Author Topic: Twisting the standing parts of the falsely tied Hunter s bend  (Read 31158 times)

xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #30 on: July 16, 2011, 12:03:06 AM »
  
 where does this variation of the Rosendahl fit in?

 
   We can now offer another reason why the Mark s A and Mark B bends should not be considered or named as Zeppelin (Rosendahl) bend variations. The 8 different Reef-family-of-knots "bases", when retucked through their central opening, generate all the known interlocked-overhand-knot bends, as expected : The Alpine butterfly bend, the ABoK#1408 bend, the Ashley s bend (ABoK#1452), the Hunter s bend, the Shakehands bend ( a simpler form of it, where the tails are not crossed), ...all, but one : the Zeppelin bend. ! Obviously, the Zeppelin bend does not belong to this series, it is not a retucked knot of any of those 8 bases, so the Mark s A and Mark s B bends, that do belong to this series and are the retucked knots of two of those 8 bases, indeed, should not be considered or named after the Zeppelin bend.
   It took me quite a while to offer a plausible justification for the first naive impression I had when I saw Mark s A and B bends for the first time... and a few number of pictures to take...because I had to tie and take pictures of all the 8 different Reef-family-of-knots "bases" and all the different retucked bends. I believe that agent smith will be satisfied with the careful handling of his two unexpected and strange artefacts... ;)
« Last Edit: July 25, 2011, 09:04:03 AM by xarax »
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agent_smith

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #31 on: July 16, 2011, 01:45:45 AM »
With reference to your top image (reef family base) at post #29, this is also a starting base for tying Phil D Smith's 'Riggers bend' (aka Hunters bend) - the difference being the position of the tails.

I know this because I incorrectly tied the Rigger/Hunter bend a few times over the last few days and arrived instead at what you called the 'shakehands x bend'... you can try this yourself - simply by swapping the tail positions in the interlocked loops (ie over-under..instead of under over) you either end up with the Rigger/Hunter bend or what I termed an 'interlocked anti-doppelganger bend'.

Its an ungainly looking knot - and you have to be careful to dress it up properly to make it secure. I was earlier concerned by a few hand manipulations that started to work it loose...

Mark

xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #32 on: July 16, 2011, 02:51:53 AM »
   That is what we suffer when we do not have pictures of knots to discuss !  :) I have not understood anything of the verbal description of your knots...
   There are only 8 different bases, those shown in (1) and (2). ( And their mirror symmetric, of course, that generate the same=mirror symmetric knots ). And, of course, there is only one way to retuck each of them through the central opening, so you end up with  interlocked overhand bends. So, there are only those 8 possible bends, and no other. I have been careful to present and discuss only the "not X", i.e, only the -X forms here, that is, I have not crossed the tails anywhere. (The Shakehands -X bend, is identical with the Shakehands bend, modified so that their tails are not crossed at their final tuck through the central opening).
   The Hunter s bend can be generated only by retucking the B1b base. If you generate it by retucking any other base, you make some mistake... :) However, there is one single case, where two different bases generate two knots that are identical, ( See 3), but this happens only there, because of the high symmetry of the configuration.
   You are a much better photographer than me, so, Show me the pictures:)

1) http://igkt.net/sm/index.php?topic=3204.msg19380#msg19380
2) http://igkt.net/sm/index.php?topic=2826.msg19395#msg19395
3) http://igkt.net/sm/index.php?topic=2826.msg19396#msg19396
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McKnottee

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #33 on: October 14, 2013, 01:35:28 PM »
Is this knot (Reply #14 on this thread) the same as this one?:


Luca

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #34 on: October 14, 2013, 11:54:34 PM »
Hi McKnotte,

I think so, the one in your photo is a mirror version, but I think it's the same bend.
You can notice that the bottom side twist version of the "falsely tied Hunter's bend / false Zeppelin"( http://igkt.net/sm/index.php?topic=3204.msg19170#msg19170 ), is the same as ABoK #1425, then the version that you show can be considered as a version of #1425 with crossed ends.

                                                                                                               Bye!

McKnottee

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #35 on: October 15, 2013, 06:40:44 AM »
Thanks Luca.

I must confess I do not have the ABOK yet.  :-[

But I have ordered it (1993 edition).

Luca

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #36 on: October 15, 2013, 04:20:30 PM »
No problem, I enclose a picture from ABoK for comparison:

McKnottee

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #37 on: November 08, 2013, 08:09:07 AM »
Thanks for that, Luca. (I thought I had thanked you already, but obviously not. Apologies.)

Got my copy of ABOK a couple of days ago  :), which might help in keeping up with the discussions ;).

xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #38 on: October 25, 2014, 12:10:22 PM »
   As Luca has noticed ( Luca always notice my mistakes, so I feel relaxed to make more, because I know there would be somebody out there to correct me !  :) ), the Reef bases A1a and A2a shown at the pictures of Reply#23 (1), are identical, so the corresponding knots generated by tucking the ends through the same opening are identical, too. The fact that this obvious thing has remained unnoticed by many people for so long, proves what I keep telling all the time : An asymmetric knot is difficult to inspect : in a symmetric one, any mistake disturbs the visible pattern so much, that it can not remain unnoticed for long. In practical knots, especially in bends, symmetry is not "only" a matter of aesthetics : it makes the knot easy to inspect, and this is a matter of security !   
   
1. http://igkt.net/sm/index.php?topic=3204.msg19380#msg19380

   It is gooood that we have one less asymmetric=odd bend to consider - because one Mark s bend, as asymmetric and odd as it is, is already too much !  :)
« Last Edit: October 25, 2014, 12:11:54 PM by xarax »
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Luca

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #39 on: October 25, 2014, 09:44:25 PM »
Hi xarax,

For me it is an honor to be the your reviser! :D (But I feel sorry for you because I think you deserve a better one! :().
Anyway, no, I would not want it to be thought that I spend all the time analyzing your posts with the maniacal intent of finding errors ...if occasionally I happen to find a mistake,for me is only a confirmation of the value of the large amount of knots and informations with which you enrich this forum!
Basically things have gone in this way:fiddling with Knot Maker,drawing the various simple interlinked Overhand knots-based bends like the Hunter's,the Butterfly, Ashley's etc. + their corresponding symmetric forms,I came to draw the two bases shown below in the first pic,persuaded that they would produce two different  bends,but when I finished drawing their corresponding symmetrical forms, I realized that something was not right,because the symmetrical form of the first base was identical to the second base,and viceversa...but the power of persuasion is great  ::) ... so I been struggling for nearly half an hour with my brain ...trying to figure out what part of it prevented me from achieving the "seventh" bend!(because I was really persuaded that existed!)This until the moment when I decided to go look in the thread where I remembered seeing the Mark's bend"s"... :o

After all this,at this point remains in me the doubt that the Reef family bases for those six bends are not eight, nor seven, but that in fact are just only six: with regard to the bases of the four bends that are symmetric (Ashley's,#1408/9, Hunter's, Shakehands), exchanging the under/over of all the four crossing points of the bases it is obtainable that the simmetry of the corresponding forms is immediately perceivable.With regard to the bases of the two asymmetric bends(Mark's,Butterfly),to obtain the symmetrical forms, it may be sufficient to exchange only the under/over at the two points where the two links of their bases are intersected,but maybe is precisely here that is the misunderstanding(I think also of the similar case of the two bases for the Butterfly), because acting in this way,and moreover,in my case,on the armchair,using two-dimensional images, the symmetry with the respective original figures is not immediately perceivable,but,to obtain that such symmetry is immediately perceivable, we need to operate an addictional rotation of 180 degrees on the second(or the first..) figure obtained (on two different axes, perpendicular to each other depending on which is the basis,for the Butterfly or for the Mark's).

                                                                                                                                                Bye!






xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #40 on: October 25, 2014, 11:32:39 PM »
   As you had noticed, there is one pair of "bases" in each category ( so, two pairs, in total ) that generates the same bend :
   In the first category ( where the Tail Ends leave the nub towards opposite directions ) the first pair ( A1a, A2a) generates the Mark s bend :
   http://igkt.net/sm/index.php?topic=3204.msg19381#msg19381
   In the second category ( where the Tail Ends leave the nub towards the same direction ) the second pair ( A1b, A2b) generates the Alpine Butterfly bend :
   http://igkt.net/sm/index.php?topic=2826.msg19396#msg19396
   So, now the correspondence between the members of the two categories is perfect, and this alone should had been an indication that something was wrong in the initial enumeration.
   
   However...
   However, I think that the kind of asymmetry of the Mark s bend is different from the one of the Alpine Butterfly bend. The former seems to me more asymmetric than the later. I will not attempt to analyse or explain this difference in precise terms ; at the end of the day, it may well be just a vague, subjective "feeling" - or it may be something concrete that can be defined objectively, but it would require a more careful and detailed definition of what "symmetry" in bends is - and after the previous "experience" I had in this Forum with the issue of the symmetry or the asymmetry of the Zeppelin X bend, I have lost my appetite for more such discussions !  :) :)
   
« Last Edit: October 25, 2014, 11:34:39 PM by xarax »
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Tex

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #41 on: April 12, 2015, 01:58:14 PM »
I don't know why I took an interest in this. But I did.  I'm not sharing this post because it's revolutionary.  I'm sharing it because I went through the exercise of counting the distinct knots myself, rigorously(but not quite formally), and maybe someone else will find my process interesting.

I started by NOT defining the standing ends.  I left all ends equal at first to define "base knots".  Why? Well it helps realize later which knots are actually the same knot form BUT just with different ends tucked, and makes it easy to associate an ashley-like knot with its Hunter-like sister. The first part of that turns out to be mostly irrelevant, which maybe I could have figured out at first, but the irrelevance is very interesting too.

Anyway, in this way I can describe any of these base layouts with three specifiers each being something like over or under, u or o, etc.
I'll use -1 for under and 1 for over so I can indicate reversals/negations easily.

If we label the top left end, and the top middle left loop-segment, and the top right end, then for instance A1b is 1,-1,1 and A2b is -1, -1, -1 etc. Check visually here and you'll get my scheme:

http://igkt.net/sm/index.php?topic=2826.msg19395#msg19395

The lower three crossings are fully determined by the upper three so I don't need to consider them.

I will assume that any knot that I can see in a mirror is identical for practical purposes of form and function to the knot that I'm holding in front of the mirror, so I'll count those as the same knot. By this symmetry, any knot that can be written A,B,C can be written instead as its mirror C,-B,A.  The middle flips because the middle indicator is defined as the over/underness of the LEFT top middle loop segment which becomes the right top middle loop segment in the mirror. So if the left bit was on top, in the mirror the right bit is.

This means that I can ignore all A,1,C combinations and just use combinations with -1 in the middle (just as has been done in this thread which is why I use -1 and not 1)

Let's look more at what happens with rotations and mirror reflections.  All of these assume that all ends are equal (no working ends chosen yet).

Rx:    We can see that a top to bottom rotation over the x axis never changes a layout.  :  ABC -->  ABC

Rz:    We can see that a rotation of 180 degrees in plane (around z axis) creates:  -C,B,-A.                               
           1,1,1 --> -1,1,-1  but 1,1,-1 remains unchanged.

Ry:   A left to right flip over the vertical axis does the same thing as the 180 rotation.. because it's just like a rotation with a top to bottom flip.
                -C, B, -A

Mx:   A left to right mirror reflection (x axis inversion) ----->       C,-B,A   (already explained)
My:   A top to bottom mirror reflection (y axis inversion) ----->      -A,-B,-C
Mz:   A Z-axis inversion (knot viewed on end with a mirror) --->    -A,-B,-C  (same as My... for now)

So let's start with all the A -1 C combos and go from there.

1) 1, -1, 1   A1b-like
2) 1, -1, -1    B1a-like
3)  -1, -1, 1    B2a-like
4) -1, -1,- 1      A2b-like

Number 4 is just number 1 with Rz applied, same base knot.

These( 1 and 4) are A1b and A2b, the two Alpine butterfly forms.  More later.

..and so we just have

1) 1, -1, 1   A1b-like     
2) 1, -1, -1    B1a-like   
3)  -1, -1, 1    B2a-like

I can't find a way to reduce the base set further.  Knots 2 and three textually look l/r mirror symmetric but they aren't because of the asymmetric nature of the middle index as explained before.  Rotation symmetry won't change them and a combination of Mx and My produces no change.

Now, if we want ashley-like (opposing ends) knots, then once we select the left standing end there is only one ashley-like choice for the right. So we have two opposing choices of standing ends for each knot, which I will label as P=1 for left end up and P= -1 for left end down. 

I can now rewrite all the knots with a 4th descriptor A, B, C : P   My designations are not exactly like those used by xarax.

1a) 1, -1, 1 : -1  A1b (not just A1a-like, this now IS the A1b knot because the working ends are now selected)
1b) 1, -1, 1 : 1 

(I'll call P=-1 the a versions and P=1 the b version)

etc.

So I get 6 ashley-like knots at this stage (this will get fixed)

Now the odd thing is that xarax listed my 1b in his list of four, but not my 2b and 3b.  If you rotate 1b by 180 degrees you see(again) it's the same as 4a, which he did list. So why list 1b at all and not 2b and 3b?  He did then point out that really it's the same though, so here I'll prove it (I didn't YET prove that 1a and 1b are equal only that 1b and 4a are).

2b and 3b are also identical to their partners by symmetry, we'll see, but so is 1b (which we also still have to prove) so I guess it was just odd to me to see 4 in the "base set"

Remember how that vertical flip (rotation) over the x axis did nothing to the knot before? Well, now it still does nothing ... EXCEPT flip the working ends!

Now:
Rx: A,B,C: P  --->  A,B,C : -P 


So 1a=1b and 2a=2b and 3a=3b.  And indeed, there are 3 distinct ashley like knots, and there should be 3 distinct hunter type knots.
So here they are again with their names:
 

1) 1, -1, 1   A1b-like    :  Alpine Butterfly              / ?? (no clear Hunter's-like name)
2) 1, -1, -1    B1a-like  :  Ashley "evil imposter"    / ?? (no clear Hunter's-like name
3)  -1, -1, 1    B2a-like :  Ashley                          / Hunter's 

I'm not saying anything really new, and I'm sure knot theory papers have this all in it too with S01 symmetry and the like.  Like I said, just went through the process so thought I'd share my experience and notes.

Just for fun here are the rest of the transformations.

Rx: A,B,C: P  --->  A,B,C : -P 

Rz: -C,B,-A : -P*A*C   (Diagonal styles don't change P under this rotation.  A*C is 1 for both ropes up or down, -1 for diagonal)

Ry: -C,B,-A: P*A*C   (so Rz is different from Ry now, diagonal style knots DO flip P under this rotation.)

Mx:   C,-B,A : P   (already explained)
My:   -A,-B,-C : -P
Mz:   -A,-B,-C: P  (no longer same as My)

So now all 6 transformations are different now.

None of these will ever change knot 1 into knot 2 or 3. Though.  If they were different before selecting ends, they are after too.



« Last Edit: April 13, 2015, 04:01:43 PM by Tex »

Tex

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #42 on: April 12, 2015, 02:24:36 PM »
... and even after all this, I still won't remember how to tie the correct version of these, dressed properly, when I need to, which is why I'll stick to a zeppelin Bend or, when I'm feeling fancy, a Carrick bend. 

These interlocked half hitches always frustrated me because it was obvious that there must be at least a half dozen ways to tie them, and most don't do what you probably want.  In real life, not very useful.  The Alpine still makes a handy loop though.

xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #43 on: April 12, 2015, 03:12:23 PM »
   Congratulations ! ( I can recognize a lion by its paw, :) :) therefore I need not check the details ). Now, do the same thing with the Carrick mats, turned into bends.
   For snug hitches, a systematic enumeration of all the possible combinations has been attempted by Charles Warner and Pieter van de Grient at :
   Knotting Matters 61, p. 44 ( Sept. 1998 ).
   Also see Chang s scheme :
   http://igkt.net/sm/index.php?topic=1411.0
   http://igkt.net/sm/index.php?topic=1411.msg9764#msg9764
   For bends, and what I have called the "Reef family of knots" pattern, I have tried my hand at :
   http://igkt.net/sm/index.php?topic=3086.msg18601#msg18601
   For the Thief knot :
   http://igkt.net/sm/index.php?topic=3611.0
   For &-shaped bends, at :
   http://igkt.net/sm/index.php?topic=4445.0
   For bowlines, see the recently presented very general and interesting scheme by Stagehand, starting from initially undefined 3-line crossings :
   http://igkt.net/sm/index.php?topic=5244.0

...any knot that I can see in a mirror is identical for practical purposes of form and function to the knot that I'm holding in front of the mirror...

   No. Unless their constituents are weakly interacting particles  :) :) (*), mirror-symmetric knots are identical, period - for practical and theoretical purposes as well. Of course, when tied on laid ropes ( or even on ropes where the inner twists of the bundles of the fibres are very asymmetrically woven ), the behaviour of knots is affected, indeed, to some degree. I have seen supposedly kernmantle ropes ( which, in fact, were just laid ropes "dressed up" with a disguising braided envelope ) being asymmetrically and badly deformed after their exposure to torque-inducing forces within certain knots nubs.   

(*)  http://en.wikipedia.org/wiki/Asymmetry
  "Although parity is conserved in electromagnetism, strong interactions and gravity, it turns out to be violated in weak interactions. The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model. A consequence of parity violation in particle physics is that neutrinos have only been observed as left-handed particles (and antineutrinos as right-handed particles)."
« Last Edit: April 12, 2015, 05:47:59 PM by xarax »
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xarax

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Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #44 on: April 12, 2015, 03:31:00 PM »
I still won't remember how to tie the correct version of these, dressed properly... which is why I'll stick to a Zeppelin Bend

   No, you do not tie a Zeppelin bend because you do not remember how to tie another bend !  :) You tie a Zeppelin bend because it is the best bend we have - and to learn why it is the best, read why the so-called "Zeppelin loop" is the worst loop we have  :). The simplest, one and only genuine Zeppelin knot, the Zeppelin bend, which I describe as a rope-made hinge, is a unique knot - we tie it because of its superb properties, not because we can remember how to tie it  :).
   I believe I have, by now, tied and tried almost all the known bends ( dozens of dozens of them...) and most, if not all, of all the possible simple ones as well. There are only five bends I place in the first row of bends : the Zeppelin bend, the Double Harness bend ( ABoK#1420), the Fisherman s knot ( Single and Double), the retraced fig.8 knot, and this little marvel, the simplest bend there can be, the Tumbling Theif knot. 
   As for the "old", widely known loops, you are right, AFTER the bowline, the Alpine Butterfly loop is the next great knot - it is TIB, and it can be loaded by both ends in almost the same way. 
« Last Edit: April 12, 2015, 03:34:28 PM by xarax »
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