Club-Bend, Rosenwind-Bend, crossed Club-Bend, crossed Rosenwind-Bend

[Edmund Berndt]

Hi X1
Sorry, I made a mistake complete eye knot is wrong. Complete overhand knot is right. I corrected ist just now.
I'll make pictures of all. 

[Luca]

Hi X1,

  When I started to re-tuck the 8 possible different Reef family of knots "bases" through their central openings, I thought that I was going to tie 8 different bends. Noope !  They were only 7 ! ( Marks s A, Mark s B, Alpine Butterfly, ABoK#1408, Hunter s, Ashley s, Shakehands X ). The reason for it was the symmetry of A1b and A2b bases... which generated the same knot, the Alpine Butterfly bend. So, since that time, I am very cautious about calculating the number of bends, in vacuo ! Show me the bends !  I hope that, by now, you have found a camera somewhere...

As far as the camera:in my land is said "Hope is the last to die!",then I firmly believe that you have all rights to continue to hope ..



http://igkt.net/sm/index.php?topic=3929.msg26471#msg26471

I think that the pictures posted by Edmund (maybe not perfect, but with the zoom tool one can partly remedy : the only "unknown" is the darker rope , but I think there is no reason to doubt that his knot's nub is the same of the others there represented, and in the same position) are sufficient to show what he speaks: 8 different fixed functional end-loops from a single asymmetric knot's nub(or from a single bend, the only one that I should show , but  i will show it  to do? Agent_Smith, yourself, and then Edmund,you all have already shown this only bend  I have spoken about(x 3 versions)(perhaps I should to show  the other 16 loops (at the end is a talking about loops here,and I admit that I have no all tied, not about bends)) .-(Edmund, I think that some of the images posted by X1 are sufficient to show that the twisting / crossing of the tails in the other direction can be made ​​in the context of the knot that you present, and that there is another combination of interlinked Overhands that you seem not consider.About #1425:the totally reversed version is not a real Hunter's,but a "falsely tied Hunter's/false Zeppelin" bend with crossed tails,that seems to me to be the supersymmetric bend mentioned by you too.)-
Now that I have seen and understood the pictures by Edmund, I believe that this can be easily applied to the other two versions of the knot's nub:as said before, I have not actually physically tied all the combinations that I mentioned, but it seems to me that there are no unforeseen circumstances (such as 7bends against 8  reef family combinations) here, just because nothing is symmetrical in this case(well,the two links are Overhands);I think that this kind of unespected results appears when there are symmetries in the knot's nub (maybe sometimes  "hidden": the Butterfly, for example, is a knot a little bit special, one can say that is not symmetrical, but in a certain sense it is not even completely asymmetric: I find that it expresses its symmetry in a somewhat unusual manner: one way is perhaps because of the fact that it can be obtained from two different  Reef family combinations as mentioned by you , the other is, as for more symmetrical knots in shape such as # 1452 and # 1408, the fact that the totally reversed the version is exactly the same of the original).

                                                                                                             Bye!

[X1]

   I think that the pictures posted by Edmund ... are sufficient to show what he speaks: 8 different fixed functional end-loops from a single asymmetric knot's nub

   I thought that the thread was about bends !  ( Read the title...) Loops or bends ? Make up your mind guys, because they are not the same thing, as we all know...There are many ways to turn a bend into a loop, and vice versa ! There is no one-to-one correspondence, but there in no mention of how exactly those bends are turned into those particular loops - and why they are not turned into other possible loops.

8 different fixed functional end-loops from a single asymmetric knot's nub 

   I can not see that... Where is this one knot ? What is the operation that turns it into each of those 8 bends / loops / whatever ? Are those the only possible ones ?
   I have shown a certain "base", in all the possible variations of it, and I have defined a precise knotting operation ( the re-tucking of the working ends through the central opening of this base ), that is sufficient to generate those 7 knots - and not any else. And I have taken pictures of those knots, although most of them were already known. So, I guess have the right to ask /hope for a presentation less ambiguous than this, and more general. Moreover, I ask/hope that somebody would figure out a general way to generate all the interlocked / interlinked / interpenetrating knots, starting from somewhere, and applying a certain well defined procedure. Then, we will see if this method produces new knots, and how it relates the already known knots to each other.
   I have not yet understood the method used in this thread - if there is any. The two knots that were presented in detail were shown to be already known knots - moreover, those knots were shown to be generated by a well-defined procedure, and were shown to be related, and it is shown how they are related, to the other already known knots. Of course, the generated knots continue to be named by their standard, common names, while, in this thread, I see new names used for old knots - but not one single new knot ! 
   The pictures are not the only means to represent knots, and it might not be the better either. One can use the KnotMaker program offered free in the web, which takes much less time to learn how to use than all those endless discussions about knots that are not shown, or they are not even tied...
   Show me the knots !   

[Edmund Berndt]

Here are the bends in T-shape

[Edmund Berndt]

the next

[Edmund Berndt]

Sorry, Im still working on the bend Ashley 1453. I think that this picture is not right. I allready tied Ashley 1453 as shown in the book, but then I had to tie this knot mirrored getting the same sight of the overhandknot in the white blue spottet rope. This procedere is necessary for comparing the bends.

The problem is that this bend as shown in the picture could be transformed into Ashley 1452 by changing just one fixed end of one rope.

I' still going on...I proved it. Ashley 1452 and 1453 are the same. Thy can be transformed into each other. The diagramm pictures are o.k.
This knot e.g. bend could be strained from every side.

[Luca]

Hi X1,

Yes, the thread starts from a speech about bends, but Edmund, starting with its first post, puts the "seeds" to give birth to a speech about the end-loops that can be generated from the bends that he presented: I believe that the most value of his speech lies here, rather than in the bends that he presented (who knows how many people already made the Mark's bends in the days when they learned the most popular interlinked overhand bends, and who knows how many  people have made them before Agent_Smith presents them in this forum(maybe I'm too fundamentalist to follow what time ago you have explained to me in this thread)).
I believe that, at least with regard to Mark's A X2 bend, Edmund has done a systematic and complete work(maybe not presented in a perfect way),with respect to render how many different end-loops can be obtained using the knot's nub of the bend as the basis:if one of the Overhand links has a tail end "A"  and another tail end "B", and if the other Overhand link has a tail end "1" and another tail end "2", "melting":1)end A with end 1
                                                                           2)end B with end 2
                                                                           3)end A with end 2
                                                                           4)end B with end 1,                                         
all multiplied x 2(the standing parts possible in respect of each of these four combinations) = 8.
Which in this case correspond to 8 different working  fixed end-loops,given the asymmetry of the knot, but not only(one can think of doing the same with the asymmetric Sheet bend, but the "trick" in this case does not work, because,after getting:a standard Bowline,a left handed Bowline , an Eskimo / Inuit, and then the other version of the Eskimo / Inuit, changing the Spart of each of these knots one will get 4 sliding loops).
I apologize if  once again  I have not posted pictures or diagrams, but do not have much time these days;however the base-knot of which we speak is here shown several times(now maybe we will have fun everyone to find out how many loops are obtained from the bends obtained by retucking the other combinations of the Reef knot family using the method by Edmund).

                                                                                                                      Bye!

[X1]

   Thank you Edmunt,
   All those bends are well known - something that should not take us by surprize, because they are very "simple" knots. However, one can never be 100% sure, because we do not have a well-defined and exhaustive method that would generate all the possible interlocked overhand knot bends. The somehow intuitive procedure described in the beautiful book on symmetric bends by Roger E. Miles, is heuristic - it does not even attempt to enumerate all the possible symmetric bends. Since the publication of this book, we have met a few interesting bends, that were not included in it.
  So, one thing is the particular knots, and another thing is the method that can generate them, by some transformation of something even simpler. I have not been able to understand your method, but this may be entirely my fault. When one is accustomed in one particular view of some common, familiar things, he always runs the danger to feel comfortable in his little "secure" corner, and become lazy...
   
   P.S.
   I do not say that the all the asymmetric bends would be, due to this asymmetry of theirs, less secure than the symmetric bends. On the contrary, I question this belief. (1). However, I have many reasons to argue that they would be less strong knots. See the attached pictures of the most simple asymmetric interlinked-overhand-knots bends. 
   1.   http://igkt.net/sm/index.php?topic=3793.msg22203

[X1]

...a systematic and complete work... with respect to render how many different end-loops can be obtained using the knot's nub of the bend as the basis
...the base-knot of which we speak is here shown several times

   I have not been able to understand your method, but this may be entirely my fault.

   I can not see that... Where is this one knot ? What is the operation that turns it into each of those 8 bends / loops / whatever ? Are those the only possible ones ?

[Edmund Berndt]

Hi X1

My so called "Club Bend" is not identical with your bends shown in the post.
The feature as I think wich is missing is that the loose ends don't came out from the nub of the bend togehther in line.

[X1]

My so called "Club Bend" is not identical with your bends shown in the post.

  I did nt say that it is identical- it is not even "similar", whatever this might mean. I wonder where you had imagined you read this...   I only said that it is a asymmetric bend (*)- which can become symmetric, if one crosses its tails the one or the other way. Then, the Club bend is transformed into the one or the other form of the two Shakehands bends, the Shakehands I ( the "common" Shakehands bend ) and the Shakehands II - ABoK#1453 bend. I had mentioned those two simple interlinked overhand knots bends just as examples of asymmetric bends ( like the Club bend ) which, although they might be less strong( brake earlier), they might be more secure ( slip less ) than the symmetric bends.

   P.S. 2013-2-17
   As noticed by Luca, the "Club" bend is identical to what I have called " Shakehands -X " bend (shown at the attached pictures ), where the tails are not crossed ( hense its name : Shakehands -X = Shakehands with non-crossing tails ).
   * Dressed in the form of the Shakehands -X bend, as two interlinked shape "8" overhand knots, the "Club bend" is not asymmetric - although its underlying symmetry is not evident at the first sight, when it is presented the way it was presented in this thread, with the overhand knots in their asymmetric common / usual shape.

[Edmund Berndt]

Hi X1

How do You define interlocked overhand bends?
The 8 interlocked bends have the feature that the are locked together both tails also were locked by the both overhandknots. All this happens in the most easy way as possible. ThisI think is a distinct family of knots.
Next variation is twisting the tail. But this is I thik is the next step.
You started the evaluation from areef knot base.
I started after a lot tangling around just from one overhand knot.
Of course there are a lot of more variations possibel. The question is how much?

[X1]

How do you define interlocked overhand bends?

   Good question !  I was under the impression that I had answered it long ago - but just the day before yesterday I had read something that has awakened me. ( I hope it will be published soon, and then we will talk about it.)
   So, till this day I was just considering the topology of each link of the bend. If each link/part was topologically equivalent to the overhand knot, the knot that was composed by those two links, inter-connected in no matter which way, I defined as an interlocked/interwoven/interpenetrating/interlinked overhand knots bend.   

I started ... just from one overhand knot.

    NOW I see your method !    ( Well, at least I hope so...)
   If you had just said : " I start from the one link of the bend, in the "usual / common" shape an overhand knot can have, and I see how the other link can be linked with this..." , I would had understood it right from the start.
   When you say :" I start from an overhand knot..." , I am confused - bacause both links are overhand knots already- so how one can "start" and "finish" at the same point, without its path/argument be considered as cyclical ?  You speak of the "overhand knot" as a geometrical figure - it is not. On the contrary, I believe that this particular geometric shape of the overhand knot is responsible for great misunderstandings - like the current one !  I do not like this shape at all - unless it is resembling ( it is a portion of ) the symmetric shape of a trefoil knot - i.e. unless it has a three-fold point symmetry. 
   So, my current understanding of what you are saying is this : You start from the one link of the bend, in this particular shape an overhand not can hace, and you leave it unchanged/fixed till the very end. Then, you try to figure out how you can penetrate this link with the working end of the second link, keeping in mind that this second link should not get itself more entangled than an overhand knot.
   I am afraid that this method, however simple and plausible might look at first sight, will not generate all the possible overhand knot-based bends. You will need some additional ideas, that will complicate it much more. Another disadvantage is that it can not distinguish, in advance, the symmetric from the non-symmetric knots. However, I can not be sure about its effectiveness or not - so I will wait and see the outcome of your efforts, with great interest.
   Now, if you generate a knot that it is already well known, it would be better to label it with the already known name. If this method will produce all the known overhand knot-based bends, then the labelling of all those knots with new names, indicative of the their particular place in the greater scheme where they will  belong, according to this method, would make sense, indeed  ( although, and unfortunately, the already given traditional name will not change - nobody calls oxygen by the numbers of protons, i.e, with their place in the periodic table of elements !  )
   

[Dan_Lehman]

Sorry, Im still working on the bend Ashley 1453.
I think that this picture is not right.  I allready tied Ashley 1453 as shown in the book,
but then I had to tie this knot mirrored getting the same sight of the overhandknot in the
white blue spottet rope. This procedere is necessary for comparing the bends.

The problem is that this bend as shown in the picture could be transformed
into Ashley 1452 by changing just one fixed end of one rope.

I' still going on...I proved it. Ashley 1452 and 1453 are the same.
They can be transformed into each other. The diagramm pictures are o.k.
This knot e.g. bend could be strained from every side.

Firstly, Ashley's #1452 & #1453 are distinct knots --not "the same."
(And I'm going to assert that they are not topologically
the same, either --but figuring that can be tough!)
In #1452, the tails exit adjacent to each other, not in opposite
sides as in #1453; the SParts enter opposite the opposing
overhand component's tail's exit in #1452, not #1453.

Secondly, tying #1453 is tricky, debatable : it's clearly
a potentially symmetric knot but getting the tails' crossing
to lie symmetrically is difficult.

There is a #1452 orientation shown by Ashley as a lanyard
knot #781 & #783; and loading #1452 in reverse can be
manipulated into . . . #1452 itself (ditto for the butterfly
and I'll surmise various other such knots).  As remarked in
some other thread here, the capsizing --in some in-use case--
might not go evenly, and the #781/2 form can just spill
--a startling discovery for me, who'd thought it a candidate
for an offset, abseil-ropes-joining end-2-end knot!


--dl*
====

[Edmund Berndt]

Hi,
It is not so tricky to achieve the loos tail symmetrical .

Of coure the lanyard knots are like As 1452.
Do You think that our Knot*s Admiral Ashley investigated all his collected knots for theis properties?
If You define that 1452 and 1453 not the same knots or bends than we have 9 interlocked overhandknots, not only 8