Term Post Eye Tiable i.e. PET

Knotting Concepts & Explorations
1

I would like to discuss about the history of the term post-eye-tiable (PET for short) and about the concept in general and about closely related concepts and definitions in this thread.

I found a couple of descriptions for the term:

  1. https://igkt.net/sm/index.php?topic=5254.0 that also discusses about some other terms:
    “PET - Post Eye Tiable. This is the concept of tying a rope end to an endless rail (or a toroid) where the knot can be fully formed in a one-step process after the rope has been passed around the rail, or through a ring. That is, a knot-free rope first makes a loop around the endless rail, then the knot is tied.”

  2. is an answer https://outdoors.stackexchange.com/a/22087/20453 for a related question:
    “Post eye tiable means that the rope is passed through the eye or harness before any part of the knot is tied.” (other ‘any’ trimmed by me)

The concept is non-trivial for loop knots i.e. eye knots, I mean fixed loop knots that do not contain a knot that can move along the working part. A noose knot is always tied in PET way so it is trivial.

I think it is not needed to pass the rope end through the eye, if you use a bight.

I wonder what was the original meaning of the ‘eye’ in the term? Does it refer to the eye, the object, to which the knot is tied to, or to the eye of the knot that is to be constructed by tying a knot? One could think the eye of the knot does not exist before tying the knot :slight_smile:

Attempt for an alternative definition for post-eye-tiable without mentioning an object that the eye is connected to:
A knot is post-eye-tiable in respect of its eye if and only if there exists a tying method for the knot such that no knot except maybe a tiable-in-a-bight knot is needed before the first threading that forms the eye of the knot and that threading must make the eye smaller, and a bight is not threaded over the eye later on in the tying process.

Example: With that definition the Bowline on a bight (ABoK#1080) is PET in respect of its first eye (provided you have access to the working end), but not in respect of its second eye. The knot is also tiable-in-a-bight, but not by the same tying method than it is partially PET.

2

Hello jarnos:

Go to this link: http://www.paci.com.au/knots.php

Download and read: ‘An analysis of the structure of Bowlines’ (VER 3.0)… at #4 in the table.

Perhaps most of your questions will be answered in that document…

3

The PACI password I have used before no longer works.

4

The password is given in the document.

Besides, the “Knotting terminology” document (http://www.paci.com.au/downloads_public/knots/Knot_Glossary_Robert-Birch.pdf) has terms explained, too. It does not have a password.

5

Hello agent_smith. Thanks for the directions. The document has this definition for PET without mentioning an object the eye is connected to:

If all knot tying maneuvers can be completed after the eye has been formed ? the knot is ?PET?.

My definition is somewhat different: E.g. a TIB knot may exist before forming the eye. Even if there was no such a knot needed some other maneuvers such as forming a loop (like in case of a bowline) may be needed before forming the eye.

6

My error thank you.

7

Greeting jarnos:

My definition is somewhat different:
Feel free to invent your own theoretical body of work - and publish it. This is how science progresses over a period of time. Let me know when you have published - so I can download and read it.

In relation to the definition of ‘PET’:

E.g. a TIB knot may exist before forming the eye
The key point is whether any knot tying maneuvers are [i]required [/i](ie be pre-existing) [i]before [/i]the eye is sized and formed. If such maneuvers are a necessity, and the eye [i]cannot [/i]be sized and formed without such a pre-existing condition, then the knot cannot be deserving of the title of 'PET'. From a technical standpoint, your alleged pre-existing 'TIB' knot could be tied after the eye has been sized and formed. A 'TIB' structure is equivalent to the 'unknot' (ie an unknotted length of rope).
some other maneuvers such as forming a loop (like in case of a [b]bowline[/b]) may be needed before forming the eye.
With regard to a 'Bowline', it is [u]not [/u]a pre-existing condition that a [i]loop [/i]is formed [i]before [/i]attempting to size and form the eye.

…

In terms of the history of the invention and use of the term ‘PET’; it was likely that grandmasters such as Xarax and Dan Lehman evolved the concept either independently of each other or in one of their great debates… not sure which.

Mobius also appeared to be motivated to add a dimensional object to qualify the definition of ‘PET’.
I believe that it isn’t necessary to add such a qualifier.
However, one could state that; “By default, the eye of a PET knot can be formed through a ring”.
Although, the inclusion of a ‘ring’ to qualify the definition is not essential to understanding.

…

You appear to be struggling to understand many basic concepts…
Not sure why?

8

Could you please be more exact about what you mean by forming and sizing an eye? One could think that the whole process of tying an eye knot is forming and sizing of an eye. Forming an eye is not the same thing as forming a bight or a loop, right?

In case of a bowline, you could start by tying a loose overhand knot and capsize it later. Anyway, when the knot is ready and you follow the cord from the standing part into the knot, the first thing the cord does is a loop before you get to the eye part of the knot.

A 'TIB' structure is equivalent to the 'unknot' (ie an unknotted length of rope).

What is your definition of equivalence relation between knots? Do you regard tying a TIB knot equivalent of tying nothing? In mathematical knot theory unknot is like a circle, an endless closed loop.

9

To tie the knot in the photo, you could first tie a TIB Span loop (ABoK#1049) and then tie the working part to its eye (loop).

I would say the knot in the photo is PET in respect of the eye marked by the green loop. The knot has also two other eyes marked by black and white loops. The green loop (if big enough) could be moved to meet the white and the black one. If the bight marked by the green loop was much shorter, the tip of the respective eye would be located at the region of the other eyes.

span-loop-based-pet-knot.jpg

10

Maybe post-eye-tiable is not the best term for what I am looking for. The key thing is that you do not have to thread the part of the cord that becomes the eye through/behind anything except maybe the object that the eye is connected to. It is handy to use that kind of knot especially, if the eye has to be very large.

11

Hi Jarnos.

I am somewhat confused now. >>> ? The key thing is that you do not have to thread the part of the cord that becomes the eye through/behind anything except maybe the object that the eye is connected to.?<<<

How else is the eye to be formed when using an object that the eye is going to be around or through, such as a ring, tree, spar, pole, or anything?

With some post (after) eye tiable knots, the eye is easily sized before tying the core that finishes the knot.

I can form a bowline with a very large eye or adjust it to a very small eye.

So, is there a communication challenge or typos to be considered?

SS

12

Hi SS,

Some part of (the cord that will become) the eye may have to be threaded through a ring, if the eye is to be tied to a ring, but the knot as such could be made without any additional object.

You can form and size a bight, or U turn, but I would call it an eye only after it has been somehow connected to the standing part or to an inline knot so that the unity encloses a region. It is unnecessary to require that no knot tying maneuvers must be made before accomplish such a closed region.

13

?! There is a lot of effort here expended to take
something that is simple and effective and turn
it into … --I don’t know what.

no knot except maybe a tiable-in-a-bight knot is needed before the first threading that forms the eye of the knot and that threading must make the eye smaller, and a bight is not threaded over the eye later on in the tying process.
How would an NSUE (=TIB) knot be "needed", as that character of it ensures that it can be put in ... whenever!?

The simple point is that one has NO KNOT in the line,
and will (be able to) make the eye forming --e.g., the
putting the line through a mooring ring on the quay–
in this state, “size” it to whatever size appropriate,
AND THEN tie the knot.
–a simple and sometimes important quality.

–dl*

14

This is rather academic, but I suppose it can be discussed about in this sub forum.

How would an NSUE (=TIB) knot be "needed", as that character of it ensures that it can be put in ... whenever!?

Well, take a look at the knot in reply #8. You can not tie the TIB part of the knot after you have tied the returning eye-leg to it, but you can tie it even before forming the bight/collar for the eye.

The simple point is that one has NO KNOT in the line, and will (be able to) make the eye forming --e.g., the putting the line through a mooring ring on the quay-- in this state, "size" it to whatever size appropriate, AND THEN tie the knot. --a simple and sometimes important quality.

That is practical point of view. Maybe call it post collar tiable eye knot, then :slight_smile:

Other definition would be that it is an eye knot where no non-TIB knot is required before the eye part. Do we have a term for non-TIB knot i.e. for a knot that requires access to the working end?

15

If not, I think we could use terms like tying requires extremity (TRE) or end knot.
And maybe middle knot for a TIB knot, respectively; using an end knot in the middle of a very long cord would be unpractical.

Another way would be to use agent_smith’s terminology: unknot for middle knot.
Then end knot would be something like proper knot. This might be confusing for as middle knots can be substantial knots, too, in practice.

16

In the image I apply terms of graph theory to knots, which helps in talking about more complicated knots. In graph theory an edge that connects vertex to itself is called loop, self-loop or a buckle. That is what is usually called eye when talking about knots. More general eye corresponds to cycle. Post eye tiable corresponds to wend (i.e. working end) not needed before connecting (i.e. tying) the enclosing edge of the cycle. (There is also a geometrically smaller cycle in the knot.) Core or nub corresponds to vertex.

graph.jpg

17

Hello jarnos,
Hope 2021 is shaping up well for you.

Everything I write herein is intended in good faith (just to remove any doubt)…

I have carefully read through all of your posts - including your latest post.

Okay… I am left wondering about exactly what you are trying to achieve or what exactly is your proposition?

There doesn’t appear to be a question in your most recent post.
Your post appears to be framed as a statement of fact, rather than a question seeking an answer.

May I please direct some questions to you as follows:?

  1. Do you have a concern with the concept of ‘PET’?
  2. Is the term ‘PET’ and its basic meaning a source of irritation to you?
  3. Do you believe that the term ‘PET’ is ill defined - and needs to be revised?
  4. Do you fundamentally disagree with some knot terminology that has been used (eg eye instead of loop)?
  5. Do you believe that you most recent posted image is proof that the concept of ‘PET’ is flawed or wrong in some way?
  6. Do you believe that the concept of ‘PET’ is limited only to certain classes of knots - and cannot be universally applied to all categories of eye (loop) knots?

If you could provide some answers to these questions - perhaps others might be able to supply constructive discussion…

Thanks in advance :slight_smile:

18

Also Robert G Birch defines eye (knot) in his “Annotated Glossary for Practical Knot Tyers” that can be found by title “Knotting terminology” in the linked page in reply #1.

Eye is not just a bight. It needs also a nub by which both legs of the bight are connected. When you have an eye, you already have connected the legs of the bight in a nub and you might not have to tie anything thereafter. That is why talking about post eye tiable is conceptually troubled.

If we want to define an eye knot that has more than one nub (like in my previous post), it might be good to expand its definition or add another term for such a structure.

It is sad that the concept of loop in graph theory is not analogous to the concept of loop when talking about knots; it corresponds to eye, instead. Traditional naming of eye knots as loop knots may also cause some confusion.

19

Hello and greetings jarnos,

I am continuing to engage with you in good faith.
I am trying to zero-in on the source of your concerns with respect to the concept of ‘PET’ (Post Eye Tiable).

I don’t speak your first language - I only speak and understand English (sorry). So I can only correspond in English!

Okay, I will try to extract some meaning from your most recent post:

Also Robert G Birch defines eye (knot) in his "Annotated Glossary for Practical Knot Tyers"
Please be aware that Robert Birch did not invent the concept of 'PET' - he merely attempts to report it. I have read his document and here is the definition he typed:

Per Robert Birch:
An eye knot is PET (post eye tiable) if it can be made with the eye around a post, without
accessing either end of the post and without needing to form a preliminary knot before passing
the line around the post.
The first part of his definition is incoherent and confused - and needs to be re-worded.
The second part (in red font) is accurate.

I think it might be useful to specify an object such as a fixed ring within the definition of ‘PET’ (Note: A fixed ring is different to a post).
By specifying a ring, it narrows the definition.

Eye is not just a bight.
An 'eye' is not a 'bight' (they are two different descriptors). However, I can see that in the case of a #1047 F8 - when it is tied-in-the-bight, the 'eye' can be formed and sized before the core is tied. I can see your correlation between a 'bight' and an 'eye'. In this example, the 'bight' of rope in the F8 is [i][b]destined [/b][/i]to become the 'eye'! The 'bight' is (in effect) a preliminary 'eye'.
It needs also a nub by which both legs of the bight are connected.
The term 'PET' only refers to a situation where the beginnings of an eye can be formed and sized without any conditional knot pre-existing in the line. I used the word 'beginnings' - to emphasize that once the 'eye' has been formed into the desired size, the core of the knot can then be completed. Lets take a [b]fixed ring [/b]as an example. In a 'PET' knot, the line can be passed through a [b]fixed ring [/b]and then the core of the knot is tied and completed. No pre-existing knot is conditional. In the case of #1047 F8, there is no way that the 'eye' can be formed through a fixed ring without a pre-existing knot. That is, it is conditional that a knot is tied in the line [u]before [/u]feeding the rope through the fixed ring.

The line that is passed through the fixed ring will become the ‘eye’.
As the line is fed through the fixed ring, it is not yet tied into the core (nub).
It is in a preliminary state - because at this point in time, it is not yet fixed.

#1047 F8 is an interesting case because it can also be tied in-the-bight. That is, it is ‘TIB’.
The initial bight that is formed will become the ‘eye’.

SUMMARY:
If it is necessary to specify a fixed ring within the definition of PET - I am in favor of such a modification.
By narrowing the definition of PET to eye knots that can be tied to a fixed ring without any pre-existing knot - it will help to remove doubt.
The #1047 F8 is ‘TIB’, and so technically, the ‘preliminary eye’ can be formed and sized before any knot is tied in the line. But if we narrow the definition to include a fixed ring, this eliminates #1047 F8.

Let me know what you think and if you agree - perhaps we can gather support?

20

Personally I find the Birch definition to be totally correct and to aptly describe the restrictions imposed on a knot for it needing to be defined as PET. However, for completeness he might have written “around a post or ring” in order to ensure clarity that the formed loop could not simply be passed over the fixing point.

However, despite this, the term PET is virtually meaningless as any desired components or ‘pre-knots’ required can simply be tied with the WE after it has been passed around the fixing point, then drawn back around the fixed object / ring leaving a protoloop around the object, then finish off the knot using the WE.

Unless we are dealing with a ring whose eye is so tiny that only a single cord diameter can be passed through it, then the whole concept of PET is meaningless.

Derek