Author Topic: Twisting the standing parts of the falsely tied Hunter s bend  (Read 31163 times)

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #45 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.











xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #46 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 ! 
   
This is not a knot.

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #47 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 ...
This is not a knot.

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #48 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.

« Last Edit: April 13, 2015, 09:07:17 AM by Tex »

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #49 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.
:) :) :)
This is not a knot.

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #50 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.

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #51 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
« Last Edit: April 13, 2015, 04:39:27 PM by xarax »
This is not a knot.

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #52 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.
« Last Edit: April 14, 2015, 12:32:30 AM by Tex »

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #53 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.
This is not a knot.

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #54 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.

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #55 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.   
« Last Edit: April 23, 2015, 09:16:10 PM by xarax »
This is not a knot.

Tex

  • Guest
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #56 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.




 

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #57 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 !   :) 
« Last Edit: April 16, 2015, 04:24:46 PM by xarax »
This is not a knot.

Dan_Lehman

  • Sr. Member
  • *****
  • Posts: 4072
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #58 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*
====

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Re: Twisting the standing parts of the falsely tied Hunter s bend
« Reply #59 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.  :)
« Last Edit: April 23, 2015, 08:03:17 PM by xarax »
This is not a knot.