Author Topic: The relationship between 'bends' and eye knots  (Read 5379 times)

Andreas

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Re: The relationship between 'bends' and eye knots
« Reply #45 on: October 05, 2024, 06:57:56 AM »
There is another idea for "knots of one kind" which is hard to miss as you started the list already Kostas:
 knots that stand out in terms of strength and stability.

I think criterion+ more than two SELECTED! examples (and anti examples) is a winner for understanding our subject, knots in general.

Like this looking for other examples and in the process understanding why they are examples as well as searching new examples becomes clearly directed. This might meet our most dire need, as we're dealing with knots, which exemplify "direction" in somewhat complex manners.

« Last Edit: October 05, 2024, 07:13:44 AM by Andreas »

Dennis Pence

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Re: The relationship between 'bends' and eye knots
« Reply #46 on: October 18, 2024, 05:07:50 PM »
While it is slightly easier to start with a bend, there is no real difficulty starting with a specific eye knot.  Either way you isolate the knot structure to derive 8 related eye knots and 4 related bends.  I found it nice to explore the Corrick Bend which Dr. Asher (in The Alternate Knot Book) used to demonstrate a related eye knot. {I finally found this bend in Ashley [#1451].}  Below is the core structure with all the possible related eye knots and related bends.
« Last Edit: October 18, 2024, 05:18:45 PM by Dennis Pence »

Dennis Pence

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Re: The relationship between 'bends' and eye knots
« Reply #47 on: October 18, 2024, 05:09:55 PM »
Dan is correct (Reply 38) in his comment that for a symmetric knot structure (tangle), you do not necessarily get this many distinct knots.  For the Corrick Bend Structure, Loop 1B (the transposition of Loop 1A) is identical to Loop 2A (rotate 180 deg, turn over).  Loop 2B (the transposition of Loop 2A) is identical to Loop 1A (rotate 180 deg, turn over).  Loop 3B is identical to Loop 3A, and Loop 4B is identical to Loop 4A (turn these each over).  Partial Transpose Bend 2 and Partial Transpose Bend 3 are identical (turn over).

Kost_Greg (Reply 44) is also correct when he comments that we do not always get interesting knots.  Thus, we have to tighten each to see which might be useful, practical, and/or decorative.  Here I found all seven seemed to be at least interesting.

In particular, the Corrick Loop 2A and the Corrick Bend, Fully Transposed both have a "square side" that resembles one side of the Chinese Crown Knot [808, 809, 1032, 1423].  In scouting, this Chinese Crown Knot is often called the Friendship Knot and is tied with the square side out with a neckerchief.  In Internet paracord sites, the same knot is tied with the opposite side out and is called a Cross Knot.  Here for the Corrick Loop 2A and the Corrick Bend, Fully Transposed, the other side is not so attractive.  See also Ashley [810] for his attempt to get this square look on both sides.
« Last Edit: October 18, 2024, 05:12:10 PM by Dennis Pence »

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #48 on: October 19, 2024, 02:12:49 AM »
Quote
While it is slightly easier to start with a bend, there is no real difficulty starting with a specific eye knot.
For me  personally, beginning with an end-to-end join ('bend') is more intuitive.
The concept of "easier" is relative.
What is easy for one, is hard for another.
It really has nothing to do with 'ease' or being 'easier'.
Each person must follow a path that is logical and intuitive for them.
In that context, there is no absolute 'right' or 'wrong' in the different approaches taken.
The starting base is always a choice, it is never a rigid rule that must be followed.

As I had posted several times previously, for me personally, it is both intuitive and logical to begin with a parent 'bend' - and then try to derive its corresponding eye knots.

I would also point out that it is perfectly fine and acceptable to begin with an eye knot!
We live in a free world (well, the 'West' is not North Korea, or an oppressive regime - at least not yet).
No one will be punished for beginning with an eye knot!

Your first image in your post at reply #46 above sets the 'scene'.
You have borrowed my idea of showing the 4 possible linkages in different colour tones.
This now provides a roadmap to create the 4 'principal' corresponding eye knots.
Your third image shows the transpositions to derive 4 more corresponding eye knots.
(that is, image '3' is a transposition of your image '2').
NOTE:
I had advanced the use of the term 'principal' to describe the 4 corresponding eye knots that are closely related in terms of loading profile.
A transposed eye knot may be unstable relative to its 'principal' cousin (but not always).
This is where new ground can be broken... because from my limited examinations, this depends on the core structure.
I therefore advance the following theory:
If the core of a 'bend' consists of 2 geometrically similar halves, the transposed corresponding eye knots are likely to be stable.
In the core of a 'bend' that is constructed from dissimilar halves (eg Sheet bend #1431), the transposed corresponding eye knots are likely to be unstable (unviable).

Harry Asher wrote that he thought that he was the first to describe and explore the correspondence between 'bends' and eye knots:
per "The Alternative Knot Book" published 1989 at pages 81 & 82.
Asher also missed an opportunity with the Butterfly bend and its well known corresponding Butterfly eye knot.
He shows the 'bend' at page 57, and the eye knot at page 79. He ought to have explored the relationship - showing side-by-side images,
and also showing all of the 4 principal corresponding eye knots (he might also have found the 'Mobius' Butterfly had he done so).
Asher also wrongly attributes the 'Butterfly bend' to Brion Toss (1975) - ignorant of the fact that Phil D Smith had already shown this in 1953.
In fairness to Asher, he was breaking new ground, and likely hadn't grasped all of the concepts and intricacies involved.
Also, the internet and social media did not yet exist at the time... written letters, books, and face-to-face meetings were the principal means of communication.

Your last image in your post at reply #46 has more to do with transposition than deriving corresponding eye knots.
« Last Edit: October 19, 2024, 02:18:00 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #49 on: October 19, 2024, 02:58:57 AM »
Quote
SO, I cannot
conceive of how altering the nub from a double OH
to a single or triple OH (dbl. Strangle) can make
a difference in having "identical twins" or not
...
Ashley #1415 is geometrically an inter-penetration of 2 opposing
double overhand strangles. ...

And Yes, this particular 'bend' does indeed produce 2 sets of
identical twins eye knots!
As previously stated, I have no underlying theory to explain why
this is so...

Quote
only of what chosen (single, double, triple...)
knot is being played with : they are all symmetric
in fore/aft faces & structure.

As you have apparently pointed out, there is fore and aft symmetry
...
#1415 Double Fishermans bend has different fore Vs aft symmetry.
I'm still waiting for an explanation as to how the
Grapevine Bend can have <whatever in twinness>
but not the single Fisherman's or Dbl. Grapevine (etc.)!?

--dl*
====

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #50 on: October 19, 2024, 03:13:52 AM »
Asher also wrongly attributes the 'Butterfly bend' to Brion Toss (1975)
--ignorant of the fact that Phil D Smith had already shown this in 1953.
I pointed this out to Brion, and that, really, an ends Joint
is implicit in every mid-line EK expected to hold in through
(Joint) loading --it doesn't need someone to say this
(or take scissors to the eye :o).
Quote
In fairness to Asher, he ...
... wasn't aware of the small-circulation knots book by Smith
(or a smaller-circulation(?) caving newsletter).
And decades prior Smith's book were presentations of the
Butterfly knot, presumably in some linemen's manual
(as yet unfound by me) and Burger's 1915 book and others.

--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #51 on: October 19, 2024, 09:19:22 AM »
per Dan Lehman:
Quote
I'm still waiting for an explanation as to how the
Grapevine Bend can have <whatever in twinness>
but not the single Fisherman's or Dbl. Grapevine (etc.)!?
You'll be waiting till hell freezes over because I was wrong.
They are NOT identical.
See attached image below.

They are close, but no cigar...
The 2 eye knots lying on my desk looked identical at a glance,
but a more thorough examination showed that your suspicions were indeed correct!

EDIT NOTE:
Second image added.
2 'identical twins' eye knots.
Summary:
This bend (#1415) only produces one set of identical twins (not 2 sets).
And that's good because I previously had no clue why this 'bend' produced
2 sets of identical twins (which it does not).
« Last Edit: October 19, 2024, 10:05:23 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #52 on: October 23, 2024, 04:38:57 AM »
per Dan Lehman:
Quote
I'm still waiting for an explanation as to how the
Grapevine Bend can have <whatever in twinness>
but not the single Fisherman's or Dbl. Grapevine (etc.)!?
You'll be waiting till hell freezes over because I was wrong.
They are NOT identical.
Your "I was wrong" pertains to the loading of the
particular knots and then resultant "look" as twins;
my challenge was to how those particular sub-knots
--i.e., strangles but NOT (so you insisted) OHs or
dbl.Strangles substituted-- could make any effect
on "identical twinness".

Quote
The 2 eye knots lying on my desk looked identical at a glance,
but a more thorough examination showed that your suspicions were indeed correct!
Well, there goes your shot at being a Knot Assessor!


--dl*
====
« Last Edit: October 26, 2024, 04:12:29 AM by Dan_Lehman »

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #53 on: October 23, 2024, 05:08:42 AM »
In reply to Dan Lehman:
Quote
Your "I was wrong" pertains to the loading of the
particular knots and then resultant "look" as twins;
No - "the I was wrong" was with respect to geometry.
The geometry of the 2 eye knots is very close - but no cigar!
Loading is irrelevant in this instance - its purely geometric.
I made a mistake - (I've been known to have made mistakes throughout my life).
Next time, I will be more careful to closely examine the geometry before making
a definitive comment.

Quote
--i.e., strangles but NOT (so you insisted) OHs or
dbl.Strangles substituted-- could make any effect
on "identical twinness".
?
I never insisted OHs (are you alluding to a 'single Fishermans bend'?).
'Insisted' is not an accurate characterisation...
I simply made a mistake thinking the 2 eye knots were identical twins.
At a glance, they do look identical - one has to look closely to notice
the alternate positions of the tails and S.Parts.
(a slight rotation in both eye knots shifts the relative positions of the protruding segments,
and this is what fooled me).

Quote
Well, there goes your shot at being a Knot Assessor!
Ha!
I wonder if I'm the only person in knotting history that has erred?   ;D
I've owned up to my error - I thought they were identical twins - but they weren't.
Is there some penitence that I must now undertake?

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #54 on: October 26, 2024, 05:35:32 AM »
This discussion thread has carried an alternative/complementary
notion of "corresponding" --one that tries to retain the loading
geometry of the e2e joint in the Eye Knot--,
which I'll reiterate here on page 5.
Quote
There is no dispute that if you take the joint as a 2-Tangle
then there are 8 per definition EKs (possibly with duplicates).
Except, alas <sigh>, I found that the purely logical direction
of a Tangle + Loading_Profile doesn't ensure that there's not
variation in this specification --that going from the Tangle
to this state by simple loading these "ends" just so! can
run afoul of practical consequences ("Just how does one get
to just so?!").

Quote
But there is another way to see "correspondence" of an EK
to a joint.  I remarked about Ashley's #1043/5 --and I should
add #1016 (or some version of...)-- being seen as corresponding
to the Sheet Bend; in a way, they do so in the spirit I take of your
looking for preserving loading profile and so on --which they do
by altering the reference joint from a 2-Tangle to a 3-Tangle
in which one piece forms the eye and presents thus its two
ends qua single end to fill the path of the joint.  Having done
this, then look to how to *fuse* the single-S.Part'd piece's
Tail into one of the twinned pieces' Tails to restore a 2-Tangle.

A good example of a Joint that by the above method of
"correspondence" well achieves the likeness in loading
is the angler's "Blood Knot" ("in-coil" --as results from tying
even in out-coil form in fish line upon setting transformation).

"a good example":: well, in fact what brought this idea to
mind, for me, reading of the "2-by1 knot"[?! --name not sure]
in Stanley BARNES's 1951 ed. Angler's Knots ::
one has the S.Part making all its incoils complemented
now by TWO parts --the legs of the eye piece being
joined as though a single opposing end-- making similar
wraps (half in number).  Here, one might alter the setting
by putting more force to set the two tails, as in expected
loading they'll be only at 50% of force upon the S.Part.
**MY insight to this revelation was to see that one could
*fuse* together one of the eye-part's Tails to the S.Part's
Tail and so render the structure in a nearly identical
single-line Eye Knot.

Not all knots have such happy results as this,
which might be pretty near ideal.

--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #55 on: October 28, 2024, 07:13:20 AM »
Quote
Quote
There is no dispute that if you take the joint as a 2-Tangle
then there are 8 per definition EKs (possibly with duplicates).
Except, alas <sigh>, I found that the purely logical direction
of a Tangle + Loading_Profile doesn't ensure that there's not
variation in this specification --that going from the Tangle
to this state by simple loading these "ends" just so! can
run afoul of practical consequences ("Just how does one get
to just so?!").

My approach is to constrain 'correspondence' in terms of a geometric relationship, rather than the result of loading.
You may prefer to choose a different approach.

Quote
But there is another way to see "correspondence" of an EK
to a joint.  I remarked about Ashley's #1043/5 --and I should
add #1016 (or some version of...)-- being seen as corresponding
to the Sheet Bend
#1016 is topologically equivalent to #1047 Bowline with a bight:
The different being loading profile (and the fact that the original eye has been shrunk.
I recall Xarax did this with #1080 Bowline on a bight - shrinking one of the eyes.

In any case, you can begin with Ashley's #1016 eye knot and then take your classic
'cookie cutter' and work backwards to obtain corresponding 'bends'.
You do seem to prefer this approach - that is; beginning with a 'parent' eye knot and then
deriving its corresponding 'bends'. There is nothing wrong with such an approach.

Presumably, you can also adopt the same approach with many other knots - #1017 Anglers eye knot
being another candidate for your cookie cutter!

My point being that it really doesn't matter... all one needs to have is a logical beginning.
I'll refer to this 'beginning' as the parent structure.
Correspondence is relative to a parent structure.

...

Quote
"a good example":: well, in fact what brought this idea to
mind, for me, reading of the "2-by1 knot"[?! --name not sure]
in Stanley BARNES's 1951 ed. Angler's Knots ::
Dan, I don't have a copy of this book.
I would tender that few people would have access to a printed copy.
This makes it difficult for readers to follow your ideas.
Googling "2 by 1 knot" is not helpful - the search results being inconclusive.
Might be helpful if you took some photos of the knots from that 1951 book?

Quote
**MY insight to this revelation was to see that one could
*fuse* together one of the eye-part's Tails to the S.Part's
Tail and so render the structure in a nearly identical
single-line Eye Knot.
Again, hard to visualise your revelation without a reference image.
Fusing one 'eye parts tails' to the S.Parts tail sounds like a revelation... but
very difficult to provide any meaningful comment.
« Last Edit: October 29, 2024, 01:13:04 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #56 on: October 28, 2024, 11:56:48 PM »
The continuing conversation about 'correspondence' between knots (not tangles).
It is difficult to visualise any correspondence between a tangled mess relative to another tangled mess.
Only you keep imputing this silly notion to satisfy your
I-don't-know-what; "Tangle" is defined for the purposes
of my articulation w/o any notion of "mess", but of pure
*entanglement* of material, various parts between/around/
against each other, and being defined knots by applying
a Loading Profile.  --a seemingly attractive PoV, until, alas,
the hard nitty gritty sets in, and there come some leakage
of that hoped-for articulation of knots.  <sigh>

Quote
My definition of a tangle being:
An unintentional confused mass of twisted cord/rope - that has no ...
... bearing on MY use of the defined term per MY
system of articulation.

Quote
My broad definition of a knot:
... tied structure with a distinct geometric form ...
The problematic aspect of "intention" & "recognition"
have been discussed elsewhere; here, let's lean on
"tied structure" & "with a distinctive geometric form" ::
Knots well known & used can run through some range
of geometric shapes, as I previously noted with the case
of the BWL's range of helix angle in the central nipping
loop --getting the the point where one really doesn't
want to call it a "loop" anymore, but at what helix angle
is this to be decided --which angle, btw, will likely change
per force upon the knot!
.:. This is a tough issue!


Quote
My definition of a 'bend':
An end-to-end join of cord/rope/webbing (ie textile material).
There are 2 ends, and they are united to enable through loading.
Noting that "bend" from the nautical-cordage-using
world has a different meaning --why press Ashley's
lean to ignore this, and lose the connection to the past,
vs. going with --as you have nicely offered/done, too--
"join(t)" --though one might think a hitch also joins ...,
and ...!?  (I find "join" irritating, also as I find "tie" which
some writers use.)


Quote
My definition of a 'hitch':
A structure that requires a 'host' to form around and function under load.
Somehow you're getting the cart before the horse,
rather than making your "structure" at once :: i.e.,
there is this hitch thing looking around for its host;
to me, rather, it is a knot in which cordage is tied
to some object.  And I'll avoid the superfluous note
that --true or not-- removing the host does ... <whatever> ::
the "hitch" has this "host"/"object", and what happens without
that is just out of discussion.  (kinda like saying that if you
remove the other end of a joint then the joint will lose ...)

Quote
My definition of a 'knot'
 (taking into consideration the broader definition of what a knot is):
A self-supporting structure tied from cord/rope.
No 'host' is required, and there is no union of two ends.
So, if you come across a Butterfly Knot you'll say
"this knot vanishes when I cut its eye!"
I leave "knot" as the for-everything term,
which includes hitches, binders, et cetera.

Quote
With regard to correspondence:
All 'bends' have 4 possible linkages that can be made between the S.Parts and tail ends.
These linkages create eye knots.
A further subset of 4 eye knots can be created by way of transposition of S.Part and tail end.
Not all of these structures will necessarily be stable/viable.
I think you want that warning re stability to cover the
whole 8-items lot --think of the SquaReef Joint, e.g.;
but then wonder what is meant by working/not-working,
in light of the variety of *cordage* (my catch-all for
"knottable material", which I've otherwise called
"Piece of Flexible Material" to generalize).

Quote
Definition of transposition:
For transposition of eye knots:
Where an S.Part is exchanged with a tail end but without altering the knot core geometry.
Transposition can be likened to a reversal of polarity.
Again, I think that the Tangle+LoadProfile=Knot articulation
gets here more quickly, obviously, understandably, and without
having to invoke another concept :: one doesn't exchange
anything, but rather uses a different loading profile
(which sort of alteration could occur in practice).

Quote
Definition of 'core':
The part of a knot that is central to its existence or character.
This begs the question "What is it's "character"?!
I'd like your example of what sort of knot has a core
that is not what Chisholm calls its "nub" and what the
Tangle articulation sees as the tangle --though how
to treat the Sheepshank and the shared-eye joints
is baffling me so far <argh>!  E.g., the Twin BWLs
of Ashley, where each BWL's Outgoing Eye Leg
is the Ret.EyeLeg to the opposite BWL !  How
to treat this "shared eye" span of unentangled
cordage (like that in a Sheepshank --which also
challenges how to regard the nipped u-folds that
lie beside each S.Part!?


Quote
Definition of 'eye knot':
A self-supporting structure that has a connective eye that is non-slipping.
The eye has no chirality.
"Self-supporting" seems superfluous, perhaps informative?
"connective eye" begs for definition.  "non-slipping" hints
at troubles to encounter with vagaries of materials & forces!
(How do you regard the fabled --we might have to rely on fable--
Tarbuck Knot?  --intended to slip BUT only so much, then not.

Quote
Quote
There is no dispute that if you take the joint as a 2-Tangle
then there are 8 per definition EKs (possibly with duplicates).
Except, alas <sigh>, I found that the purely logical direction
of a Tangle + Loading_Profile doesn't ensure that there's not
variation in this specification --that going from the Tangle
to this state by simple loading these "ends" just so! can
run afoul of practical consequences ("Just how does one get
to just so?!").

Quote
My approach is to constrain 'correspondence' in terms of a geometric relationship, rather than the result of loading.
You may prefer to choose a different approach.
Rather than result it is simply THERE, logically;
actual loading might lessen one's value for the logic, though.


Quote
But there is another way to see "correspondence" of an EK
to a joint.  I remarked about Ashley's #1043/5 --and I should
add #1016 (or some version of...)-- being seen as corresponding
to the Sheet Bend
#1016 is topologically equivalent to #1047 Bowline with a bight:
I think you're missing my point :: that one seeks to find
correspondence and preservation of the loading
via tying an end(1)-to-endS(2 --of the U-fold eye) joint
AND THEN somehow fusing one of the eye-leg ends
into some part of the S.Part's flow.  The example above
re the angler's Blood Knot is of a very good one; that
of the #1043/5 cases illustrates the concept also nicely;
whereas trying to make a Fig.8 joint=>EK this way ...
simply looks absurd vs. the usual Fig.8 EK.

...

Quote
Quote
"a good example":: well, in fact what brought this idea to
mind, for me, reading of the "2-by1 knot"[?! --name not sure]
in Stanley BARNES's 1951 ed. Angler's Knots ::
...
This makes it difficult for readers to follow your ideas.
But readers should know the Blood Knot of anglers,
and otherwise can find it.  To that, one need only
follow the words and form the joint 1 line-vs-2.
The version of the Blood knot that works simplest
would take the two ends' Tails and fuse them;
then you cut off one S.Part to amount of material
for fold back to form the eye,
and run it back twin to its extant course.
(In practice, one will I think want fewer of the
binding wraps from EACH eye leg, summing to
about the number in the S.Part's wrapping.

Quote
Quote
**MY insight to this revelation was to see that one could
*fuse* together one of the eye-part's Tails to the S.Part's
Tail and so render the structure in a nearly identical
single-line Eye Knot.
Again, hard to visualise your revelation without a reference image.
Fusing one 'eye parts tails' to the S.Parts tail sounds like a revelation... but
very difficult to provide any meaningful comment.
The reference is the Blood Knot; tying 2-to-1 will see a trio
of Tails in the nipped center; now, the task is to make a fusing
of them to render a single-cordage piece Eye Knot.

--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #57 on: November 01, 2024, 12:10:24 AM »
My reply has been transferred to this topic thread.
Dan Lehman had questions in relation to the Butterfly bend and
the derived corresponding eye knots.

I'll reiterate that this entire subject matter is yet to be fully fleshed out.
The theory is still evolving - and terminology is still being worked out.
Be that as it may, some concepts are reasonably understood.

In relation to a 'bend' and its corresponding 'eye knots' - I'll summarise as follows:
1. There are four possible linkages that can be made between the S.Parts and the tails ends.
2. These linkages result in four corresponding eye knots.
3. Some of these eye knots may have loading profiles more closely aligned with the parent 'bend'.
4. By way of transposition, additional eye knots can be derived - up to a maximum of eight.

You seem to hold me to a higher standard than other IGKT forum members when it comes
to English language usage.
Presumably because you see me as a native English speaker, and possibly because I engage
in intellectual discussions with you. And likely the fact that I'm trail blazing this subject area
and trying to define concepts puts me squarely in the firing line!
And so you become irritated by my varied use of words such as "possible", "principal", and "primary".
I concede that each of these words has differing meanings.
I have stated that I am breaking new ground with correspondence - it is a work in progress.
All of the deeper technical details have yet to be fully fleshed out.

Okay - lets take a temperature check:
1) You appear to be in agreement that there are 4 possible linkages between the S.Parts
and the tail ends.
2) You also appear to concur that these linkages result in corresponding eye knots.

It is from this point that the theory gets complicated...
I see 2 areas of complexity:
1) Once you have derived 4 corresponding eye knots, you can then derive another 4 eye knots
by way of transposition (S.Part and Tail end change identity).
2) Some of the corresponding eye knots have loading profiles more closely
aligned with the 'parent bend'. Describing this is difficult.

For example:
The 'Mobius Butterfly' has a loading profile that is quite different relative
to the parent Butterfly bend (and therefore I would not describe it as being 'prime').
And here I'm using 'prime' as a derivative of 'primary'.

It is clear that some of the corresponding eye knots share common load segments
from the 'parent bend'. They are more closely aligned to the parent bend in terms
of how load propagates throughout the knot structure.
It is these eye knots that I have struggled to assign an appropriate descriptor.

I had used the term 'primary' to identify these eye knots, thinking in terms
of these eye knots being 'prime' (like a prime number).
At the same time, I had also used the term 'principal'.
The key concept being a closer relationship with the 'parent bend'.
And here I would remind that the whole notion of 'correspondence' can only have
meaning relative to a knot that is declared to be the starting base (or the 'parent').

For example, I had declared the 'Butterfly bend' to be the 'parent' bend.
Using that as the starting base, one can then derive the corresponding eye knots.
Assigning terms that are accurate, descriptive, and meaningful is difficult.

...

In relation to the Stanley Barnes 1951 book on fishing knots ("2 by 1 knot"):
Quote
But readers should know the Blood Knot of anglers,
and otherwise can find it.  To that, one need only
follow the words and form the joint 1 line-vs-2.
You now reveal "blood knot" - but previously you use 2 by 1 knot.
Okay, as I stated, a search for 2 by 1 knot was not bearing any fruit.
Now readers can at least search 'blood knot'.
I personally did not know the relationship between 2 by 1 knot and blood knot.
My point was this:
You were referring to a very old book (1951) that few would have access to. Also,
you drew attention to an obscure '2 by 1' knot.
A casual lay reader would find it tough to comprehend without access to the book
and/or an image of what a 2 by 1 knot is.
Anyhow, now we have 'blood knot' to think about...

Quote
I think you're missing my point :: that one seeks to find
correspondence and preservation of the loading
via tying an end(1)-to-endS(2 --of the U-fold eye) joint
AND THEN somehow fusing one of the eye-leg ends
into some part of the S.Part's flow.  The example above
re the angler's Blood Knot is of a very good one; that
of the #1043/5 cases illustrates the concept also nicely;
whereas trying to make a Fig.8 joint=>EK this way ...
simply looks absurd vs. the usual Fig.8 EK.
The alleged 'confusion' is likely due to your lack of clarity
in the way you write.
Its hard to extract what your underpinning thought processes are.
Look, correspondence between knots can only have meaning if you
first establish a baseline parent 'bend' - and working from that baseline,
you then try to derive its corresponding eye knots.
[NOTE: You can also work the other way around - beginning from an eye knot].
Ashley's #1043 is an 'eye knot'.
So you need to define your terms... you appear to prefer to begin with an
'eye knot' (being your 'baseline').
The point being, one first needs to begin from a baseline. You then work from
that baseline.

EDIT NOTE:
I've added an image showing #1043 and the other corresponding eye knots
that have been derived from the 'parent bend'.
One of the corresponding eye knots is in fact the infamous 'Yosemite Bowline'.
« Last Edit: November 01, 2024, 06:53:44 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #58 on: November 01, 2024, 03:44:23 PM »
EDIT NOTE:
I've added an image showing #1043 and the other corresponding eye knots
that have been derived from the 'parent bend'.
One of the corresponding eye knots is in fact the infamous 'Yosemite Bowline'.
You break a rule of correspondence in this set with
the 4th one as it alone has a parent Tail qua S.Part.
In Tangle designations, with your
  yellow rope = "1-2" and
 the blue rope = "A-B",

you show
[A] 1-vs-2+A   (most commonly seen correspondence),
[C]    ...   +B   (your 3rd , RELeg being former Tail)

[B.] A-vs-B+1   (your 2nd)
[na]   ...   +2   (4th case missed of this logical sequence.
                        with you showing
[D] B-vs-A+1    (A-B's Tail vs. two parent S.Parts)


(Btw, "C" looks dubious of blue-rope/REL->Tail security;
 I'd put in another tuck of some kind if trying this!)


--dl*
====

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #59 on: November 01, 2024, 06:44:20 PM »
I should remark that for the --like that "2-to-1" knot--
correspondences I was pointing to, the "parent"
is one of the Sheet Bends (direct or oblique ; aka
"same-side" or "opposite sides"), begun with
either the U-fold half or the loop half,
to which then the eye U-fold's twin legs
are then reeved as per whichever Sheet Bend;
AND THEN there is a fusing of one of these
twin legs into the Tail of the opposite part.

This method might not have happy results;
but it's a way to try to preserve the loading
effects in the knot that are in the end-2-end parent.


--dl*
====