowline appropriately collapsed & loaded,
but that brings in some *ends*, fused into a segment,
and bursts my cookie cutter boundary.


--dl*
====

[Mobius]

1)  If two knots are topologically equivalent then both knots are 'the same', especially if one knot is deemed to easily capsize to the other. Therefore there is not a good reason to use the name "Mobius Loop" when it is the same topological knot as a Butterfly Loop, and it can be capsized to Butterfly Loop. The same viewpoint was expressed about the Farmer's Loop and the Plait Loop recently, so this idea is not without supporters.

No, I have never expressed the opinion that, because the Farmer's loop and the Plait loop can be transformed topologically one into the other, they are the same . That's a misinterpretation of my statement "Probably better used in it's ABoK #1054 Farmer's Loop form". I made that statement for two reasons. 1) to see if anyone, including xarax, had noticed the relationship between the two forms, and 2) suggest that IMO the Plait loop has no advantage over the Farmer's loop.

Ok, fair enough I probably misinterpreted your statement because, "Two topologically equivalent knots are not identical ! ", which I thought was written responding to your post. That put the idea in my mind that you were thinking that the knots were 'the same'.  My mistake, sorry, so maybe nobody thinks in terms of 1) then?

Fixed up my first post in this thread to reflect alpineer's comment above.

Cheers,

mobius

[edit: added the last sentence]

[Mobius]

The Munter hitch / crossing knot is an interesting form that can be loaded on one strand of the other, transforming itself in the process, but nevertheless remain stable.

Indeed. It took me ages to see it, however the Bowline I have bee working on does have a Munter hitch shape to it's turNip. It was hard to see since the tying method doesn't use a Munter hitch and depending on how the loose knot sits it can look like a 'pretzel'. I have done quite a few trials on it and will share with everyone in due course.

Cheers,

mobius

Mobius, the knot you're describing is the singular form of the Karash Double Loop, aka the Fusion Knot.   http://en.wikipedia.org/wiki/Karash_double_loop

Thanks for pointing me to this. I would have hated presenting a new knot that wasn't really a new knot, after all the time I've spent on trialling mine.

I could be wrong, however if I correctly tied the singular Fusion form (tied the double version and collapsed one eye, correct?), I don't think it is my knot. It does look a little like my bowline, though the collapsed eye version I tied of the KDL is not post eye tiable (PET). How can the Fusion or KDL be PET if you start from a Figure 8 Loop (not PET, as we know) and add twists?

My bowline is PET and the gamut of other acronyms, so it isn't topologically equivalent to a Fusion Loop.

Cheers,

mobius

[xarax]

my posts are regarded as "page-long" by none other than the keystroke king (who provides examples in this very thread!). 

   Thank you, my keystroke Queen   ! I have to inform you that the "King s" ratio of K / W ( the number of knots tied, with PICTURES of them, divided by the number of words blah-blahed in posts ) is almost infinite times bigger than the "Queen s" ratio.
   I would love to delete, right away, ALL the words I had ever used, in all my posts, if the Forum allowed me to do so, and leave only the pictures of the knots I had tied... Just imagine what will happen if you, too, do the same !