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General => Practical Knots => Topic started by: xarax on July 06, 2011, 05:46:00 PM

Title: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 05:46:00 PM
    From a exchange of views with DDK about another bend, it became obvious to me that the "twisted falcely tied" Hunter s family of knots was not as extensively documented as it should. So, I felt I had to take my camera, a 600mg Brufen anti-inflammatory pill for the pains of my spinal cord, climb on the peak of a ladder so my camera can focus on the knots on the floor, and start shooting pictures...D e D i K ated to DDK... :)
   A falsely tied Hunter s bend (1) has one main difference from a properly tied Hnter s bend : Its standing parts are not crossed, twisted around each other, so the whole bend works more like a Zeppelin bend, than a genuine Hunter s bend, i.e. it is a kind of rope made hinge : It is revolving around its tails. Of course, it is a very poor bend, while the Zeppelin bend is superb.
   From the moment we make the standing parts of a falsely tied Hunter s bend twist around each other, embrace each other, we turn this bend into a more genuine Hunter s bend, because now the standing parts are crossed. So, a twisted falsely tied Hunter s bend can be considered as a variation of a twisted Hunter s bend as well. With the correct un-tucking and re-tucking, we can transform the twisted falsely tied Hunter s bend into a twisted properly tied Hunter s bend, and finally into a Hunter s bend. In this thread, I follow the direct path, and I examine the bends that are generated by twisting the standing parts of a falsely tied Hunter s bend, and not the opposite path, that of un-tucking and re-tucking a twisted properly tied Hunter s bend and a Hunter s bend, to generate twisted falsely tied Hunter s bends.
   As I have said elsewhere, the operation of twisting the standing parts of the falsely tied Hunter s bend, in particular, and of the Hunter s family of bends, in general, has a few twists of its own...Indeed, there are more bends there than some people would have thought, and they come in many variations. The Hunter bend, unlike the Zeppelin bend, has different "top" and  bottom" sides, so the twist of the standing parts can be on the one or the other side. ( It can also be at both, but this belngs to another thread). I have specifically examined here the simplest variations, where the tails cross each other before they exit the knot s nub, that I call X variations ( X : crossed tails). These variations come in pairs of different knots, because each tail can pass under, and then over, the other tail before it exits the knot s nub - or the opposite. I call them variations A ( first under, then over) and B (first over, then under), respectably. So, there are two twisted falsely tied Hunter s bends, and two x two twisted falsely tied Hunter s X bend variations, that is, 6 different bends in total.
   I start by presenting the twisted variations where the twist is on "top side", the bottom side staying as it was ( the standing parts remain parallel). Then I will continue with the "bottom side" twisted variations.

1) http://igkt.net/sm/index.php?PHPSESSID=cccb55c76f162ec461f0ff528d1386a4&topic=1992.msg13968#msg13968
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 05:50:44 PM
   The compact form of the "top side twist" variation.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 05:52:42 PM
   The X ( X ; crossed tails) loose knot form of the  two variations of the "top side twist" bend. In the first two pictures, the Vatiation A, where, on the side of the twist, the tails are crossed in the "first under, then over" way before they exit the knot s nub - and in the following two pictures, the Variation B.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 06:22:17 PM
   The collapsed, compact form of the "top side twist" X , variation A.

P.S. 2011-10-30 : This bend is identical with the B11 bend, named "SNUG bend", by Roger E. Miles : Symmetric bends. (How to Join Two Lengths of Cord), 1995.(p. 89, p.110)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 06:41:35 PM
   The collapsed, compact form of the "top side twist" X , variation B.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 07:09:57 PM
   Now, the "bottom side twist" variations.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 07:50:13 PM
   Two more pictures of "bottom side" twisted standing parts variations.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DDK on July 06, 2011, 09:29:37 PM
   From a exchange of views with DDK about another bend, it became obvious to me that this family of knots was not as extensively documented as it should. So, I felt I had to take my camera, a 600mg Brufen anti-inflammatory pill for the pains of my spinal cord, climb on the peak of a ladder so my camera can focus on the knots on the floor, and start shooting pictures...DeDiKated to DDK... :)

Thank you very much, I think.  :)

...   From the moment we make the standing parts twist around each other, embrace each other, we turn this bend into a more genuine Hunter s bend, because now the standing parts are crossed. So, a twisted falsely tied Hunter s bend can be considered as a variation of a twisted Hunter s bend as well. ...

I would agree that a twisted falsely tied Hunter's bend could be considered as a variation of a twisted Hunter's bend only to the extent that a Reef Knot would be considered a variation of a Granny Knot.  Because it is indeed the case that the same process of untucking and retucking that would allow one to convert a twisted False Hunter's Bend into a twisted Hunter's Bend would also allow one to convert a Reef Knot into a Granny Knot or possibly a Reef Knot into a Grief Knot for that matter (in general, allows one to convert from one single carrick to another).  This should be of no surprise as twisted False Hunter's = tucked Reef Knot and a twisted Hunter's = tucked Granny Knot.

DDK
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 06, 2011, 11:49:24 PM
   Thank you, DDK,

   I have followed your reasoning, and generated all those bends from the twisting of parts of a falsely tied Hunter s bend. I can also follow the opposite path, and generate the twisted properly tied Hunter s bend from all those bends !  :)
   I think I have already proved that there are not only 4 different bends , as you have suggested earlier... ( I will show more twisted bends that belong to the Hunter s family of bends, in a future thread). As I said, the Hunter s family of bends - in which I include the falsely tied Hunter s bend *- has a few twists of its own...You should tie the bends, try all the possible modifications, decide which might be proven to be interesting, possibly practical knots, and then take pictures of them and publish them. How could I make comments about knots that you described verbally in a vague way, but not shown in pictures taken by you ? As you see here, there are no identical pictures, because there are no identical knots. The cases where two different knots have two identical views are very rare, because, with simple knots, the differences in the back side are somehow revealed in the front side as well. When this happens, we just look at the back side view, which must be included in our presentation. I always try to follow this procedure in the pictures of the knot I myself tie and I myself take pictures of.  
   In the matter of the knot "base" that generates bends, you have not made any progress, I am afraid...  :) You still start from the very special, restricted cases of the Reef family of knots, when we have almost 768 different knots, that can be generated by various re-tucking of the different knot "bases", at our disposal ! You need some more time to discover the vast landscape that this general method opens in front of our eyes and fingers, but I am sure you will arrive there, sooner or later. However, that is not the issue of this thread.
    There are many ways one can tie one knot, and many more names one can call it...But one knot is one knot, and remains the same knot, however tied or named. I have posted pictures of many interesting simple knots, that you can examine, test, and express your opinion about them. That is my only concern :  Know the ropes and the bends !   :)
    
   * in the general division of the similarly-looking, interlocked-overhand-knot bends, into two broad categories, the Zeppelin family of bends, and the Hunter s family of bends. However, the falsely tied Hunter s bend has a deep, functional similarity with the Zeppelin bend, as it is a rope made hinge, just like the Zeppelin bend.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DDK on July 07, 2011, 02:08:41 AM
. . .   I think I have already proved that there are not only 4 different bends , as you have suggested earlier . . .

I am afraid you must have misunderstood me if you believe I have suggested that there are only 4 different twisted bends.  Possibly my reference to the Reef-Granny-Thief-Grief Knots as 4 bases is to what you are referring.  Even these I remember specifically acknowledging as a SUBSET not only of the total bases that one might use but also as a SUBSET of the single carricks which is only one class of knots that might be used as bases.  And for the single carricks, surely I have never suggested that tucking the ends through the central opening was the only option given the other six openings which are obviously available.

I have made and continue to make no claims about the diversity of the twisted bends that might exist.  My comments have been purely to state that given a specific twisted bend, a unique and specific untwisted bend will be recovered if those twists are completely removed.  It has taken considerable time to ascertain that our definitions of "twist" and its "removal" are substantially different.

By a twist, I mean a very specific type of structure as found in the Constrictor Hitch and which differentiates it from the Clove Hitch, eg. a Constrictor is a one twist Clove Hitch.  It is the same type of structure found in a Reef Knot which has its ends tucked through its central opening.  A twist completely encircles the other rope.

By complete removal of a twist, I mean its removal in a topological/differential geometric sense in which a geometric element is cut producing two cross-sectional areas, parts of the geometric element are repositioned so that they no longer wrap around or encircle a second geometric element and then those cross-sections are rejoined and the original element spliced.  Having mentally envisioned the process and resulting structure, its physical undertaking is then very straightforward and unambiguous for every twisted bend.

DDK
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 07, 2011, 02:31:30 AM
  I am afraid you must have misunderstood me if you believe I have suggested that there are only 4 different twisted bends.

  Yes, I admitt that I did... :)

 A twist completely encircles the other rope.

  No, according to my poor nomenclature... :) A rope "twist", is a rope "embrace", is an "elbow" configuration of two ropes, is ABoK#35. A 180 degrees helicoid rotation around a central axis, is a twist for me. When I see a rope strand, that goes from the "left" side of another rope strand to the "right" side, and the opposite happens to the other rope strand, then I say that those two rope strands are twisted.
.
a geometric element is cut ...and then those cross-sections are rejoined and the original element spliced.

  I see. I have never imagined cutting, and then rejoining, a rope strand ! I un-tuck the rope strand by pulling the free end out of the last hole, then I un-twist it by eliminating the twist/embrace/elbow, and then I re-tuck it, driving the same free end through the same hole, but now in the opposite direction than before.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: TheTreeSpyder on July 07, 2011, 02:42:49 AM
It has been long my contention that a Square, Granny, Thief, Grief, Whatnot etc. should be shown as a family/class of lacings.  Their similarities shown that make them a class, and the slightly different properties that differentiate them from each other, and there by dictate different mechanical commands to the flow of forces in them.

Then show, how altering only 1 side (leave other as bight)  of this family, we 'evolve' to SheetBend  class.

So many lessons, seen at the simplest jointings and what makes them fail in the inferior forms.  These lessons are the simplest in rope, and rule all loaded lacings IMLHO.  One of which is how squared something has to set to be stable, so i think Square Knot is better  than Reef (but Reef historically richer and more colorfull).



i think to be scientific, should show element bases, combinations into 'molecules' etc.  Compare like things to see what empowers them as a class, find one to hold as base form like control group, remove and add things and doc. the effects to define those altered parts effects etc.

Rope itself would belong to a class/family of support devices that only resists/support on the unique inline axis, and only in the tension direction.  Other members of this class are chain, cable, webbing, mono-filament etc.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 07, 2011, 03:35:30 PM
   The "bottom side " X variations (the loose knot forms). The first two pictures are from Variation A, and the last two from Variation B.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 07, 2011, 03:41:20 PM
   The compact forms of "bottom side twist X", Variation A.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 07, 2011, 03:46:10 PM
   The compact forms of "bottom side twist X", Variation B.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 07, 2011, 03:58:08 PM

  I have re-arranged the 36 pictures of this thread, so the interested reader can follow the presentation of the 6 "twisted" "falsely tied Hunter s bend" variations more easily. The labels of the pictures have also been changed a little, and some new pictures were added.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DDK on July 09, 2011, 01:56:37 PM
It has been long my contention that a Square, Granny, Thief, Grief, Whatnot etc. should be shown as a family/class of lacings.  Their similarities shown that make them a class, and the slightly different properties that differentiate them from each other, and there by dictate different mechanical commands to the flow of forces in them.

Part of their relationship is described here  http://en.wikipedia.org/wiki/Grief_knot (http://en.wikipedia.org/wiki/Grief_knot)  where they use the terms "trans" (opposing side) and "cis" (same side) to label the arrangements of the standing parts and working ends.  They use this nomenclature is chemistry as well where they describe the two possible configurations of the aromatic (carbon ring) structures.

DDK
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: agent_smith on July 10, 2011, 11:33:43 AM
xarax, where does this variation of the Rosendahl fit in?

I tried trawling through all of your photos but my eyes are growing weaker by the minute... in frustration, I took some photos of this bend for you.

Again, you might have already shown this structure but I am just getting lost in the sea of knots...which all appear to be Smithunters variations but couldn't find Rosendahl variations (but I am not very good at searching through this forum) :)

Mark

Edit: This variation can also be tied from #1408 as a starting base - and then untying one side and then re-threading so that the tail goes in the opposite direction to obtain the crucifix / Rosendahl form.
Edit: Forgot to add the other variation when I first tied these bends...new image now added.
I like this bend..its a variation of a Smithunter with a twisted/overlapped core. Seems very secure and stable...might even load test in comparison to ABoK #1415 and perhaps Rosendahl (also to test stability and security under loading).
Edit: The Smithunter variant with twisted/overlapped internal core seems remarkable compared to the original as described by Phil D Smith. The act of twisting/overlapping the tails makes the bend jam resistant.
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Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DerekSmith on July 10, 2011, 04:18:19 PM
It has been long my contention that a Square, Granny, Thief, Grief, Whatnot etc. should be shown as a family/class of lacings.  Their similarities shown that make them a class, and the slightly different properties that differentiate them from each other, and there by dictate different mechanical commands to the flow of forces in them.

snip...

Rope itself would belong to a class/family of support devices that only resists/support on the unique inline axis, and only in the tension direction.  Other members of this class are chain, cable, webbing, mono-filament etc.

Hi TreeSpyder,  I feel the need to take exception with a couple of things you say in this post.

First up - from a 'Decoratives' standpoint, there can be no argument that the 'Square Knots' - RGGT/W can be laid out to show a fundamental similarity of structure.  However, this is the Practical Knots forum where the primary reference is the use of these structures as 'Force Machines', and when force is applied to these structures they fold into totally new 'load stable' (we hope) shapes.  In doing so, as we have seen with 1406 / 1407 / 1490, they are capable of creating or eliminating key functional knot structures such as the 'Positive Feedback, Negative Cog' (PFNC).  This function of 'Load Response' is a major part of the Practical Knotters game plan.

A grouping of knots that share( under load) the 'PFNC' functional structure - now that would be a 'Practical Knots' family, but the purely decorative unloaded 'Square Knots' is for me a family only in the decoratives weaves/mats sense.

Second, I have learnt a lot from you about knots as force machines, so I am surprised to read your claim that cordage (rope) is "a class of support device that only resists/support on the unique inline axis..."  -  if this were so, we would have no knots...

Of greatest importance to cord usage and knots is the fact that cordage also 'resists/supports/transmits' forces laterally through linear and/or rotational frictional contact, and by lateral compressive forces...  Consider round turns around a beam, after only a few turns, all of the linear tension has been shed by lateral frictional contact, or the collar of the bwl where a large part of the tension is transmitted by lateral compression...

Perhaps it is time that Practical Knotters start to formulate 'Families' of knots based on functional structures rather than the 'Pretty' mats or weaves we make as memory devices to produce our working load bearing knots.  The Carrick and the Myrtle are said to be members of the 'Carrick Family', yet following each knots structural refolding under load, these two knots bear no resemblance to the pretty mats they hail from and more importantly, they have almost nothing in common as Force Machines.

Derek
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 10, 2011, 05:48:52 PM
where does this variation of the Rosendahl fit in?

   Oh, I would love to have been confronted with a question about "How"..." How would this variation fit in ? " Then, I would have had the opportunity to answer by the annoying, megalomaniac :  " With great difficulty ! "  :)
   Mark, I have been studying your knot some hours now, and I have gone nowhere ! It looks like a variation of the Zeppelin bend indeed, because of the way the standing parts enter- and the tails exit - the knot s nub. However, it is not a "rope made hinge", meaning that its function is not depending upon the transverse position of the tails : the two main bights, the two first curves, are themselves crossed with each other, like what is happening in the case of all the other interlocked-overhand-knot bends, except the Zeppelin bend ! 
   Even If this was not enough, we have a variation of one of the most symmetric knots, that destroy this symmetry completely...The aspect of this bend is, to me, awkward, to say the least, in comparison to its, supposedly, parent knot, the Zeppelin bend. It is not the scale of the modification, it is the fact that the changes are disrupting the lines that we are used to follow by our sight of the Zeppelin bend, at exactly the most important areas.
   After some thought, I have reached to the conclusion that the obvious name "twisted Zeppelin bend" , would not  be a accurately descriptive name for this bend. I might be mistaken in this decision, of course. So, for the time being, I think of this knot as "mark s" bend"  :).
   I post two pictures of the "twice twisted Zeppelin bend", to facilitate an easy comparison. To my eyes, the two knots are, and look, very different, but I can not offer any persuasive explanations about this...Your knot is a very strange animal ! It has something of a domesticated pet that is lost in the wild, and turned into a something resembling its rough ancestors....
   ( I have no doubt the whole or parts of the structure of this simple interlocked-overhand-knots bend would be also present in some knots in the ABoK, but I do not think that this is of any importance.)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 10, 2011, 05:54:09 PM
    And here is an X version of "mark s bend" ( X : the tails cross each other before they exit the knot s nub )
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DDK on July 10, 2011, 10:25:29 PM
where does this variation of the Rosendahl fit in?
. . .  After some thought, I have reached to the conclusion that the obvious name "twisted Zeppelin bend" , would not  be a accurately descriptive name for this bend.  . . .

I would concur with xarax's conclusion.  This bend is, however, one of the first bends that one ties when trying to include interlocking in the Zeppelin, or, at least it was in my case.  This bend is a single interlocking of "b" and "q" loops (as are found in the Zeppelin, w/o interlocking).

As an example of the use of symmetry, it is clear to me (partly from my study of this bend) that the interlocking of the loops must occur minimally in pairs (and possibly in pairs of pairs) to maintain the central inversion symmetry found in the Zeppelin.  Any interlocking not occuring in pairs immediately disrupts this symmetry.  An example I have come across with these paired interlockings for the Zeppelin is the Thief Knot with its ends tucked through its central opening and depicted by xarax above.  This twice twisted Zeppelin actually has two pairs of interlocking.  If one examines the Thief Knot and positions the working ends slightly (roughly at right angles to the standing parts) you will readily see the "b" an "q" loops which make up the Zeppelin and the four (two pairs) crossings or interlockings.  So, the Thief Knot, which BTW has the same symmetry as the Zeppelin Bend is a good starting place for the interlocking of the Zeppelin Bend.

I hope this helps to answer the question of where this bend fits in, at least from a structural perspective.  Other comments about the twice twisted Zeppelin can be found here . . . http://igkt.net/sm/index.php?topic=3196.msg19098#msg19098 (http://igkt.net/sm/index.php?topic=3196.msg19098#msg19098)

DDK

edit:  I will note that two consecutive crossings or interlockings can produce a single twist (with my usage of the term "twist").  Thus, four crossings produce two twists as is seen in the twice twisted Zeppelin Bend, and so, to my esteemed colleague xarax I would like to say in good fun  :P  
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 11, 2011, 12:45:43 AM
   I have not been able to find a satisfactory answer to one question about all those "twisted" knots, that belong to the greater Zeppelin bend-, and Hunter s bend-, looking families of interlocked-overhand-knot bends : and, until, I have a plausible explanation, I will not rest my case. :)
   Wandering around Knotland, I have seen - without been able to anticipate something like this in advance - that the twistings of the standing parts of the Hunter-like bends generate very convoluted  knots, (1), while this is not happening in the case of the Zeppelin-like bends ( where we can meet only this strange but simple nevertheless animal, the "mark s bend").  It seems as there is little that can be modified within, or added on, a Zeppelin bend, while the Hunter s bend is more fertile to such acts, and it can even be transformed almost completely by them. (See 2, and attached pictures). I wonder, is it an indication that the very simple-symmetric knots / things are also crystallized / frozen in time, that they are they sterile to the transformations by evolution, ? In other words, is a certain, minimum "strangness in the proportion" absolutely nessesary, right from the beggining of the generation of a knot / thing ?

1)  I strongly suggest to the interested reader, to tie the knot in (2), and see how unexpectedly and miraculously a Hunter-like bend can collapse, compactify and be transformed to something completely different !
2)  http://igkt.net/sm/index.php?topic=3204.msg19189#msg19189  
     http://igkt.net/sm/index.php?topic=3204.msg19190#msg19190
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 14, 2011, 06:03:49 AM
xarax, where does this variation of the Rosendahl fit in?

   Well, I still do not agree that "Mark s bend" must be called a "Zeppelin variation" at all, for the reasons outlined in Reply#19.
   However, we can make it fit in a greater scheme, indeed. We have just to retuck all the possible variations of the general Reef-family-of-knots "base". Doing this, we will meet the Hunter s bend, the Mark s bend, and two other bends as well.
   The different possible "bases" of the Reef family of knots are 8, of which 4 can be retucked in a Hunter s bend - like way ( with divergent tails : tails retucked through the central opening, and pointing to opposite directions ), and 4 can be retucked in an Ashley s bend - like way ( with convergent tails : tails retucked through the central opening, and pointing to the same direction ). In this thread, I post pictures of the 4 bends with divergent tails, one of which is the Hunter s bend, and one the Mark s bend.
   See the attached pictures for the 4 (out of the 8 possible )"bases", those which can be retucked in a way that the tails exit the knot s nub pointing to opposite directions. Then, proceed to the next two posts, where I present the "top and "bottom" pictures of those 4 bends.
 
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 14, 2011, 06:06:24 AM
   Pictures of those 4 bends.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 14, 2011, 06:08:55 AM
   Pictures of those 4 bends.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: agent_smith on July 14, 2011, 02:43:49 PM
EDIT...added images to my post #17.

This ones for you xarax!

Forgot about these in my rush to study Bowlines...too many images on camera and computer...files going astray.

Mark
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 14, 2011, 03:31:25 PM
This ones for you xarax!

   Thank you, Mark,
   I have already edited my relevant labels of the pictures.  :)  So, we have the Hunter s bend, the Mark s A bend, the Mark s B bend, and the fourth, still unnamed, but also very interesting bend.
   I do not associate your two knots with the Zeppelin bend, as they have crossed first standing part bights/curves. The way the standing parts enter the knot s nub - from the same or the opposite side of the knot - is of secondary only importance. We should not name the knots based upon this merely pictorial characteristic. These bends have in common that they are retucked knots on the various Reef family of knots "bases", and they are retucked in a way that the tails are divergent, and not convergent, in relation to the centre of the knots. ( So these knots have somethibg in common with the Hunter s bend, because their first bights are crossed, and because their tails exit the knot s nub just like the way they do at the Hunter s bend)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: DDK on July 14, 2011, 03:45:43 PM
xarax, where does this variation of the Rosendahl fit in?

   Well, I still do not agree that "Mark s bend" must be called a "Zeppelin variation" at all, for the reasons outlined in Reply#19.

Yes, I also still agree with xarax's position.  The single interlocking totally disrupts the Zeppelin-like symmetry as I mentioned previously and which for me is of notable importance.  IMO and as discussed in numerous posts of others, rather small changes in the structure of overhand bends result in large differences in their behavior.  -- DDK
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on July 15, 2011, 11:27:00 PM
    I have now named this fourth ( probably unnamed till now) bend that belongs to this series, as the "Shakehands -X bend", because that is what it reallly is : A Shakehands interlocked-overhand-knots bend ( ABoK#1031, as a bend), where the tails are not crossed (  X : crossed, so  -X : not crossed) as they pass through the central opening. ( In this sense, the Shakehands bend is the X version of the retucked  B2b "base", one of the 8 different Reef-family-of-knots bases.)
(See pictures of this bend, with this label)
   Any reference/suggestion for a given/better name is welcomed
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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... ;)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: agent_smith 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
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: McKnottee on October 14, 2013, 01:35:28 PM
Is this knot (Reply #14 on this thread) (http://igkt.net/sm/index.php?topic=3204.msg19192#msg19192) the same as this one?:

Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Luca 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!
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: McKnottee 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).
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Luca on October 15, 2013, 04:20:30 PM
No problem, I enclose a picture from ABoK for comparison:
(http://)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: McKnottee 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 ;).
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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 !  :)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Luca 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!

(http://)

(http://)

Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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 !  :) :)
   
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex 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 (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.



Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex 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.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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)."
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax 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. 
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 13, 2015, 02:19:54 AM
" No. Unless their constituents are weakly interacting particles  :) :) (*), mirror-symmetric knots are identical, period "

I'm pretty sure I have to disagree.  Only "pretty" because.. if you can tell me  that you can untwist one into the other without un-tucking any end, then I'll agree, otherwise, well I will still agree but only up the point of semantic definition of what we mean by the "same knot".

The handedness of a knot is I believe, unlike helicity of a massive particle such as a neutrino, Lorentz invariant.  Now it is not known yet if left and right handed neutrinos as they manifest in nature (as neutrinos and antineutrinos) are  actually identical or not.  Neutrinoless double beta decay experiments might reveal an answer. 

But I think so long as we aren't taking our knots near the speed of light, it's all fairly irrelevant anyway.  So long as my heart is in the left side of my body and I've had enough coffee, I will always be able to distinguish the right handed knot from the left handed one and you cannot I think turn flip or contort one into the other.

Lets imagine a knot that has a bulk shape something like this:

  |
\|
 O
 |\
 |

Maybe one of the Hunter varieties actually does something like this.

The O indicates some blob sticking out of the page and maybe flatish on bottom.  It's possible  to conceive of a real crack in a rock where under just the right conditions this knot would get stuck and its mirror would not.  Worst case we just consider that the crack contains a small green gremlin with a heart in the left side of its body who simply doesn't like right handed knots.  I drew it like this to get rid of the "just turn the rope upside down (before you rappel)" way out.  I want a real mirror asymmetry, not a rotation asymmetry. Obviously there is a symmetric crack (with mirror twin gremlin) where the opposite would happen but if you're hanging half way down the rappel, I guess that doesn't comfort you nor does it comfort you that xanax says the mirror knot is the same. 

It's true that when a knot is named, both cracks are probably equally likely to get in our way later.  So at that time there isn't much point in making a fine point about their distinction (which is why I didn't) and yes I would tend to call it the "same" knot.

I agree entirely about the Zeppelin bend unless as you say you want a jamming knot. The Carrick is just pretty and yes some people seem to find it difficult to tie correctly because there are things LIKE it (in the same "class" maybe, and I guess, as you point out, many of them) that are not as good.  But, to me, what's good about it compared to these, is that the "right" way to tie it is more distinctive. That's probably just to my mind though.  Maybe I actually will now remember that all that matters for the Ashley is that the outside crossings are symmetric, but I never tied an Ashley bend on purpose anyway.










Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 13, 2015, 04:13:21 AM
...only up the point of semantic definition of what we mean by the "same knot".

  Same basic practical knots properties : slippage, easiness to memorize, tie, inspect and untie, strength... Also, same mathematical knots properties : topology, crossing number, etc... We can distinguish two mirror-symmetric knot forms, of course, but we do not care to do this !  :) We are interested in their physical properties, and we say that they are identical, just as a left-handed nut and bolt simple machine is identical, relatively to how tightly it can be fastened, to a right-handed one.
  If you want to split hairs, you can say that, ceteris paribus, a left-handed and a right-handed person will not dress each one of two mirror-symmetric knots in exactly the same way, and this may affect, somewhat, the properties of the loaded knot as well - but we are already going too far, there are many much simpler and more important issues we have to settle in practical knots, which are almost under our noses, and yet remain controversial, or they have not been spotted at all  ! 
  Do not pay much attention to my irrelevant "example".  :)  I only wanted to say that, provided the material on which a practical knot is tied is not laid rope, or any other very asymmetrically constructed rope, we always suppose that mirror symmetric knots are the same. 
  " All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics."

  It's possible to conceive of a real crack in a rock where under just the right conditions a knot would get stuck and its mirror-symmetric  would not.

  You shift the goalpost, by inserting the handedness/chirality of the environment into the equation !  :) You have to define the handedness of the knot AND the handedness of the "real crack" itself, to conceive this  :) - that is, if the two pairs of knots/cracks do get stuck, the other two pairs will get stuck or will not get stuck - but we will always have pairs of knots/cracks which will behave the same way. Symmetry !  :)
   I repeat : Do not pay much attention to the handedness of the knots - we have MANY bigger fishes to fry ! 
   
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 13, 2015, 04:35:48 AM
   An example of a minor, yet interesting problem of practical knots, regarding handedness.
   When we have a "sliding halves" bend, like the Fisherman s knot, the two ( single or double ) overhand knots of the two links may have the same or the opposite handedness. We do not know which knot is stronger, or will slip less under heavy loading - that would be an interesting question, which I guess can be settled only by systematic testing. For the moment, we prefer to tie opposite-handedness links, because this way they "kiss" each other better, and they make a neat nub - but we do not really know if this has any practical, or even just measurable effects ...
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 13, 2015, 07:23:12 AM
"You shift the goalpost, by inserting the handedness/chirality of the environment into the equation ! "

Yes of course I was doing that (and stated as much). Yes, reality changes things. Right gloves and left gloves are the same too, but also obviously are not the same, especially for practical purposes.

The main reasons we can "ignore" them in knots are a) it usually doesn't matter (it matters a ton for some things, like DNA or LCD screens) b) understanding the mirror images is trivial once we understand the original and we don't want to risk double counting.  The easiest way to enumerate is to let the mirror images be "understood" to exist and then make sure we don't count any of them twice in the "originals". 

I'm not too hung up on it or I wouldn't have arrived at the "right" answer, but to say two things which are not identical are "identical" (bold is part of the quote) is not right either without putting the asterisks on it, which is what I did originally, and it's an asterisks that I stand by firmly as does the imaginary guy stuck on his imaginary rope.  You were the one who wanted to make a fine point of them being identical, and they just are not, not even in the fundamental particle sense of being indistinguishable.  Don't read my tone wrong.  In writing this could start to all sound bitterly argumentative.  I'm not offended nor irritated about it.  It's all in fun.

Your point (edit: I guess it wasn't your point.. anyway...) about rope helicity is a good one.  I should recall a few knots that have preferences based on this, and the back of mind might, hopefully even does, know the right way to tie some knots where it matters (and on some twisted ropes with some knots I vaguely recall hearing and or being convinced by some experience that it does) but consciously I no longer have any specific knowledge about that.

Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 13, 2015, 01:11:13 PM
Right gloves and left gloves are the same too, but also obviously are not the same, especially for practical purposes.
:) :) :)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 13, 2015, 03:24:34 PM
.. and darn it, I already did forget even while saying I wouldn't.  I the alpine butterfly is the one with symmetric ends of course.  The Ashley is one of the other two which I'll still never remember, but I'll edit the post to label them.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 13, 2015, 04:29:47 PM
...alpine butterfly is the one with symmetric ends of course. 

  Of course, NO !   :)  :)
  There is no ( = there can be no ) symmetric single TIB loop !
  It would be nice if one could actually prove this, rigorously=mathematically.. .( I have just "saw" that it is the case, but my argumenta are, unfortunately, of our beloved hand-weaving kind !  :) )
  http://igkt.net/sm/index.php?topic=4425.0
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 14, 2015, 12:29:15 AM
I didn't say it's a symmetric knot.  I said it has a symmetric arrangement of the outer crossings.  It's a 1 -1 1 or -1 -1 -1 (or the mirrors or those) That's all.   All six knots  have various symmetries.  The hunter and Ahsley's have in plane rotation symmetry which I think also means it's symmetric under an interchange of the two ropes (you can switch red to blue and after some rotation can't tell the difference, probably the kind of symmetry you mean), but I'd have to look again.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 14, 2015, 12:41:20 AM
   I was talking about the TIB loop. I thought that with this "symmetric ends" you meant that the TIB Alpine butterfly loop is symmetric in respect to its two ends, that it can be loaded by either one of them in exactly the same way. This is not the case, neither for this nor for any other single (=one eye) TIB loop ( although most of our too-many double ( = two eyes ) loops are TIB and symmetric ), and in my cited post I had tried to explain why.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 14, 2015, 01:20:33 AM
To be very specific what I really meant, and it was kind of a note to self, so in my self notation system, was that the outer left and right base crossings are mirror symmetric left-to-right. One could refer to other symmetries for those as well.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 14, 2015, 01:44:51 AM
  See the first curve of the Standing End ( which is what, <supposedly>, determines the strength of the knot more than anything else, because it bears the 100% of the load ) when the Alpine Butterfly loop ( or the bend, for that matter ) is loaded by the one or by the other end : the one curve is much wider than the other. We seek symmetry not per se, but because it leads to easily inspected knots ( an erroneously tied symmetric knot, is spotted instantly ), and also because it means that the distribution of the tensile forces within the nub is optimum, and the differences between the more and the less tensioned parts are minimized. This asymmetry is not only formal, it is functional, and I believe it would manifest itself under heavy loading.   
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 16, 2015, 03:59:20 PM

I understand the point about functionality perfectly well, although I have no idea(without tests) how to judge in a given knot if it might be 1% effect, or a 50% effect.

Anyway, clearly the type of symmetry this is referring to is rope-interchange symmetry.  The knot should be the same, when seen from one rope or the other, and if you swap the red and blue rope you should not be able to tell that a change was made, with the exception of possibly a change in handedness (red rope goes from right to left handed). 

I'd like to call this color conjugation symmetry.  If we refer to the mirror as a parity change then we need C or CP symmetry, which I think should imply we can go backwards in time too if we tie the right knot. 

Since ropes exist in geometrical space this should be expressible as simple geometric symmetries.  I think any 180 rotation symmetry will due and I think any mirror symmetry will also or any symmetry found by a combination of one of each (in all cases assuming ends are chosen and considered in the symmetries),  but I'm not sure what the simplest set of necessary and sufficient symmetries is. The fact that ropes can't usually pass through each other should surely provide some limitations.




 
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 16, 2015, 04:23:45 PM
if it might be 1% effect, or a 50% effect.

   MUCH closer to 1% than to 50%, that is for sure !  :)

   If we refer to the mirror as a parity change...

   I was referring to the mirror, and I had noticed that we consider the two mirror-symmetric knots as the "same" knot. Even if we do it only to half the size of our taxonomic scheme, as you had mentioned.

   Do not waste your time thinking about what symmetry is, and which kinds of symmetry exist - every physical quantity which is conserved, is related to a symmetry. Better implement symmetry transformation, to reveal all the different knots which can be generated by them, if you start from a simpler, or a less unambiguously defined, basic knot. The Carrick mat and the bowline ( following Stagehand s idea ) are waiting !   :) 
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Dan_Lehman on April 23, 2015, 06:36:27 PM
  See the first curve of the Standing End ( which is what, presumably,
determines the strength of the knot more than anything else,
because it bears the 100% of the load )
NB "presumably" : we lack good data from actual
testing, et cetera.  And we often lack knowledge of
exactly what this bend is --i.e., when forces are
applied, there are often changes to the geometry
of which we might not suspect/consider/know!
(A "first curve" might be straightened; by how much
force and with what effect ..., but likely then the point
of rupture is found beyond it.)

Quote
when the Alpine Butterfly loop ( or the bend, for that matter ) is loaded by the one or by the other end : the one curve is much wider than the other.
Please show this in imagery; I don't see it.
AND, I do note that there is the common geometry
--where "end abut" and rise up (as tails or into eye legs)--
and the "crossed legs" (of eye) geometry,
where one side is in much the "pretzel" orientation
and the other is like a minimal "timber hitch" shape;
in this latter tying (what Wright & Maggowan specified, fyi),
both geometries appear to give nice curves, albeit
different.  And some of prior loading, precise setting and
so on could make determining (likely minor) differences.

But, really, IMO, the "common"/legs-abutting geometry gives
equally not-so-good-looking, nearly 1diameter u-turns, vs.
both of the turns of the legs-crossing orienation.  And, though
I favor the latter (have pointed out in another thread that
Alan Lee shows this, in his video), I must admit that some
of the good test results surely resulted from common tying.

Quote
We seek symmetry not per se, but because it leads to easily inspected knots
( an erroneously tied symmetric knot, is spotted instantly ),
and also because it means that the distribution of the tensile forces within the nub is optimum,
and the differences between the more and the less tensioned parts are minimized.
This asymmetry is not only formal, it is functional, and I believe it would manifest itself under heavy loading.
Noope, not so.  Firstly, as suggested by your elsewhere-posted
guess-the-"correct"-fig.8 dressing, discerning knot geometry
can be difficult, even in what we might regard as simple knots.
Secondly, as I note above, the butterfly looks good in both of its
differing parts, in the legs-crossed version (one could imagine the
difference showing in, e.g., one material on average doing better
in one end, another doing better in the other, largely attributed
to material friction or stiffness or compressibility !?)
And in actual practice, end-2-end knots will at times see
unmatching ends --differences between lines.

(All of which above consideration/speculation gives rise to Agent_Smith's
warning that talk of knot strength is nonsense, especially in the
acknowledged absence of well stated theories given good testing
and generating good data
for further study!
--and is thus merely indulgence for the theoreticians
 (or is that "idealists" ?!)
  ;D  )


--dl*
====
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 23, 2015, 07:41:37 PM
  NB "presumably"

  My bad English ! Supposedly, reputedly...

...discerning knot geometry can be difficult, even in what we might regard as simple knots.

   True, but my point is that a mistake in a symmetric form, which disturbs that symmetry, can be spotted more easily than a mistake in an asymmetric one.
   Mind you that all three plus one ( the one is the odd man out, the Ring bend ) of the not-perfect forms of the fig.8 bend/loop are symmetric, regarding their front/back and left/right sides. Not symmetric forms can be spotted more easily - and that is why I had not used them in my tricky post.  :)
   Platonists are a particular subset/variation of Idealists, which is a particular subset/variation of Theoreticians.  :)
   I simply believe that ( provided that the fundamental geometry of the Universe does not change ), all knots "exist", in a sense, as potentialities ( Aristotle s δυναμει ) - just like numbers and mathematical theorems do. Therefore, when a mathematician "discovers" a theorem, or a knot tyer "discovers" a knot, he just reveals what had happened to remain, until that time, hidden - but he does not "invents" them. All intelligent civilizations in the Universe tie the same knots, simply they had not informed us about that yet.  :)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 24, 2015, 07:56:28 AM
   Please show this in imagery; I don't see it.
 
   First, there IS, indeed, a bend where both first curves have the same, one-rope-diameter radius : the ABoK#1408.
   As ABoK#1408 is, obviously, different than the Butterfly bend, one can suspect  :), at least, that there is a fly in the ointment... and that Butterfly bend s first curves would be different, too.
   See the attached pictures - from the detail of the "top" view, one can clearly see what I am talking about so long...
   ( Click to enlarge )

   http://igkt.net/sm/index.php?topic=5269.msg34592#msg34592

Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on April 25, 2015, 05:19:10 AM
 xarax said:
Quote
  I simply believe that ( provided that the fundamental geometry of the Universe does not change ), all knots "exist", in a sense, as potentialities ( Aristotle s δυναμει ) - just like numbers and mathematical theorems do. Therefore, when a  ... knot tyer "discovers" a knot .. he does not "invents" them. All intelligent civilizations in the Universe tie the same knots, simply they had not informed us about that yet.  :)

I hate to break your platonic bubble, but the same can be said of iphones.  Their form and structure is something which simply exists as a possible solution to the fundamental properties of the universe we live in, given the right initial conditions to put one together.  The iphone was thus also not invented, but was a  discovered form of matter (many Samsung or HTC enthusiasts would probably agree with that, but that's kind of a different argument)
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on April 25, 2015, 11:59:33 AM
I hate to break your platonic bubble, but the same can be said of iphones. 

 :) :) :)
To be precise,, it is sort of Pythagorean... :)
( Two less will-known inhabitants of this bubble, shown in the attached picture. )
I believe that the Universe is probably made of mathematics - or it is a product of a computer simulation, a computer game, made by a computer scientist ( and from the so-so skill of the construction, I would guess he is just an undergraduate student ).
1.
http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
"The theory can be considered a form of Pythagoreanism or Platonism in that it posits the existence of mathematical entities; a form of mathematical monism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism."
"we invent the language of mathematics but we discover the structure of mathematics."
2.
http://en.wikipedia.org/wiki/Simulated_reality
http://www.simulation-argument.com/
a. Human civilization is unlikely to reach a level of technological maturity capable of producing simulated realities, or such simulations are physically impossible to construct.
b. A comparable civilization reaching aforementioned technological status will likely not produce a significant number of simulated realities (one that might push the probable existence of digital entities beyond the probable number of "real" entities in a Universe) for any of a number of reasons, such as, diversion of computational processing power for other tasks, ethical considerations of holding entities captive in simulated realities, etc.
c. Any entities with our general set of experiences are almost certainly living in a simulation.

   At least one of the following statements is very likely to be true:
1.The fraction of human-level civilizations that reach a posthuman stage is very close to zero;
2.The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero;
3.The fraction of all people with our kind of experiences that are living in a simulation is very close to one.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Dan_Lehman on May 01, 2015, 10:35:17 PM
   Please show this in imagery; I don't see it.
 
   First, there IS, indeed, a bend where both first curves have the same, one-rope-diameter radius : the ABoK#1408.
   As ABoK#1408 is, obviously, different than the Butterfly bend, one can suspect  :), at least, that there is a fly in the ointment... and that Butterfly bend s first curves would be different, too.
   See the attached pictures - from the detail of the "top" view, one can clearly see what I am talking about so long...
   ( Click to enlarge )

   http://igkt.net/sm/index.php?topic=5269.msg34592#msg34592
Thank you for the imagery (and one citation w/neat highlights!).

I remain unconvinced : what you show is (a) a particular
dressing of your own fancy, and not something common [n1],
methinks --where a common guidance (for the fig.8
but presumably w/broader effect) is to smooth away
crossings, which would loose your apparent broad turn--;
and (b) you are making a dubious static analysis,
and not seeing things when "push comes to shove"
--where it is likely that the crossing-over-other will
change to pulled-off-of-being-over-other, resulting in
a hard turn around the eye leg, for the most part.

[n1] In the common orientation, the *crossing* of S.Parts
comes in a sense where they are turning around the
abutting eye legs --i.e., the one rising to the other's falling--
rather than as you show, the one changing position over
the other (at that point, they'd be at their levels).]

Similarly re #1408.  (One might cite the zeppelin end-2-end knot
as having such weakness.  The curvatures in these knots
are often not so bad, with maybe #1452 & #1425 likely
good, & Harry Asher's shakehands & SmitHunter's bend
less so (with the latter having a version not-so-bad (which,
in one test I had done, was not-so-much-better!  :P )).


--dl*
====
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on May 01, 2015, 11:49:16 PM
...where a common guidance (for the fig.8 but presumably w/broader effect) is to smooth away crossings, which would loose your apparent broad turn--;

  In this knot, the X-crossing can move to the one "flat" side of the knot or to the other - but it an not be smoothed out, and disappear ! Think about this a little bit, and you will see why.
   Whatever side this X-crossing is pushed to be transported to, and to be fixed at, it will remain as an X-shaped crossing - and once we have this crossing, the one first curve will pass around the other, and it will have to trace a wider path, so it will be more gentle.
 
Quote from: Dan_Lehman link=topic=3204.msg34863#msg34863 date=1430516117
you are making a dubious static analysis, and not seeing things when "push comes to shove"...

   True. I had noticed that a number of times. We can never be sure how much/bad a nub will be deformed, after a really heavy loading. However, as I said above, given the fact that there will be a X-shaped crossing somewhere ( a tangible/material proof of the asymmetry of this knot ), I predicted that there will be a difference in strength - and I was proven to be wrong, yet another time !  :) Not because of the absence of the asymmetry, but probably because such the strength differences due to such geometrical differences, especially in thin lines, are not significant or even measurable at all.

the one rising to the other's falling-- rather than as you show, the one changing position over the other

   As I said, this is irrelevant ! Which line goes over which, and in which point/side of the knot, does not matter. The one has to be wider than the other, for pure geometrical reasons. Take any flexible rod which retains, more or less, its circular cross-section everywhere, and try to make a 3D model of the knot in which the two first curves will have the same diameter. You will see that it is impossible.
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Tex on May 02, 2015, 02:13:44 AM
xarax I'm not sure why you're giving in now.  As much as I don't care, and even mocked you a little,  still a man should not give up his principles too easily ;) .   You had already well established that you thought 5% would be huge and 1% would even be big.   1% has certainly not been ruled out, let alone 0.1%.  There is clearly a geometrical difference.  This is undeniable.

Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on May 02, 2015, 02:44:27 AM
 
There is clearly a geometrical difference.  This is undeniable.

  Dan Lehman remain unconvinced - and myself I admit I want to see to believe ( meaning, to measure the differences of the first curves of knots near or after rupture ). I have seen strange things happening inside nubs under heavy loading, probably because of torsion, which we had not taken into account in our discussions.
   And I repeat that we have not established yet that strength of knots is scale independent. Especially when the construction of the ropes ( the way the fibres, and the bundles of fibres, are interwoven into their core ) certainly does depend on the sixe of the ropes. Even ropes of the same brand sold under the same name, are constructed differently in small and large sizes.
   I expect that the differences would be bigger ( I do not know if they will become significant or not, whatever that may mean...) when the Butterfly knot is tied on larger sizes - the sizes usually used for climbing and rescue purposes ( 9-12.5mm ).
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Dan_Lehman on May 02, 2015, 06:58:53 AM
... the one rising to the other's falling-- rather than as you show,
the one changing position over the other

   As I said, this is irrelevant ! Which line goes over which, and in which point/side of the knot,
does not matter. The one has to be wider than the other, for pure geometrical reasons.
At the point of U-turn, the reversal of direction,
which is our focus, is where the assessment of
curvature should matter, and in your highlighted
image above one can see that the there-indicated
wider-turning one should simply slide (its crossing
over point) leftwards and sharpen its U-turn (which
is at the right).

OTOH, I'll grant that this U-turn shows more similarity
in sharpness to the other end's when loaded "through"
(end-2-end), than qua eye-knot --where there is some
bearing-against (if not crossing over) of the then SPart
vs. the unloaded other end.  (#1408 does pretty well
in rounding its U-turn as it symmetrically twist-tightens
its ends, I think; whereas these things are problematic
for the zeppelin.)

Quote
Take any flexible rod which retains, more or less, its circular cross-section everywhere,
and try to make a 3D model of the knot in which the two first curves will have the same diameter.
You will see that it is impossible.
Nonsense : in THIS plan, you have --for the butterfly--
the opposing SParts coming in left vs. right with one atop
the other as they pass across the "abutting" eye legs,
and then one U-turns --the 1dia of eye leg-- from below
upwards, the other complementarily and also 1dia around
an eye leg downwards; and THEN somewhere away from
the U-turns of focus, there is an asymmetric crossing of
over/under --to my side of the debate, make it at the
opposing S.Part's U-turn, reaching then into the collar.

The part that you fill the bottom of your larger/red circle
with I say moves the crossing-over point leftwards to make
that circle a horizontally disposed ellipse, and at its point of
focus ("U-turn") on the right you have an equal 1-diameter
turn as for the opposing side.  That is the how-I-see-it that
led me to this question.  One will need to set this left-side
eye leg pretty tight to deform the left SPart's shaping
around this area to make the shifting I describe here
such as would then otherwise maybe give curvature,
"bearing against" to that left SPart.  --and I don't see
this happening, as a general rule.  (And now we're into
vagaries of dressing, fine-tuning an orientation!)

But space is short, and the crossing over ... can it really
influence much the U-turn's sharpness?  --and moreover
the vagaries of what happens when eye-loaded?
.:.  So, I do see your view, but still find it dubious.
I'm more happy to pursue the crossed-legs version,
with distinctly different overhand components each
of which looks to curve rather favorably (though, again,
when loaded with the eye, how things actually shape up
is less clear, and probably differs with rope type).


--dl*
====
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on May 02, 2015, 01:38:12 PM
  The issue will be resolved instantly, when knot rigger will test Butterfly loops tied on thicker ( climbing and rescue ) ropes ( 9-12.5mm ), and measure the first curves of the almost solidified knots, after the rupture. Hic Rhodus, hic saltus !
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: Dan_Lehman on May 03, 2015, 07:49:10 AM
  The issue will be resolved instantly, when knot rigger will test Butterfly loops tied on thicker ( climbing and rescue ) ropes ( 9-12.5mm ), and measure the first curves of the almost solidified knots, after the rupture. Hic Rhodus, hic saltus !
Again, measuring post-rupture is dubious at best.
And beyond that there are so many factors to consider
--prior measurement, even the dressing,
and still one can wonder at material, firmer vs.
compressible rope and so one.
Even the actual making of such a measure of
curvature I think entails difficulty in placing one's
measuring points and so on.

--dl*
====
Title: Re: Twisting the standing parts of the falsely tied Hunter s bend
Post by: xarax on May 03, 2015, 09:27:02 AM
...factors to consider :
1. even the dressing,
2. material, firmer vs. compressible rope

1. Probably wrong. Under such heavy loading, the differences in the initial dressing will, most probably, be smoothened out.
2. Correct. However, I expect that the differences in the two curves will be analogous, in firm and compressible ropes.

  Regarding the way one measures "curvature", it is true that things are not so simple, because curvature is a local thing, and varies along a curvilinear segment. That is why I asked for a measurement of the ( external ) width of the (total) "curve", which, when the angle between the first and the second segment at the ends of it is "negative" ( when the ends are parallel, it is zero degrees - when the ends are aligned, and there is no curvature anywhere, it is 180 degrees ), it is easy and unambiguously measurable.