Author Topic: The relationship between 'bends' and eye knots  (Read 2873 times)

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #30 on: January 04, 2024, 04:03:15 AM »

With regard to the 'correspondence between bends and eye knots':

Clearly - I am biased because I do believe there is a relationship between a 'parent bend' and its offspring 'eye knots'.
I will simply again point out that w/o throwing anything
out of consideration (with a focused view) one has, from
whatever *knot* is up for consideration, a *tangle*;
and a *tangle* has all these possibilities re its *knots*
via the loading profiles.

But formalizing this is really tough.  That yChan
dressing of SmitHunter's Bend quite impressed me
--the "same" knot?!  Not by my reckoning, but then
it shows how differences can sneak around formal
barriers.

Quote
[HINT]: #1425 is topologically equivalent to the 'False Zeppelin bend' (with crossed tail segments).
And I'd like to see its performance for strength.
We've seen Thrun's Joint/PoorMan'sPride/zep. go out
of form, in the HowNotTo guy's video (amazing!).

--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #31 on: January 06, 2024, 02:43:14 AM »
from Dan:
Quote
I will simply again point out that w/o throwing anything
out of consideration (with a focused view) one has, from
whatever *knot* is up for consideration, a *tangle*;
and a *tangle* has all these possibilities re its *knots*
via the loading profiles.
Am unclear as to what the ultimate purpose of this comment is?
I am not being offensive - I am simply being factual - in that I am left wondering what your point is?
Ok.. the 'knot' that is up for consideration is presumably a 'bend' (an end-to-end join).
I'll refer to this "knot" (a tangle per your words) as the 'parent bend'.
Note: Definition of 'tangle' = a confused mass of something twisted together
I am of the view that any knot that is tied with an intended specific geometry is not a confused mass.

per Dan:
Quote
But formalizing this is really tough.

I am making the following claim:
A deliberately tied parent bend which has a specific intentional geometry has a defined number of [derived] corresponding eye knots.
These corresponding eye knots have a [core] geometry that is congruent with the [core] geometry of the parent bend.
Note: I am using the word 'core' to denote the part of the knot that is central to its existence or character.
I find this definition better than 'nub'.

I am using the term 'eye knot' in lieu of loop knot.
An eye knot is analogous to an eye bolt - the eye being round/oval and permits connectivity (eg a carabiner).
The 'eye' of an 'eye knot' has no particular chirality (handedness).

I am (by definition) making the claim that the correspondence (or relationship) between a parent bend and its derived eye knots is geometric in character.
This claim is valid where load (or a loading profile) is not considered.
That is, the correspondence is purely geometric in character.
All knots respond to load in different ways - and the particular loading profile plays a significant role in this 'response'.
Typical responses include (list is not exhaustive):
[ ] compression
[ ] distortion
[ ] extrusion of rope segments out of the core
[ ] instability
[ ] insecurity
[ ] collapse

Dan Lehman may wish to make an alternative claim (or perhaps make no claim whatsoever).
He is entitled to do so.
Dan may wish to reject a geometric relationship and consider loading profile as the dominant factor to consider.
If this is his preferred approach - this may explain his reference to "possibilities".
There may indeed be a number of possible 'eye knot' derivatives - perhaps being difficult to quantify?
In contrast, if a geometric approach is taken, it ought to be easier to quantify the number of possible eye knot derivatives.
And again - my preferred approach is to begin with [a] 'bend' and then try to derive the corresponding eye knots (rather than the other way around).
In my view, the logical approach is to use a 'parent bend' as the basis for deriving corresponding 'eye knots'.

Quote
That yChan
dressing of SmitHunter's Bend quite impressed me
--the "same" knot?!  Not by my reckoning, but then
it shows how differences can sneak around formal
barriers.
In my view, this is potentially straying off-topic - and is best examined in a separate topic thread.

Quote
Quote
Quote
"[HINT]: #1425 is topologically equivalent to the 'False Zeppelin bend' (with crossed tail segments)."
And I'd like to see its performance for strength.
We've seen Thrun's Joint/PoorMan'sPride/zep. go out
of form, in the HowNotTo guy's video (amazing!).
Possibly best dealt with in a new topic thread.
But, 'strength' is irrelevant in my view.
Possibly you meant some kind of 'response to load'?
Response to load (or from some particular loading profile) allows one to assess things like; stability, security, jam resistance, etc.
For example, strength is not a relevant factor in the use of #1410 Offset overhand bend in abseiling/rappelling.
Focussing on 'strength' leads one to wrong conclusions (because stability, security, knot footprint, and jam resistance are more important factors).

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #32 on: January 06, 2024, 09:58:38 PM »
from Dan:
Quote
I will simply again point out that w/o throwing anything
out of consideration (with a focused view) one has, from
whatever *knot* is up for consideration, a *tangle*;
and a *tangle* has all these possibilities re its *knots*
via the loading profiles.
Am unclear as to what the ultimate purpose of this comment is?
I mean to push towards reaching the Tangle level
and then going from there with whatever particular
loading profiles (eye knots, e2e joints, knot hitches...)
are of interest.  Whereas, in this ...
Quote
I find it logical to begin with a 'bend'
- and then try to derive the corresponding eye knots.
... I felt a bit constrained.  In a sense, one isn't
so much deriving ... but showing --they're
right there, in the Tangle, to be ID'd per the Tangle
pieces (1-2 & A-B, for a 2-Tangle).

Quote
Note: Definition of 'tangle' = a confused mass of something twisted together
I am of the view that any knot that is tied with an intended specific geometry is not a confused mass.
... and that of course we're not using "Tangle"to mean this,
but simply an entanglement of cordage devoid of loading.
(Deliberateness might be overrated; in any case, one has
THIS or that Tangle, however wrought, for the consideration
of its various Knots via loading.

Quote
Note: I am using the word 'core' to denote the part of the knot
that is central to its existence or character.
I find this definition better than 'nub'.
What happens if "core/nub" is omitted --esp. re e2e joints!?

Quote
Quote
That yChan
dressing of SmitHunter's Bend quite impressed me
--the "same" knot?!  Not by my reckoning, but then
it shows how differences can sneak around formal
barriers.
In my view, this is potentially straying off-topic - and is best examined in a separate topic thread.
Well, it points out a significant change of your
vaunted geometry in a knot that is put together
able to have such difference.
(Consider also how there are different dressings
of the Fig.9 EK.)


--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #33 on: January 07, 2024, 11:02:54 AM »
This post is directed to Dan:

We are getting technical here...but it is useful to sort out definitions... because I think this is fundamental to any progress.
Also, this is a forum for technical discussion about knots - with deep dives into underlying concepts.
I don't know of any other forum on planet Earth where these types of peer-level discussions are possible?
In this regard, I'm happy to explore this subject matter with a view to finding some common understanding and agreeance.
At the very heart of this subject matter is the English words we choose to convey complex ideas...Words have meaning.

In reply to your points...
Quote
I mean to push towards reaching the Tangle level
and then going from there with whatever particular
loading profiles
We need to agree on definitions.
I hold the view that the word 'tangle' has a particular meaning as follows:
"a confused mass of something twisted together".
A random knot that accidentally formed in a rope might fit this definition (eg due to wind, strong hydraulic water flow in a stream, shaking/jostling, etc).
However, I am strongly of the opinion that when a person ties a knot he has a particular outcome and purpose in mind.
The knot tier directs his mind to the task - applying cognition - to achieve a particular and/or specific geometric outcome.
For example, I intend to tie a Butterfly eye knot (Ashley #1053).
The result I end up with can be verified against a known standard (I can look up #1053 in a book and verify it).
The end result (ie outcome) is either correct or incorrect. I am of the opinion that you can't say that a knot is half correct (or 25% correct).

There must be some basis for establishing and agreeing upon certain standard geometric knot forms - for example, we all agree that a simple Bowline is depicted at #1010 in Ashley's book.
In the same way, we have the 'SI' metric units of measurement - and we all agree on what a metre length is. And we all agree on what 1 kilogram mass is.
Without a standard model to compare against, there would be no way for an assessor to assess a trainee. A trainee could tie anything into a confused mass of twisted rope and demand to pass an assessment.
For example: An assessor asks a trainee to tie #1053 Butterfly. The trainee presents a confused twisted mass of rope to his assessor.
The trainee demands to be assessed as competent.
An assessor needs measurable criteria to enable decisions/judgements to be made about a student competence.
However, for this to be true - there must be an agreed standard for a knot that is assigned the name 'Butterfly'.
Without an agreed standard - there can be no agreement - only confusion.
EDIT NOTE:
Can we assume Ashley and CL Day to be primary reference sources?
If I look up a knot that is assigned the name 'Bowline' - I anticipate finding the exact likeness as depicted at illustration #1010 in ABoK.
I would not expect to find the knot illustrated at #1047 (F8).
Humans assign names to things - eg I know what a tree looks like, and a chair, and a dog, etc.
If you asked me to tie a Zeppelin bend, I would assume that you had a specific geometry in mind - it wouldn't be in the likeness of #1415 Double Fishermans?
If I tied and presented #1415 (instead of a Zeppelin bend) - I would surmise that you would look at me in astonishment?

You yourself have complained about which geometry is the 'ASCii Bowline'.
You sent me a number of emails with ASCii code in an attempt to depict a certain knot geometry.
That is, you had a particular geometry in mind.

Quote
... I felt a bit constrained.  In a sense, one isn't
so much deriving ... but showing --they're
right there, in the Tangle, to be ID'd per the Tangle
pieces(1-2 & A-B, for a 2-Tangle)
In order to show or demonstrate that something is being related to something else - one must derive it from a 'source'.
For me, the 'source' is the 'parent bend'.
I begin with a parent bend - and I derive the corresponding eye knots by linking the Tail(s) and S.Part(s) in various combinations.
I had posited that there are only 4 possible linkages that can be made.

Per your words... "showing they're right there" suggests that you were able to identify something visually.
You observed some kind of congruence or correspondence from one thing compared to the other.
Could this "showing" be geometric in character? How else would you be able to "show' something?
I had posited that it is the core structures that can be compared - the correspondence being that the cores have the same geometry.
Here again I use the word 'core' as my preferred way of identifying the 'nucleus' of a knot structure.
I define a knot core to denote the part of the knot that is central to its existence or character.

Quote
...per the Tangle pieces (1-2 & A-B, for a 2-Tangle)
I think you mean the segments that protrude/project from the knot core?
The 1-2 and A-B don't have a clear-cut definition - hard for a layperson to understand (you would need to establish definitions).
Presumably you refer to the 4 segments (protuberances) exiting the knot core - and you are assigning an alpha-numeric coding to ID these segments?
In 3D space, which orientation gives rise to assigning a particular segment as a "1" in contrast to a "2", or "A/B"?
In other words, how do I determine which protruding segment is "1"?
EDIT:
Given that a 'bend' has 2 Tails and 2 S.Parts...
Perhaps assigning the following alpha-numeric values might make it easier to understand:
S1, S2 and T1, T2
S1 = "S.Part 1" (one of the standing parts)
S2 = "S.Part 2" (the opposite standing part)
T1 = "Tail 1" (one of the tails)
T2 = "Tail 2" (the opposite tail)

S1 can link to S2 (S1-S2)
T1 can link to T2 (T1-T2)
S1 can link to T2 (S1-T2)
S2 can link to T1 (S2-T1)
*Note that S1 cannot link to T1 (both originate from the same rope)
*And S2 cannot link to T2 (both originate from the same rope).

I find this alpha-numeric system and my descriptions to be more 'logical' than your 1-2 / A-B annotation.
You may choose to disagree (and that's fine).

Quote
What happens if "core/nub" is omitted --esp. re e2e joints!?
In a 'bend', there will be 2 S.Parts and 2 Tails?
I think you might also have contemplated another type of 'bend' which is an edge case - eg the linking of 2 eye knots?
For example; I could link the eye of a #1010 simple Bowline to the eye of another #1010 simple Bowline.
Would this be your alternative definition of a 'bend'?
For me, I see this as a composite union of 2 eye knots - with each eye knot possessing its own core.
Perhaps a stricter definition of a 'bend' is that the union only has 1 core (not 2 separate cores).
In the case of 2 cores (linking 2 eye knots) - this is a composite structure - and each knot core will respond to load accordingly.
[it could be the linkage of #1010 simple Bowline to #1047 F8...an eye-to-eye link... Each eye knot responds differently to load.]

Quote
Well, it points out a significant change of your
vaunted geometry in a knot that is put together
able to have such difference.
(Consider also how there are different dressings
of the Fig.9 EK.)
I note the use of "your vaunted geometry" phrase.
It isn't 'vaunted' per se - its simply a logical choice.
If I tie a Zeppelin bend - it will have a known geometry.
(although again, there must first be an agreed definition/geometry for what constitutes a Zeppelin bend).
If I tie #1411 F8 bend - it has a known geometry.
Here I assume the energy stable dressings - the simplest most symmetric dressing that is demonstrably stable under load.
With an 'F9', its simply a matter of declaring a particular dressing - again - the most energy stable dressing is logical.
For all 'bends' and 'eye knots' one must settle on a dressing - nominally the most energy stable dressing.
For example: An F8 bend (#1411) can be tied with a flat parallel dressing state - but this is unstable.
One can also apply the same general principle to an offset joining knot - eg #1410 - where some dressings will be more unstable.

Again - we need to have agreed standard to reference against.
An F8 and an F9 eye knot can have different dressing states.
However, we know that there are geometries that are more stable in response to load.
Example:
A trainee is asked to tie an F8 eye knot.
The trainee presents the F8 to his assessor.
What is the criteria the assessor is making judgements about?
What evidence does an assessor require to form a judgment about the trainees competence?
What evidence is required for an assessor to declare a trainee 'competent'?
Note: Assessment should also capture consistency of performance - to rule out random chance success, the trainee should accurately tie the F8 at least 3 times.
Accuracy and consistency ought to be part of the assessment criteria.

EDIT NOTE:
I've added an image to illustrate the concept of a standard reference.
An assessor could look up what an 'F8 bend' looks like in a primary source (eg Ashley).
An F8 bend is found at illustration number One thousand four hundred and eleven (#1411).
However, Ashley does not define what an energy stable dressing is... one can only assume that the depicted dressing is 'optimal' for loading.
I define an energy stable dressing state as:
"Being optimal for loading - to the extent that the knot remains stable and exhibits the least degree of distortion in response to load".
With respect to the attached image below: Image 'B' is energy stable.
« Last Edit: January 16, 2024, 05:30:09 AM by agent_smith »