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General => Practical Knots => Topic started by: xarax on November 21, 2010, 06:06:33 PM

Title: Two variations of the Zeppeln bend
Post by: xarax on November 21, 2010, 06:06:33 PM
Two variations of the Zeppeln bend
Title: Re: Two variations of the Zeppeln bend
Post by: knot4u on November 21, 2010, 10:38:38 PM
Zeppelin Bend = Zeppelin II ...correct?  The new name is more confusing, as opposed to less confusing.

Regarding Zeppelin Bend X, that's a different knot of course, beyond merely a variation in dressing.  My initial testing shows that it doesn't jam easily.  However, it does capsize easier than the beloved Zeppelin Bend.
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 22, 2010, 04:58:54 AM
 After a tiresome exchange of opinions and negations with Dan Lehman (1), (where we were trying hard to tell something to each other, but not trying equally hard to listen and understand each other...), I was convinced that he is right after all : There are two distinct variations of the Zeppelin bend indeed, even though not the ones he had in mind !  :)

While happy to SEE (your cordage colors inevitably brighten my spirit)
you pursuing this topic,
I'll beg off your offer to a ride along the "not listening" road :
I listened well and responded,
and your post here at least puts some rub to your mocking "notice ... not three"
except of course in your continued denial of the obvious.

1) If one sets the R.Z. bend ("Rosendahl's Zeppelin) from a loose state with
rapid tensioning of the SParts,
it is quite possible --perhaps likely(?)-- that each SPart will pull the opposite
end towards itself (i.e., in the direction that the SPart pulls),
as with the knot loose during this transition there will need to be much movement
of the SPart and so a duration of *draw* upon this end it initially u-tuirns around.
(I've avoided saying "other rope's end" for one could be tying the ends of
a single rope together; but it's easier to illustrate with the distinctness of
your cheery ropes : the Orange line will hug the White tail to itself, and
vice versa (no, not The Vice Versa --let's not Reever this thread into that one).)

It would be helpful to see this in orange & white, too.  You can do it,
even if you must position the tails more deliberately (which is the one
sure way).

You can see one of my so-oriented knots here
(thread "Ashley's Bend #1452 and Its Ilk" )
http://igkt.net/sm/index.php?topic=1446.msg10047#msg10047 (http://igkt.net/sm/index.php?topic=1446.msg10047#msg10047)
as well as a SmitHunter's bend variation (different tails orientation).

2) With appropriate minimal wasting of parts of one's precious lifetime
by pulling on the tails a bit, the above orientation I submit can put into
the SParts a more gradual curvature than in most other dressings; it can
be such that the hugged-close tail doesn't get pressed fully out of the
axis of trension, so that the SPart curves slightly around it towards
making its complete u-turn around its own tail.
Which is in contrast to the commonly presented form where the SPart
runs straight to the u-turn without much *deflection*.

3) One can see from this orientation that continued wasting of life pulling
upon the tails will begin moving them out of this orientation as each end's
Overhand is being drawn tighter/smaller, during which another somewhat
transient orientation occurs in which the tails lie adjacent/parallel in a plane
parallel to the axis of tension,
forcing the SParts to deflect harder against each collar to angle up around
them.  THIS form of SPart curvature resembles that shown by Inkanyezi
in his photos of the Carrick Bend --more hard-edged triangular than the
softer tear-drop oval or even bight-like-U in other orientations.

4) The orientation of tails in R.Z."X"  is asymmetrical ; it works symmetrically
for that False R.Z. bend because of that knot's different symmetry, with it
having same-handed Overhands.
And it is the sort of tails-exit variation that IMO improves the SmitHunter's Bend
by a similar curvature change and also getting the tails into a position that
better keeps the collars open, resisting jamming.

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 22, 2010, 03:56:11 PM
Of course these musings go far beyond the practical aspect of knots, and more particularly beyond the practical aspects of the Zeppelin Bend.

As has been stated many times before, another orientation of any part in a given knot may result in a different knot or no knot at all, and when the Zeppelin's ends are crossed, inadvertenty or on purpose, the result is something else that is not the Zeppelin. It also loses symmetry, as one of the ends here passes through the turn of the other line, while the other does not.

Whether it is a good and useful knot might be tested, but it has a tendency to deform under load that is different from the Zeppelin.

For my own practical usage, there is no virtue in the different way of tucking the ends. I discarded the Zeppelin for practical reasons, and I cannot see any virtue in the different pattern that might be of better value. The one single reason for not including the Zeppelin in my toolbox is the complicated way of tying, which has not been improved. Other properties of the Zeppelin are excellent, but it needs too much attention to detail in the course of forming its pattern.

The "crossed ends" approach is different from the crossed ends in the Double Harness Bend, which does not lose its symmetry, but becomes something different, which is what's needed to make the Vice Versa. Arguedly, another knot will be formed by crossing the ends differently also in the harness bend, but the properties of the knot will not change a lot. The difference in the Double Harness Bend is seen as in one case the ends emerging at about right angles to each other, 45 degrees from the course of the standing parts, or the ends parallel to each other emerging at 90 degrees from the standing parts.

But just the same, a different knot is formed by tucking the ends in a different way.

The different orientations of the ends in the Zeppelin bend when formed in the original way do not change the tucks, but is merely a twist of the two ends together. The Carrick Bend has more distinct different aspects when ends emerge a bit different, as there are at least three rather distinct ways the ends may emerge all by themselves when drawing the knot tight. I don't know whether any of these really changes the behaviour of the knot, making it less stable, but two of them, the ones where the ends lie tightly together where they emerge, are neater than the third, where the ends are rather widely apart from each other. In practical use, there seems to be no difference. The knot has never failed me, and on a few occasions I have used it for several months. It still was easy to undo after a long Scandinavian winter.

Anyway, the X version is not the Zeppelin in my eyes, and any expansion of the idea will produce something else that might be a new knot, but not the Zeppelin. And my final verdict over the Zeppelin remains; it does not earn its way into the toolbox if it cannot find a convenient and dependable way of tying under harsh conditions and in total darkness.
Title: Re: Two variations of the Zeppeln bend
Post by: knot4u on November 22, 2010, 09:33:45 PM
  Thank you knot4u.

Zeppelin Bend = Zeppelin II ...correct?  The new name is more confusing, as opposed to less confusing.

  Correct, most of the time...Because sometimes, in the process of tying the Zeppelin bend, while we push the b and q ends so they pass through the common opening, we cross them without even noticing it. If the opening is small enough, as in my pictures, and if the rope is stiff enough, this crossing remains as it is till the end of the tightening, so, at the end, we form the Zeppelin bend X. The loading itself, any loading, can not disentangle a crossed pair of

I've tied the Zeppelin Bend maybe about 500 times.  I can't recall ever tying the Zeppelin Bend X, neither on accident, nor on purpose.  You have a different knot there.  After reading your posts, I will still be calling the first knot you posted a plain old "Zeppelin Bend".  Anyway, I'd like to move on and analyze the Zeppelin Bend X you posted.
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 22, 2010, 09:41:14 PM
Quote from: xarax
Is the bend shown in the pictures attached the infamous "third" variation of this pervasive "trio"?

No, it is the 2nd and what is usually shown is the 1st; your "X" is the 3rd.

Quote
1) If one sets the R.Z. bend ("Rosendahl's Zeppelin) from a loose state with
rapid tensioning of the SParts, it is quite possible --perhaps likely(?)-- that each SPart will pull the opposite end towards itself (i.e., in the direction that the SPart pulls)

Quote from: xarax
 As I have said many times, it depends upon ... .
[ergo] It is uncontrolled, so we may say it is, more or less, random.

It is more controlled to those who wish to seize control,
who dare to pull on the tails when dressing & setting the knot
to achieve a particular result.  (I am happy enough to not attach
to such possibility any great benefit, and to leave it of academic interest.)

Still, I might find myself taking some extra action, ...
Quote
2) ...by pulling on the tails a bit, the above orientation I submit can put into
the SParts a more gradual curvature than in most other dressings

  True. But isn't it more wise to go all the way, and cross the tails so the nipping loops run around a bulkier compound ?

As I will reiterate below, no, they are not the same knots;
and this "X" version is not symmetric, no matter you weaseling "s. breaking"!


Quote
4) The orientation of tails in R.Z."X"  is asymmetrical ...

Quote from: raving_lunatic
 No, they are not. The knot remains a 3D point symmetric knot. ( Otherwise, I would not dare naming it Zeppelin knot...) Each tail enters into the nipping "tube" in a specific orientation in relation to the other, swings around the other in an helicoid twist, and gets out in exactly the opposite orientation.

Let's put this quite practical-simply, not trying to hide the issue with
fancy terms : one tail exits through the collar of the other rope,
the other tail does NOT.  THAT is asymmetric, from my perspective,
and I don't care to excuse it by some reference to "s. breaking".
Which is what Inkanyezi has also explained:
Quote from: Inkanyezi
It also loses symmetry, as one of the ends here passes through the turn of the other line, while the other does not.

The difference has clear practical effect : in your pictured knot, XaraX,
the white rope --within limitations of setting/elongation...-- can draw its
tail towards rolling over the orange tail, white SPart drawing rightwards ;
but not so for its opposite number, as the orange tail is held against
such like draw by both legs of the white rope's collar.

Or, put another way, whereas the Orange Spart turns towards the viewer
and the White away, both tails exit towards the viewer ("upwards"),
both cross OVER the other as their final cross,
but this knot's symmetry requires that they be opposite in this.

As they are in the version I have been talking about which you have also
now shown, which preserves symmetry in the tails.

Quote from: Inkanyezi
Of course these musings go far beyond the practical aspect of knots, and more particularly beyond the practical aspects of the Zeppelin Bend.

Perhaps, except insofar as test data become available and are cited and
... depend upon such variation (which effect we only conjecture in their
absence, at this time).  And it is fair, yes, to question the practical importance
of such data, vs. a common Rule of Thumb about conventional ropes losing
50% strength when knotted, and keep you loads below 20%.  --fair enough.

 - - - -

Now, the asymmetric tails-crossing might have some application in the
R.Z. eyeknot, which differs in loading one tail.  I'm not sure I find a
particular orientation to use.

--dl*
====

Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 22, 2010, 10:02:44 PM
... it does not earn its way into the toolbox if it cannot find a convenient and dependable way of tying under harsh conditions and in total darkness.

Whoa, this seems a severe criterion for having something in the toolbox!
--almost like saying "if it cannot make an eye, ..." : point being that tools
have their own particular purposes, and why have ALL of them needing
this severe one?  In the condition you describe, are you going to be
joining anchor rodes?  --likely not, and so why preclude a possibly
"best" knot (in terms of strength, abrasion resistance, ...) from being
used just because that knot might not be easily tied at Force 9?

How would you tie a messenger line to a cable?
Might you have a way you prefer,
and one other that though not so desirable is easily tied?

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 23, 2010, 12:03:25 AM
/.../  my gut feeling tells me that, like many other people, you just do not like the Zeppelin bend...

On the contrary, I do like the looks of the knot, and I do like its behaviour, it's just that my preferred knot is so much easier to tie, particularly in darkness.

And of course it has snuck into my toolbox in a way, because I learned it, and I don't forget easily, but the reason for not using it is that I need a bend very seldom, and then I don't want to bother with looking at it while making it. So it might eventually be used some day, it's just not that likely.
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 23, 2010, 07:47:55 PM
/.../  It is amusing that people that consider the knots as tools, as practical instruments, disregard the functional symmetry of the Zeppelin X bend and insist that the most important thing is its geometrical asymmetry /.../

i have only seen such reasoning from you, xarax. While I do regard knots as tools, I don't give a rat's ass whether they are symmetric or not. I used the "symmetry" argument only as a means of identification, to distinguish one knot from another.

Also, assumptions of why a particular knot is "stronger than other knots" are not fruitful. For practical use, knots are tested, to find out whether their properties suit the purpose. Theoretical reasoning might be fine, but has little to do with practical knots. There is a board on the IGKT forum for knot theory, but I won't theorise over any particular helix or fill and its possible virtues within a knot.
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 23, 2010, 08:21:24 PM
Also, assumptions of why a particular knot is "stronger than other knots" are not fruitful.
For practical use, knots are tested, to find out whether their properties suit the purpose. ...

The problem we face here is in the poorly reported, and I think also
poorly designed testing and understanding exactly what was in fact
tested.  The continual, obvious examples (which sadly raise little
questioning from those purporting to be interested in the data) are
of Fig.8 eyeknots and the like, where it is unknown which end
has been loaded !  Beyond this comes the question as to whether the
usual, slow-pull testing has relevance to practical applications --or should
testing be of a different sort, e.g., of cyclical slightly-higher-than-working_load
forces with the assessment being made as to the condition of the cordage
after some numbers of cycles (or of peak force recorded upon some
dynamic loading assured of achieving rupture of the conditioned knot) ?!

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: DDK on November 23, 2010, 09:15:22 PM
Interestingly, the geometric symmetry of the "X" bend under discussion is neither the point inversion symmetry of the Zeppelin Bend nor the axial inversion symmetry of the Smith/Hunter's and Ashley Bend.  It could be considered a marriage of both symmetries, i.e. a marriage of the Smith/Hunter's with the Zeppelin.

. . .  As a practical knot, the Zeppelin X bend is symmetric, as a geometrical figure it is not. On the contrary, the Zeppelin I bend is symmetric in both roles, so we can argue that it is more symmetric than the Zeppelin X bend indeed.
  It is amusing that people that consider the knots as tools, as practical instruments, disregard the functional symmetry of the Zeppelin X bend and insist that the most important thing is its geometrical asymmetry, . . .

From my experience, the use of the term "functional symmetry" would be regarded as nonsensical in the fields of science and engineering in that the exact correspondence of geometrical symmetry with function is assumed in such endeavors and is one of the reasons symmetry is such a useful tool (but like statistics, useful for those who know how to properly use it).

DDK
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 23, 2010, 10:39:22 PM
Design of testing is of course a sidetrack that might be worth further investigation.

For my own practical use I do a few tests if there's a knot that I want to know certain properties of, one of them is flogging. Flogging invariably opens a sheet bend, given enough time. Flogging does not open a Carrick Bend in most soft and frictive stuff, although it is possible in springy stuff as kernmantle. Flogging also does not untie a Zeppelin.

As I am usually not very concerned about strength, always guessing that it might be decreased by half by any knot, I wouldn't test for strength, but for security. Repeated flogging and pulling with hard jerks will show whether the knot has a tendency to creep. The Zeppelin stands up well, the Carrick Bend too.

Of course manual testing of these properties is not very exact, but they give a hint of what the knot might withstand in practical use. Knowing that flogging will open a sheet bend, I wouldn't use it where it is subject to flogging, although it can be used if I am sure that the line will not flog. The single sheet bend has more tendency to creep than the double, but the Carrick Bend does not creep at all, so that's one of the main reasons for using it. However, for my mooring lines, I have a butterfly somewhere in the middle, to which I tie a spring with a double becket hitch. It will never flog, so creeping is not an issue.

And before a knot has been tried for security, I won't discuss what particular geometric feature in its structure that might make it more or less secure than another.

The first picture shows how I arrange my moorings when tying up between a buoy and a jetty. My lines to the jetty are attached far aft, mostly at the winches, and there's a spring forward from somewhere along the line. The knot is a butterfly loop and a double becket hitch.

The second image is how I arrange moorings when tying between Y-fingers. A line is drawn along the Y-finger, with some slack and an eyeknot at a suitable point. I take that eye a couple of turns around the winch either side and lock it by passing under the line and put the eye over the winch.

The idea is to avoid jerks when waves from passing boats rock the boat. When the boat is tied up like this, it has freedom to pitch without repeatedly slacking and jerking on its leash. Geometry too is a tool, and poor geometry in the arrangement of mooring lines may cause disasters. With this geometry, no extra elasticity is needed in the mooring.
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 24, 2010, 04:06:00 PM
I know that I deviated from the original subject of the Zeppelin variations with my previous post, and it was on purpose, just because the discourse anyway strays away from the main theme of practical knots.

But I will make a small theoretical comment here. Contrary to what is said in #22, the curvature will not necessarily become less sharp when there is more fill in the Zeppelin, but curvature may increase, because the curvature that is relevant to strength is not necessarily the one within the knot, where the nub sits, but might be the one at the entrance of the knot, where the collar hugs the standing part. When a knot breaks, it seems always to be just outside but never inside its structure. The two images show a false picture, because there is no load on the junction when they were taken. When load is applied, the two standing parts will always be in line with each other. The deviation will gradually increase with increased fill, approaching a maximum of 90 degrees when the fill is infinite. The least curvature will be with the least fill inside the knot.

As the Zeppelin is amply secure (and strong, which has been tested) in its original form, any expansion only makes the knot more complicated to tie without adding significant properties neither to strength, nor security. There might of course be some extremely slippery material, where the doubling will significantly decrease any tendency to slip, but so far I have not seen a Zeppelin slip once it is set. Doubling might show some virtue when knotting HMPE, but again, it is only theory; to be sure, it must be tested.

So once again, it has been shown that assumptions may lead to wrong conclusions, and when there is a difference between the map and the terrain, the latter will always have preference over the former.
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 24, 2010, 05:37:03 PM
Interestingly, the geometric symmetry of the "X" bend under discussion is neither

I continue to fail to see symmetry at all,
when --as has been stated now several times-- the tails
have different relations to the knot (and of course vice versa)
--one exits out through the collar of the opposite rope,
the other does NOT.  THAT, to me, shows Asymmetry (not "a symmetry")!?
Please explain the contrary position.

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 24, 2010, 05:44:26 PM
Not a Hallberg Rassy, but one of the very oldest tubs made of glass and resin, a Karlskrona-Viggen, designed by Per Brohaell, from 1965. The pit is aft.

But the layout of most small sailing vessels is similar, and on most boats you can find a convenient midship belaying point for mooring lines. A funny thing with the layout is that it cannot easily find acceptance, I believe this is due to its non-conformity. Many think that it will not effectively restrain the boat from sideways movement or yaw, but in usage it has shown its efficiency. Pitching is not restrained, but the boat will not easily shift position, and the bow will not drift sideways more than with conventional mooring. I have even tried the same method with a small row-boat, where between Y-fingers it was only tied by the stern, and it was quite as effective. Here in Sweden, tying up with the bow to the jetty is common, and "mooring springs" to enhance resilience is mostly mandatory, but I don't use them. (To avoid confusion, they are not spring lines, but mechanical springs, made of resilient material, used to permit resilient elongation of the line.)
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 24, 2010, 05:54:06 PM
Contrary to what is said in #22, the curvature will not necessarily become less sharp when there is more fill in the Zeppelin, but curvature may increase, because the curvature that is relevant to strength is not necessarily the one within the knot, where the nub sits, but might be the one at the entrance of the knot, where the collar hugs the standing part.

Good point.  I think that a *doubled* collar will help, here,
in ameliorating the effects at this deflection point.

Quote
When a knot breaks, it seems always to be just outside but never inside its structure.

I disagree : I have found and have had tested-to-rupture some knots
in laid rope and insofar as I can trace the breaking point it appears to
be at a point at the initial deflection and on the concave/"inside" side
of the bend --contrary the outside-fibres-take-the-load theory.  And in
some cases where a break is seen outside, it comes in material that was
formerly inside the knot and which got abraded and degraded in being
pulled out.

This is a tricky thing to test, but note that in some slow-pull testing
it will be the case for laid rope that ONE (or two) strand will break
and the other two will remain intact (and there will be a temporary
drop in tension by this yield of material, and some devices I surmise
automatically stop (this is how my test specimens have come back,
incompletely broken, sometimes).  Which then enable one to try
to determine where the broken strand lay at its parting point.

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: [Inkanyezi] gone on November 24, 2010, 06:54:05 PM
The pit is aft.

Your picture shows a winch almost amidships...


Oh, it is a small boat with a large cockpit, but also, it is artistic freedom. It is a sketch, showing a principle, not a picrure of the actual boat. The principle can be used for any boat. It was my frustration with the mooring fingers not having a convenient belaying point that made me think up a better solution that suited my boat, and I adapted the same principle as when I tie with a buoy, but reversed the attachments. At first I tried double springs attached to the center of the Y-beam, but then, when I reversed the springs, attaching them to somewhere more central at the boat and the ends of the beam, it became a lot simpler to handle. The eye that I use for those is a fig8 tied in the bight. First I didn't use any eye, but it was more convenient, because it puts the boat in exactly the same position each time in a very simple way. 
Title: Re: Two variations of the Zeppeln bend
Post by: knot4u on November 24, 2010, 08:41:31 PM
Interestingly, the geometric symmetry of the "X" bend under discussion is neither

I continue to fail to see symmetry at all,
when --as has been stated now several times-- the tails
have different relations to the knot (and of course vice versa)
--one exits out through the collar of the opposite rope,
the other does NOT.  THAT, to me, shows Asymmetry (not "a symmetry")!?
Please explain the contrary position.

--dl*
====

I didn't even notice that at first.  A quintessential feature of the Zeppelin Bend is that it's symmetrical.  I don't think Zeppelin Bend X should have the word "Zeppelin" in it because Zeppelin Bend X is NOT symmetrical.
Title: Re: Two variations of the Zeppeln bend
Post by: knot4u on November 24, 2010, 11:03:20 PM
Even if the Zeppelin Bend X looks symmetrical initially, the bottom line is that it is not symmetrical.  In a symmetrical bend, each rope takes a "mirrored" path through the knot.  In other words, there is at least one axis around which you can flip the knot and the knot will look the same on the opposite side.  Accordingly, the Zeppelin Bend and the Carrick Bend are symmetrical.  I think the Ashley bend is symmetrical too.  However, the Zeppelin Bend X definitely does NOT fall within the meaning of symmetrical.  Neither does the Butterfly Bend.

It's OK to be wrong.  Just don't be loud and wrong.
Title: Re: Two variations of the Zeppeln bend
Post by: knot4u on November 25, 2010, 02:42:45 AM
(http://i641.photobucket.com/albums/uu131/KevlarPaperclip/double-facepalm.jpg)
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 25, 2010, 08:32:36 AM
   Why DDK understood it better and you failed to do the same ?
   Try again... :)

&

I have already spent much of the limited energy resources of our planet, [ad nauseam]

I quite agree, and am hoping for DDK to answer the question, not you,
as you seem unwilling to consider the case.

Are two Overhand components of "X" geometrically identical --no, they
are (1) opposite-handed (which only *colors* possible symmetry)
and (2) differing in how their tails exit : one tail after crossing the SPart
arcs around without much variance from its position to cross it on the
opposite side (if first deemed "under", this one "over) as it completes
the Overhand ;
but the other tail cannot follow such a flight plan, as it must dip farther
away from its SPart to allow the first tail's clearance.

Now, DDK, have you some reasonable explanation for your position,
and how the issues I et al. have remarked can fit into "symmetry"?

Let's give XaraX a rest.

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 25, 2010, 03:30:00 PM
Oftentimes it is better to leave things to settle down by themselves with time, rather than with insistent arguments.

What was insistent was an assertion; what was missing was argument.

Quote
I have argued that the Zeppelin X is somehow symmetric, ... , while most other members of this forum have not seen much or any symmetry at all, so they argued that it is asymmetric.

We saw a departure from symmetry and pointed this out;
we judge a knot not isolated parts of it --"not with
themselves" thus points to the issue:  "with themselves" is
a partial picture, of parts, not of the knot.  We have pointed
to how the asymmetry manifests itself in practical effects on
the knot's SParts.

Quote
I have also pointed out that the two interlocked parts of the bend, if viewed separately, are  mirror symmetric, ...

No, you have asserted this, but frankly it is clearly NOT the case.
For the R.Z. bend, the mirror would be put *alongside* the Overhand
component, so though mirrored SParts might both be turning down
--say, of horizontal flow *into* the knot--,
they would then show their opposite-handedness by moving say both
away from the mirror plane, and so on;
but when it comes time to flow into the tail exit,
they necessarily diverge from mirror-matching as they respectively
must flow around the opposite tail in different ways.  And why you
don't see this (or, how you can explain this as yet keeping symmetry)
is beyond the rest of us.

And so I'm awaiting for DDK to answer this challenge to an assertion
that he, too, has made.  He certainly has many words explaining the
challenge to work with.

--dl*
====

Title: Re: Two variations of the Zeppeln bend
Post by: DDK on November 25, 2010, 05:12:51 PM
Re: Geometric symmetry
I have used the phrase "geometric symmetry" in the technical sense which may be unfamiliar to those who have not worked with symmetry groups (an interesting and not too difficult mathematical discipline).  In the technical sense, every configuration has geometric symmetry, that is, it has symmetry operations (a "group" of them) which leave the structure invariant (the new structure will lay exactly on top of the original structure).  Sometimes the only symmetry operation member of the group is the trivial identity operation (i.e. you do nothing to the original structure)!  We have been using the term asymmetric for such structures while the phrase "lacks symmetry" is likely more appropriate.  By this we are saying it lacks symmetry elements other than the identity operation.   

Re: The "marriage" of two symmetries
Let's be clear, the "X" bend lacks symmetry.   Having said that, I should explain what I meant by the "marriage" of two symmetries.  I was not implying that we have combined two symmetry groups into one.  For example, a combination of a twofold rotation element and a mirror plane can produce the central inversion symmetry group found in the Zeppelin Bend.  This is a legitimate non-trivial symmetry group.

In the "X" bend, if one follows the standing parts into the knot, you find that they are related by an "APPROXIMATE" central inversion symmetry, e.g. Zeppelin-like, and at some point rather smoothly transitions into an "APPROXIMATE" axial inversion symmetry, e.g. Smith/Hunter's-like.  The transition has to occur within a particular plane in the bend, and thus, the structure is fascinating from that perspective.

Re: What is a "good" symmetry?
In my opinion, there is no such thing.  For example, both the Zeppelin Bend and the Thief Knot have exactly the same symmetry.  The turns, curves, crosses, etc. (mechanical elements) of the bend determine its performance.  Symmetry may at times allow us to understand how these mechanical elements work in harmony or at cross-purposes within a particular bend.  Symmetry does not allow us to compare one bend to another.  If one introduces new mechanical elements, which often happens with even minor changes to the structure or symmetry of a knot, obviously all bets are off.  It is my understanding that as a species we find symmetry "attractive".  I believe we should recognize this instinctive infatuation for what it is.

Re: The naming of "X"
Given my own in infatuation with symmetry, I would admit that the use of "Zeppelin" to describe the "X" bend rubs me against the grain.  Certainly, it does no justice to the interesting "marriage" aspect of the structure.  That is my issue.

DDK
Title: Re: Two variations of the Zeppeln bend
Post by: Dan_Lehman on November 26, 2010, 07:23:19 AM
It should be obvious (and, moreover, expected) that "everyone" of
normal knotting interest does not come with special mathematical senses
& sensibilities, and that the common understanding of "symmetric" is
different from what I understand from DDK.  In common senses, a bend
is *symmetric* if one half can be replicated to form the other --either in
pure copy or by mirror-image copy-- and joined exactly so (regard the first
half formed of rigid material (steel, e.g.), and posit that the symmetric
complement is materialized into place to complete the knot.  THIS cannot
be done with bend "X"; the halves have different shapes.

When I use the term "geometry", I mean the physical shape of the
structure (or component).

--dl*
====
Title: Re: Two variations of the Zeppeln bend
Post by: DDK on November 26, 2010, 05:10:45 PM
Xarax, I feel you are taking too lightly just how approximate is the symmetry of the individual components of the X bend.   This will assuredly lead to a differing behavior for the component and its, in some cases not so similar, "twin", even in a very localized sense.  The relation of the individual components to each other is important and is one of the reasons that one places a great deal of importance on the symmetry of the knot as a whole.  Those that say that the X bend is not symmetric are exactly right in my opinion.

To possibly explain my perspective on Symmetry to Dan Lehman, I might use this analogy (perhaps not a very good one, but the best I have for the moment).  If one discusses the Quantity of an item one has (let's say in inventory), he might say he has 1, 4 or maybe 0.

DDK
Title: Re: Two variations of the Zeppeln bend
Post by: SS369 on November 28, 2010, 03:34:42 PM
"I see it as one symmetry in space that is transforming into another in time, if with "time" we mean the intrinsic time of a point travelling along a line/curve/tangled rope in 3D space. "

I think we have entered the Twilight Zone now.
Perhaps this should go to the Knot Theory & Computing section.

I personally am having a small difficulty following where this thread has traveled and would like to see some real data about these ZB variations. How do they indeed compare to the "parent" ZB?

Perception, and that is what I think is being argued with and for here, will always be from the side of the speaker.

So how is the "X" version improved or nor improved if you introduce even more crossings in the center?

My own personal opinion is that the the ZB variation where the working ends are circled around and re-tucked back into the nippers is the most secure.
Even if making it a slipped ZB (tripled bundle inside).

Scott