The Tweedledee bowline

[X1]

  Good !    Can you show the same sequence of pictures / steps, with ropes, not drawn lines ? If you find it difficult to stabilize the structure, try to use pins, and start from a double loop of a smaller inner diameter, so it remains stable by the stiffness of the material. Beware, because pins are such pointy objects !  Try to take the pictures from the dame angle, perhaps using a tripod for your camera ? A one-colour rope would be better. I like the shadows on the white surface, they give a nice sense of depth.
   ( They are the same thing topologically, of course, but, geometrically, do they look like the same ?    The symmetry of the final knot is lost in your double loop, only to be found much later, at the very end, after the tightening, while on my shape "8" double loop it is retained through out the tying procedure. )

[alpineer]

The Tweedledee is an inside-out transformation of the most beautiful, compact and symmetrical knot, the 2-strand 2-fold Matthew Walker Knot.
。。。

this is interesting 

how do you find this out?

how to perform this transformation ? I tried, but failed.

Hi Ruby,

To see this transformation it's best to use two short (1m) lengths of cordage - giving easy access to all four ends - which is how I've conducted my knot explorations since the late '90s. With access to the ends it's easy to re-route all four ends under the central crossing parts of the Tweedledee to get the MWK. As the eyeknot version will allow you to do this only as a tying procedure I must apologize to you for (unintentionally) misleading.

I found this out working from the MWK. Lamenting the MWK's unsuitability as a climber's tie-on - as I love it's wonderful symmetry - lead me to re-routing the ends and discover the Tweedledee form. I suspect this is how Roger E. Miles originally came upon the knot.
One should now see intermediate and hybrid knot forms between these two extremes.     
     

[X1]

Lamenting the MWK's unsuitability as a climber's tie-on - as I love it's wonderful symmetry - lead me to re-routing the ends and discover the Tweedledee form. I suspect this is how Roger E. Miles originally came upon the knot.

   On the contrary, I am sure he did not come upon this knot that way ! 
   He was just trying to tie all the possible simple symmetric bends there exist - and I know it, because when I re-discovered it, I was trying the same thing, being unaware of his book... and because he has told me so !   
   I remember very well how I came upon it, 3 1/2  years ago - which was by systematically applying an anything but "random" method, as I was accused too easily by some "founding fathers" here... who were unable to "see" the method under the madness  . I simply collected all the symmetric hitching tangles, and tried to connect them one-to-one in every possible way. I started from the shape "8" overhand knot, the fig.8 knot, the Clove hitch, the double overhand knot / Strangle, the Constrictor and the Pretzel ( which is less symmetric than the others) - and I had connected each one of them to each one else, in every symmetric way I was able to figure out. That is, plain dumb, systematic work, that does not need any imagination to be accomplished ! Of course, the most interesting cases were the symmetric ones, where the two links were identical. The particular knot, the Tweedledee ( I had called it the "88" bend at that time, for obvious reasons ), and the somewhat similar topologically but completely different geometrically Oyster bend, were rather easy to tie. I remember that the problem was how to keep each link in one piece, by encircling/connecting the curved segments of the rims of the two bights to the straight segments of the continuations of the standing ends and the tails. It is exactly the same rationale I follow in the tying method I have presented, probably because it has been imprinted in my brain then, right at the start, and old dogs do not learn new tricks !
    By a series of unfortunate events where I was as responsible as many other members of this Forum, I had deleted the original posts, so the description of the original ideas was lost. From this time, I keep in my files some relic pictures, remnants of some non-symmetric tangles of hitches, which escaped the incidence... The interested reader can see them in the attached files.
 

[alpineer]

Lamenting the MWK's unsuitability as a climber's tie-on - as I love it's wonderful symmetry - lead me to re-routing the ends and discover the Tweedledee form. I suspect this is how Roger E. Miles originally came upon the knot.

   On the contrary, I am sure he did not come upon this knot that way ! 
   He was just trying to tie all the possible simple symmetric bends there exist - and I know it, because when I re-discovered it, I was trying the same thing, being unaware of his book... and because he has told me so !   
   I remember very well how I came upon it, 3 1/2  years ago - which was by systematically applying an anything but "random" method, as I was accused too easily by some "founding fathers" here... who were unable to "see" the method under the madness  . I simply collected all the symmetric hitching tangles, and tried to connect them one-to-one in every possible way. I started from the shape "8" overhand knot, the fig.8 knot, the Clove hitch, the double overhand knot / Strangle, the Constrictor and the Pretzel ( which is less symmetric than the others) - and I had connected each one of them to each one else, in every symmetric way I was able to figure out. That is, plain dumb, systematic work, that does not need any imagination to be accomplished ! Of course, the most interesting cases were the symmetric ones, where the two links were identical. The particular knot, the Tweedledee ( I had called it the "88" bend at that time, for obvious reasons ), and the somewhat similar topologically but completely different geometrically Oyster bend, were rather easy to tie. I remember that the problem was how to keep each link in one piece, by encircling/connecting the curved segments of the rims of the two bights to the straight segments of the continuations of the standing ends and the tails. It is exactly the same rationale I follow in the tying method I have presented, probably because it has been imprinted in my brain then, right at the start, and old dogs do not learn new tricks !
    By a series of unfortunate events where I was as responsible as many other members of this Forum, I had deleted the original posts, so the description of the original ideas was lost. From this time, I keep in my files some relic pictures, remnants of some non-symmetric tangles of hitches, which escaped the incidence... The interested reader can see them in the attached files.

X1,

You seem so willing to misunderstanding. I do not doubt what you say Mr. Miles' was trying to do and not searching for a climber's tie-on. I'm only suggesting in his endeavor to find all possible symmetric bends that he came upon the Tweedledee via transformations of the MWK (a well-known symmetric form). Now, enough of this, please.
BTW, did you know that it takes a few words only to state otherwise?   

[X1]

   You seem so willing to misunderstanding.

   
   You misunderstand, even if you are not willing to ! 

BTW, did you know that it takes a few words only to state otherwise?   

   
   I have tried a few words, I have tried many words, but I have not seen much difference ! You still misunderstand...

...he came upon the Tweedledee via transformations of the MWK (a well-known symmetric form).

  So, let me try ONE word :
   
   NO
 
   (  No, he did NOT come upon the Tweedledee via transformations of the MWK (a well-known symmetric form).)

   Now, enough of this, please.

   Now, enough of this, please.

[alpineer]

   You seem so willing to misunderstanding.

   
   You misunderstand, even if you are not willing to ! 

BTW, did you know that it takes a few words only to state otherwise?   

   
   I have tried a few words, I have tried many words, but I have not seen much difference ! You still misunderstand...

...he came upon the Tweedledee via transformations of the MWK (a well-known symmetric form).

  So, let me try ONE word :
   
   NO
 
   (  No, he did NOT come upon the Tweedledee via transformations of the MWK (a well-known symmetric form).)

   Now, enough of this, please.

   Now, enough of this, please,
   
   

Fine then. I understand.

[X1]

Fine then. I understand.

   I am sure you can, but it seems that sometimes you do not.
   I have read Miles book as carefully as I could, and I believe I know his method. He DOES NOT start from well known symmetric knots, and proceed by transforming them, as you claim. He starts by the matrices that represent symmetric 2D diagrams of  EACH LINK, and then he superimpose those two links, paying attention to the kind of symmetry of the end result. He distinguishes three kinds of symmetry, and the Tweedledee symmetry obeys the higher of them: it is symmetric along two perpendicular to each other axes : he calls the bends which obey that symmetry "triple symmetric". The 2D diagram of the Tweedledee bend, which I have re-drawn in KnotMaker and posted in this thread, is quite complex, and it can not be used as a basis for an easy to remember tying method ( I have tried it ). Even when Miles describes tying methods, he relates the Tweedledee bend with the Dee bend, which I have also shown in this thread . And the Dee bend itself to the Harness bend... NOWHERE in his line of thought or his sequence of tying methods does he relate the Tweedledee bend with the Matthew Walker bend, for KnotGod s sake ! Read his lips : " To tie [ the Tweedledee bend ] , first tie A10 [ the Dee bend ], then insert free ends symmetrically." Now, read his lips for the Dee bend : " As with A8 [ the Harness bend], a tying method begins with cords aligned in opposite directions, with four crossovers ( over, under, over, under ). Symmetric insertion of the free ends yields the triply symmetric TWEEDLEDEE bend."
   ALSO, he examines the Matthew Walker bend in a completely different way, as the first implementation of Ashley s tying method, at ABoK #1426. He calls all the knots in this sequence by Ashley s name, generalized, as N - FOLD OVERHAND BENDS. This method is related to the Oyster bend, NOT to the Tweedledeee bend. ( p. 124, p.125 ). The Oyster bend is topologically different from the Teedledee bend - its "diagonal elements" are on the outer shell, not in the inner core of the knot.
   WHERE IS THE TRANSFORMATION OF THE MATTHEW WALKER, THAT SUPPOSEDLY MILES FOLLOWS TO GENERATE THE TWEEDLEDEE BEND ? WHERE IS THE INVERSE TRANSFORMATION ?
 
   You seem too quick to dismiss my willingness and/or ability to understand - you have done it again (1), and you keep doing it now. I have not seen this kind of behaviour by you against any other member of the Forum. Am I sooo mean and dumb, I wonder...

1.

...don't call me in the morning. . Why do you insistently belabor other's statements with your incessant grandstanding? It's not just about you.
http://www.wisegeek.org/what-is-grandstanding.htm#slideshow

 
 
   

[James Petersen]

I have been playing with the tweedledee loop/bowline/bend and have settled into a method which seems, to me, quite straightforward and not to fiddly to tie. It is similar to what Ruby has suggested, but begins in a different orientation.

I happen to like X1's initial naming of the knot the "88" bend, also for obvious reasons. In Mandarin Chinese, the words "eight eight" are homophones with "father/father's" and the word for "knot" is the same as "day/holiday".  In Taiwan, Father's Day is celebrated on August 8, and "8 8 knot" and "father's day" sound exactly the same, hence the name of the video.

https://archive.org/details/FathersDayKnot

-- JP

[X1]

   Thank you J.P.
   You should had posted this video tomorrow !   
   The tricky part is at 0.30 , where you pass the working end in between one riding turn and one finger.
    I had never tied this knot on such small line ! I use stiff kernmantle lines used for rescue and climbing - where the curves are always smooth and wide. With stiff ropes, the single hairpin, U turns, and the double hairpin, S turns, are easy to follow, so the knot is formed and held in place rather easily.
   I know that knot tyers will always tie the same knots in different ways ! I just prefer to tie the knots following a mental image that is related as much as possible to the geometry and the structure of the final, tighten knot. As I tie this knot, the two "8" s are always clearly visible, and they remain symmetric to each other during the whole tying procedure. Perhaps I prefer such slow / dumb methods because the hard disk of my memory is almost full, so there is not enough free space left for new tricks ! 
   
   

[Ruby]

well , I think  the structure of the final, tighten knot is more like two double loops, not two flat 8. it's such a round knot.


and see here , I just double double it...

[X1]

the structure of the final, tighten knot is more like two double loops, not two flat 8. it's such a round knot.

  The first "flat" 8 starts to curl / bend, the very moment you make the working end of the second link of the bend ( or of the bight component structure of the eye-knot ) penetrate the two nipping turns of the first. Yes, it is round, and the most important thing it s that is very compact and dense - itsvolume / bulk is very small, considering the total rope length it consumes.

see here , I just double double it...

  Tweedledoubledee, or Tweedoubledee, for short ! 

[James Petersen]

   Thank you J.P.
   You should had posted this video tomorrow !   
   The tricky part is at 0.30 , where you pass the working end in between one riding turn and one finger.
  ...

This part is actually quite simple when I am not trying to make a video of the procedure.  The working end simply follows parallel with the part under the riding turns.

Making the video was rather awkward, so things didn't flow as smoothly as they normally do.  I was sitting on two stools with a tripod between my legs, and the top of the tripod and the camera/phone directly in front of my chest, between my face and my hands. My attention was split between watching the screen and tying the knot. Tying withe the same method and using the same line I normally tie the knot in between 15 - 20 seconds.

When tying with this method, I also find that I can better observe the formation of the second "8" than I can when I tie with the "8" laid out in my hand -- the two parallel legs keep me from seeing what is going on, much like the two legs of the collar on a bowline obscure the nip when viewed from the "front". 

-- JP

[X1]

   I was sitting on two stools with a tripod between my legs, and the top of the tripod and the camera/phone directly in front of my chest, between my face and my hands. My attention was split between watching the screen and tying the knot.

much like the two legs of the collar on a bowline obscure the nip when viewed from the "front". 

   However, in this case, following my dumb method, one can be helped by the perfect symmetry, and for-see / anticipate what happens to one part of the one link he can not see because it is hidden, by what happens to the corresponding symmetric part of the other link that is shown ( by definition, two symmetric parts can not both be hidden in a "front" and a "rear" view, at the same time !  )

[Ruby]

tweedledee bend , and its 99% similar twin tweedledum bend , both easily tied by retucking a what knot 1406.

[X1]

and its ...similar to...
both tied by retucking a ...

   
   Nooope, two topologically different knots are NOT similar ! They might even not be similar if they are topologically identical, but geometrically / structurally quite different, like the "bistable knots" (1)
   The fact that they can be tied by re-tucking the same knot, is of no importance whatsoever, regarding their "similarity". See how many completely dissimilar bends can be tied by re-tucking the Reef knot (2)(3), the Thief knot (4), or a certain symmetric Carrick mat (5).

1. http://igkt.net/sm/index.php?topic=4201
2. http://igkt.net/sm/index.php?topic=3204.msg19380#msg19380
3. http://igkt.net/sm/index.php?topic=2826.msg19395#msg19395
4. http://igkt.net/sm/index.php?topic=3611
5. http://igkt.net/sm/index.php?topic=3086.msg18494#msg18494