Author Topic: The relationship between 'bends' and eye knots  (Read 2707 times)

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #15 on: November 30, 2023, 01:00:23 AM »
Dan - you reply has confirmed my assertions about your fixation on grammar/syntax - rather than the underlying concept.

We can go back and forth to infinity with these posts.
What do you think this would achieve?

You found this phrase and had a Eureka moment!
Quote
between a tail and an S.Part segment
You are intent on drawing attention to grammar - and you cant seem to look past this hurdle.
With your pull quotes - what if you just add the letter "s" to tail and S.Part ? - does that change the meaning :)
I should have wrote; linkages between protruding segments of opposite colour.
This would have narrowed the number of possible misinterpretations and limited your ability to fixate on peripheral semantics.

Do you think you would ever be able to overcome your fixation on grammar/syntax errors?
Or has permanent and irreversible harm been done :)  ?

Here is what I think.
I think you knew what my intent was - but you like to engage in intellectual debate over semantics.
I don't mind engaging with you - but it gets very tedious at times.
To be honest with you - I prefer to engage in a way that promotes the advancement of this theoretical subject matter (the relationship between bends and eye knots).
I dislike bogging down on subject matter that is obviously attempting to score goals based on trivial semantics.
Whenever I post info on this IGKT forum - it is within the spirit of advancing the science of knots - not advancing the science of arguing semantics.

Anyhow, it would be nice to see you post your own images of bends and corresponding eye knots!
Have you got any contributions?
Or is this a lost cause?

...

I have uploaded the 'Reef derived bend' and corresponding eye knots.
This info graphic does not include all 8 combinations of linkages and loading profiles.
Dont get hung up on this... I dont have time to photograph all conceivable combinations.
I've simply included the 'primary' corresponding eye knots.
The are 2 'primary corresponding eye knots - and they are identical.

There is a risk of misinterpretation here - due to complexities of language.
eg
There are 2 corresponding primary eye knots - but they are identical.
There is an opportunity to debate this... do you count it as '1' or '2'?
If I say '1' this opens up a can of worms.
If I say '2' - maybe less worms in the can :)
To reduce language semantic arguments, I'll just say:
"There are 2 primary corresponding eye knots - both of which are identical".
This should limit the number of possible interpretations?
« Last Edit: November 30, 2023, 02:12:12 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #16 on: December 01, 2023, 05:46:15 AM »
We can go back and forth to infinity with these posts.
What do you think this would achieve?
What is hoped to be achieved is corrected/improved
descriptive material, presentation of ideas.
Quote
You are intent on drawing attention to grammar - and you cant seem to look past this hurdle.
///
Do you think you would ever be able to overcome your fixation on grammar/syntax errors?
///
I dislike bogging down on subject matter that is obviously attempting to score goals based on trivial semantics.
THIS is your fixation --that discussion is about "scoring goals".
And your defensive reaction comes as irony to your own replies
taking others to task for, say --one of your favorites-- writing
"THE bowline" (emphasis yours), instead of explicitly & exactly
stating, in your desired language, "#1010" !

Quote
Here is what I think.
I think you knew what my intent was - but you like to engage in intellectual debate over semantics.
Why didn't you instead think "He's found a point where I've
not clearly expressed my ideas --good, I'll fix that."
nb : "fix THAT" --not "fix HIM"!

And I have been contributing some good ideas in this discussion,
but you assiduously avoid them.

Every simple --i.e., of two pieces-- ends joint defines
a 2-tangle, in which one piece, with ends "1" & "2",
entangles 2nd piece, with ends "A" & "B" such that
"1" is loaded in opposition to "A" --the end joint's S.Parts--
and ends "B" & "2" are its Tails.

A 2-tangle has 8 loading profiles that potentially
define eye knots; these are (with reference to the
ends joint's S.Parts & Tails) :

----------S.Part-loaded   [parens of ends joined into eye ]

1-v-(2+A)  ---1st
      (  +B)  ---2nd
A-v-(B+1)  ---3rd
      (  +2)  ---4th

---------TAILoaded

2-v-(1+A) ---5th
      (  +B) ---6th
B-v-(A+1) ---7th
      (  +2) ---8th

These loadings "potentially" create viable eye knots;
but they might lack stability to sustain such a loading.
Also, with symmetric structures, there will be duplicate
loadings yielding a given knot (e.g., the 1st & 3rd and
2nd & 4th loadings pairs will each yield one knot, not two).

... and so on.

I'm still finding trouble getting around variations in the
geometry, in the dressing (emphasis, perhaps : "heavy
dressing" !) of knots to fit into, to flow from Tangles.
E.g., what is the (<--presumptive singularity?!) net knot
from the capsized Carrick bend tangle (which is some
remove from the lattice-form) --one can take the joint's
Tails in various directions.  (To the point re singular vs.
plural "net knot" it's a question now of angles of loading,
not merely of ends.)

--dl*
====


agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #17 on: December 02, 2023, 06:35:51 AM »
Continuing with the development of bends and their corresponding eye knots...

I've uploaded the Lehman8 variation bend
Before any nuclear melt downs occur - note the typed word 'variation'.
Its not the original Lehman8 - its a variant.

I'm examining some loading profile characteristics between these 2 'bends' and their corresponding eye knots.
Interestingly, both of these bends can produce 'offset' Lehman8 bends.
I'm currently comparing the stability, security, and jam resistance of these 2 'offset' bends.

And thank you Dan for a civilised reply - there seems to be hope that 2 knot geeks can find common ground :)
I note your alpha numeric system to denote possible combinations of Tail-S.Part-S.Part-Tail linkages + loading profiles.
I understand it - because I already understand the underlying concept.
However, the casual/average reader might scratch his head for a while trying to decipher the meaning.
That's why I prefer a graphic representation of a 'bend' (refer to my attached image below).
The colour coded image makes it clear and easy to understand that there are 4 combinations of possible linkages.
(And that linkages can only occur between segments of opposite colour).


As far as the current state of progress on this theoretical work:
I seem to be settling on a few key definitions - which I can now advance herein:
1. For any given 'bend', there are a 4 possible combinations of linkages between the segments protruding from the knot core (refer to colour coded image below).
2. These 4 linkages produce corresponding eye knots.
3. For each corresponding eye knot, there is a choice of 2 S.Part's - which therefore produce a total of 8 possible corresponding eye knots (based on loading profiles).
4. Of the 8 possible corresponding eye knots, up to a maximum of 2 will be 'primary'.
5. The 'primary' corresponding eye knots are closest to the parent bend in terms of loading profile - loaded segments of the eye knot are congruent with the parent bend S.Parts (refer to coloured dots in attached image).

...

With regard to your comment re "THE Bowline"
I can respond as follows...

There are many different type of 'Bowlines'.
If a person types 'The Bowline' - it immediately begs the question... "Which Bowline are you referring to?"
Many climbers are guilty of this - because some have an underlying agenda to attack and denigrate the use of 'the' Bowline as a tie-in knot to a harness.
In fact, several types of 'Bowlines' are inherently secure (and some aren't).
We know that #1010 Simple Bowline in not 'safe' as a tie-in to a climbers harness.
But that is not the principal purpose of #1010 (ie its not intended for life critical applications).

Per your other points:
Quote
These loadings "potentially" create viable eye knots;
but they might lack stability to sustain such a loading.
I've already pointed this out several times... not all of the 8 possible corresponding eye knots will be stable (or 'viable' as you have typed).
In most cases, I think it is possible to derive up to 4 stable corresponding eye knots - but this is not a hard and fast rule.
I am of the view that it all comes down to the core structure of the parent bend.
For example, the Reef/Square bend does not produce any stable corresponding eye knots.
This due to the union of 2 'U folds' (or 2 bights).
A phenomena called 'bight straightening' occurs.

The Sheet bend does produce 4 stable (viable) corresponding eye knots, but it appears that the remaining 4 are unstable (due to bight straightening).
Note: This is because the 'Sheet bend' is the union of a 'U fold' + a loop.

The Carrick bend is the union of 2 Crossing hitches - and this produces some stable/viable corresponding eye knots.
However, I am of the view that some of the 8 corresponding eye knots may be unstable (again due to risk of bight straightening).

And this last remark:
Quote
I'm still finding trouble getting around variations in the
geometry, in the dressing (emphasis, perhaps : "heavy
dressing" !) of knots to fit into, to flow from Tangles.
E.g., what is the (<--presumptive singularity?!) net knot
from the capsized Carrick bend tangle (which is some
remove from the lattice-form) --one can take the joint's
Tails in various directions.  (To the point re singular vs.
plural "net knot" it's a question now of angles of loading,
not merely of ends.)
In my view, the simplest way to look at this is from a geometric perspective.
The corresponding eye knots must have some congruence with the parent bend geometry.
The cores of all 8 corresponding eye knots must match the geometry of the parent bend core.
Obviously, under heavy load, some of the corresponding eye knots will deform/distort - because they are not stable in a particular loading profile.
I don't see this as a show-stopper - because its an artefact of loading.

And note:
[ ] Force is injected into the core of a bend from 2 opposing directions.
[ ] Force is injected into the core of an eye knot from 3 directions (2 eye legs in opposition to 1 S.Part).
Loading profile matters...
« Last Edit: December 05, 2023, 01:36:11 PM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #18 on: December 06, 2023, 11:07:45 PM »
Continuing with the development of bends and their corresponding eye knots...
Here I'll again interject that correspondence can --even should?!--
have different meanings.   I.p., I pointed to the process of building
an EK from a e2e Joint by using 1 single end joining to the two
("twin") ends of a U-fold, and then fusing the single end into one of
the others so to make a 2-tangle (unfused :: 3-tangle) and EK.

I think that we're best suited to speak in terms of pure *logic* of
the ends of 2-tangles (my main focus : amply but not too involved)
vs. more value-connoting terms such as "primary/secondary".
Perhaps these values will accrue to one or another knot,
got via one or another logical relationship.  And such wording
be more sensible with knots-users than Ivory Tower logics!?

The SheetBend/BWL/... structure is beguiling to the point
I've mused about "specious" --both simple and accommodating
of a planar graphical image, and nicely asymmetric.  To my
thinking via the construction of an EK given above, Ashley's
#1043/5 & #1016 are all corresponding knots to the Sheet
Bend --in one way more so than the BWL :: in that these
knots do NOT have Xarax's *pure* "nipping loop" : they
have a loop loaded principally on the S.Part end, but
don't run then out into a half-force-loaded Outgoing Eye Leg!


Quote
I note your alpha numeric system to denote possible combinations
of Tail-S.Part-S.Part-Tail linkages + loading profiles.
I understand it - because I already understand the underlying concept.
However, the casual/average reader might scratch his head for a while
trying to decipher the meaning.
One more reason to wear a helmet!
The 2-tangle shows the 4 ends, and they get labelled somehow
--simpler to do with an EK since it has by one S.Part (if one has
feelings of primary/secondary connotations resp. of "1/2"! :-).
Doing with them comes via Loading Profile.

Which all seems neat & clean/perspicuous, befitting logic;
then the struggle to fit reality of physics --dressing & setting--
becomes an issue.  yChan's particular dressing of #1425a
is one eye opener; the Tail-Loaded BWL coming out of what
I'd thought was so accommodating of the BWL 2-tangle is
another provocative case.  <sigh>

Quote
The colour coded image makes it clear and easy to understand
that there are 4 combinations of possible linkages.
(And that linkages can only occur between segments of opposite colour).
Which puts the like-connected, same-colored cases of what
one might call the "Becket Hitch" in some difference to the
actual structure --which might not connect the two
same-colored ends (for that matter, my 2-tangle EKs don't
have "connected" ends --just equally loaded opposing the S.Part(!)--,
though here there can be real-knot differences (loading being
NOT equal, though opposing : e.g., 100% S.Part vs. 35%+65% legs).



Quote
And note:
[ ] Force is injected into the core of a bend from 2 opposing directions.
[ ] Force is injected into the core of an eye knot from 3 directions (2 eye legs in opposition to 1 S.Part).
Loading profile matters...
Imagine an OWK ("EDK", "Offset Water Knot") joining two ropes
that are hanging from a narrow strip of steel:: and perhaps
someone abseils or ascends these ropes.  What type of knot
is that?  (It doesn't have force from opposite directions but
the same, on either side of the steel strip.

While we're into this fun&games corner of knotting,
what type of knot is the OH structure commonly
tied in one's plastic film produce bag, to keep the,
um, broccoli from spilling out?! --or esp. when the
bag (with contents or just air!) is compressed as to
pop it?!

--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #19 on: December 07, 2023, 05:42:18 AM »
Dan,
Quote
To my
thinking via the construction of an EK given above, Ashley's
#1043/5 & #1016 are all corresponding knots to the Sheet
Bend
--in one way more so than the BWL :: in that these
knots do NOT have Xarax's *pure* "nipping loop" : they
have a loop loaded principally on the S.Part end, but
don't run then out into a half-force-loaded Outgoing Eye Leg!
I've attached an image of the #1043 F8-Loop bend and corresponding eye knots.
I don't see how #1043 knot core is the same as #1431 Sheet bend core - unless I've misunderstood you?
The notional concept of 'correspondence' is only valid from a strictly geometric point-of-view; where the cores of the eye knots are geometrically identical to the core of the parent bend.
If you change the geometry, you change the correspondence to something else.

#1016 if essentially the same as #1074 (with the only difference being the positioning of the 'bight-tail' end.
If we build an end-to-end joint (bend) with a core that geometrically matches the core of #1016/#1074, it isn't the same as a Sheet bend.
I don't have a photo... but if I find time I will try to upload something.

Having said that...
#1074 Bowline with-a-bight (and #1016) and #1080 Bowline on a bight are all eye knots with interesting structures.
I agree that they don't fit the non TIB tied end-of-line geometric form where there are 3 (loaded) segments exiting from the knot core.
Okay - #1080 Bowline on a bight actually has 6 segments exiting from the core (but only 5 segments are loadable when there is a designated tail end protruding).
#1074 also has 6 segments (and so does #1016).- but only 5 of these segments are loaded/loadable when there is a tail end present).
What is the common denominator with these structures?
Well, they are all "TIB" (Tiable In the Bight).
So:
[ ] A 'non TIB' eye knot tied end of line has 4 segments, 3 of which are loaded/loadable when there is a designated tail end.
[ ] A 'TIB' eye knot often has 6 segments 5 of which are loaded/loadable when there is a distinct tail end.

Although;
#1043 eye knot is 'TIB' and has a total of 4 segments exiting the core (3 of which are loaded or loadable)
#1058 directional F8 is also 'TIB' and it only has 4 segments exiting the core (but only 3 of which are loaded/loadable).

What does this all mean?
I don't have all the answers!

Quote
Here I'll again interject that correspondence can --even should?!--
have different meanings.
Not for me - sorry.
I am of the view that terminology and concepts need to be defined - so as to remove as much ambiguity as reasonably possible.
Words have meaning - otherwise it would be like the tower of Babylon and people would not be able to communicate.

Quote
I pointed to the process of building
an EK from a e2e Joint by using 1 single end joining to the two
("twin") ends of a U-fold, and then fusing the single end into one of
the others so to make a 2-tangle (unfused :: 3-tangle) and EK.
You like thought experiments that employ 'edge cases'.
I like thought experiments - but they have to be grounded in reality.
In my view, an end-to-end join will have 4 segments projecting from the knot core (and an 'eye knot' also has 4 segments).
There is no 'fusing' in a real-world practical case where a person joins 2 ropes together by hand alone.
If this was done (by splicing or by swaging) - in my view it falls outside the realm of ordinary knotting.
Same with 'beckets' and 'splices' - it is outside the scope of my work.

OR;
You possibly mean tying a bend using 2 'bights' (2 U folds).
eg;
If I create a Reef/Square knot with 2 bights, this means 8 segments exiting from the core (an even number again).
If a Sheet bend is tied with 2 bights, this has 6 segments exiting the core (an even number).
Its an interesting thought experiment :)

I probably need to tighten the language construction to confine a knot structure to within specific parameters.
Eg;
A 'bend' that is formed from 2 singular rope ends - no bights.
This would have 4 rope segments exiting from the core (an even number).
A non-TIB 'eye knot' that is tied end-of-line from a singular rope (this is a bit wordy).
This would only have 4 rope segments exiting from the core - 3 of which are loaded (an odd number).

If think the overall message here is that eye knots and bends can be tied-with-bights (and this is your main point?).

I think a generic distinction is that a bend has 2 loaded segments ('S.Parts') acting in opposition - when there are 2 distinct tail ends.
An eye knot has 3 loaded segments - when there is a distinct tail end - the 2 legs of the 'eye' are in opposition to the S.Part.
But all of this is in respect of loading profile...

Quote
Imagine an OWK ("EDK", "Offset Water Knot") joining two ropes
that are hanging from a narrow strip of steel:: and perhaps
someone abseils or ascends these ropes.  What type of knot
is that?  (It doesn't have force from opposite directions but
the same, on either side of the steel strip.
I don't follow this... it seems to be another 'edge case'?
I'm trying to visualise 2 ropes that are hanging from a narrow strip of steel (likely not load rated?).
And these 2 ropes are then united with #1010 Offset overhand bend?
And then a person abseils/ascends on these joined ropes?
No comprende...sorry.
« Last Edit: December 14, 2023, 11:34:47 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #20 on: December 07, 2023, 08:45:13 PM »
Dan,
Quote
To my
thinking via the construction of an EK given above, Ashley's
#1043/5 & #1016 are all corresponding knots to the Sheet
Bend
--in one way more so than the BWL :: in that these
knots do NOT have Xarax's *pure* "nipping loop" : they
have a loop loaded principally on the S.Part end, but
don't run then out into a half-force-loaded Outgoing Eye Leg!
I've attached an image of the #1043 F8-Loop bend and corresponding eye knots.
I don't see how #1043 knot core is the same as #1431 Sheet bend core - unless I've misunderstood you?
?? I was perfectly perspicuous.  Your insistence on "identical"
for "corrsponding" blinds you to this insight, apparently.  No,
the correspondence isn't the identical structure you posit as
solely available for the claim, but the loading of the knot
is more nearly so --as I noted re the would-be-but-isn't
Outgoing Eye Leg.
Quote
The notional concept of 'correspondence' is only valid from a strictly geometric point-of-view;
where the cores of the eye knots are geometrically identical to the core of the parent bend.
If you change the geometry, you change the correspondence to something else.
That's just your current opinion, not necessary to analysis here.
One might just as well insist on like loading vs. the rather likely
imbalance one gets via your method (one that isn't so imbalanced
say with Fig.8/OH EKs (just shifting from exterior<=>interior loading).
#1016 shows this relation conspicuously in its center image ::
that ersatz "eye" on the left connects to what would be the
Outgoing Eye Leg (as per #1074 --and, as I've previously suggested,
likely WAS so and the image maker botched this, authors dumbly
copying its asserted purpose, but with no given rationale
unlike what Ashley has offered and put for #1074).
BUT, again, AS SHOWN, the center image nicely illustrates
my offered another-way-of-corresponding (to #1034.5),
and shows a Sheet Bend formed with a single "hitching"
line to a U-folded U-fold providing the eye.  And, again,
the "nipping loop" is that in form but not in the usually
intended loaded-on-both-ends sense (which for Xaras
is part of its definition).


Quote
Quote
Here I'll again interject that correspondence can --even should?!--
have different meanings.
Not for me - sorry.
I am of the view that terminology and concepts need to be defined
--so as to remove as much ambiguity as reasonably possible.
Words have meaning, otherwise it would be like the tower of
Babylon and people would not be able to communicate.
Your strict view of "correspondence" hampers; but it's nice
to see you coming around to liking good diction, after the
previous defence of some rather misleading working!

Quote
Quote
I pointed to the process of building
an EK from a e2e Joint by using 1 single end joining to the two
("twin") ends of a U-fold, and then fusing the single end into one of
the others so to make a 2-tangle (unfused :: 3-tangle) and EK.
You like thought experiments that employ 'edge cases'.
I like thought experiments - but they have to be grounded in reality.
In my view, an end-to-end join will have 4 segments projecting from the knot core
(and an 'eye knot' has 3 segments).
?!  What happened to the 4th, which is what 2-Tangles have
--for you, 2 of yellow, 2 of blue.

Quote
There is no 'fusing' in a real-world practical case where a person joins 2 ropes together by hand alone.
Knot designers/explorers might do this --some have,
as I've shown.  The work can be at times most easily
done graphically --paper & markings don't move!

Quote
this means 8 segments exiting from the core (an even number again).
?!  Do you have some single-ended cordage?!!

Quote
If a Sheet bend is tied with 2 bights, this has 6 segments exiting the core (an even number).
?!  You'll have EIGHT ends, in a 4-tangle.

Quote
Quote
Imagine an OWK ("EDK", "Offset Water Knot") joining two ropes
that are hanging from a narrow strip of steel:: and perhaps
someone abseils or ascends these ropes.  What type of knot
is that?  (It doesn't have force from opposite directions but
the same, on either side of the steel strip.
I don't follow this... it seems to be another 'edge case'?
I'm trying to visualise 2 ropes that are hanging from a narrow strip of steel (likely not load rated?).
[?!!  Hardly :: likely quite load-rated per human-body loading!]
And these 2 ropes are then united with #1010 Offset overhand bend?
And then a person abseils/ascends on these joined ropes?
No comprende...sorry.
One might be high up in a steel-lattice structure,
and the rap-rope straddles some thin (horizontally)
steel span.  The OWK is loaded vertically by BOTH
S.Parts.


--dl*
====
« Last Edit: December 07, 2023, 08:48:42 PM by Dan_Lehman »

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #21 on: December 08, 2023, 04:06:48 AM »
Dan,

Lets try to keep the language confined to a civil discourse - lets not use accusatory language.
I'll reiterate some key points (again).

This entire body of work is new - nobody has attempted to do what I am doing now.
Harry Asher started on this subject matter in the 1980's - but he did not advance any solid theoretical analysis.
There is effectively no peer reviewed body of work that I can refer to or cite.

I also think that language is complex - and it is inevitable that interpretations of typed words can be misconstrued or understood in a way that varies from the originators intent.
Lets take the #1431 Sheet bend and #1043 Eye knot as examples how things can be difficult to nail down and eliminate all ambiguity.
(I would also state for the record - that a high quality image is better than a thousand typed words attempting to describe that image).
Please examine the attached images below...

I define a #1431 Sheet bend as the union of 2 ropes/cords (ie an end-to-end join) - per image 'A' below.
It consists of a U fold (bight) + a loop (some may argue the 'loop' is a half hitch - but no degrees are declared - eg 540 degrees, 180 degrees, etc).
[ ] Per image 'A' - I see 4 segments exiting the core.
[ ] Per image 'B' - I see 6 segments exiting the core.
[ ] Per image 'C' - I see 8 segments exiting the core
[ ] Per image 'D' - I see 6 segments exiting the core (this is likely the geometric structure you were referring to?).
Image 'D' - corresponds to #1074 Bowline with a bight.
EDIT NOTE:
Image has been uploaded to show correspondence between #1074 Sheet bend against #1074 Bowline with a bight.

The Sheet bend variations ('B'; 'C'; and 'D') are not strictly #1431... they employ the same mechanism but the geometry is different.
I think of them as all belonging to the same 'genus'.

I would also state that image 'D' parent bend corresponds to #1016 (per Ashley).
I note your comments re the differences between #1016 and #1074 - the 'parent bend' is per my image 'D' for both.
Once the 'eye' of the eye knot is connected/formed, then you can debate the orientation of the tail end 'bight' (ie which side you wish it to be oriented with respect to the 'eye').

Now, with regard to #1043 eye knot (as per Ashley #1043) - I don't see any direct correspondence to #1431.
Now, you may have an edge case - and see correspondence, but I don't.
This does not mean you should use accusing language such as being "blind" and/or use belligerent comments.
I think this really comes down to definitions and interpretation of language.
And so with a viewpoint where direct geometric correspondence is abandoned, one could unpick the F8 knot structure of the #1043 'bend' - and yes, you end up with a Sheet bend.
But in doing this, you are changing its geometry - because you have changed from an F8 knot to a U fold - by unpicking the tail.
And again - from a pure loading point-of-view (rather than pure geometry) I can see how you make the case that #1043 bend is essentially based on a Sheet bend.
I would suggest that the #1043 parent bend is not a 1:1 perfect replica of the loading profile of #1431 Sheet bend. The differences are subtle but distinct enough to be regarded as belonging to a different family/genera of bends (I will assume that you will disagree!).

I am defining the word 'corresponding/correspondence' probably in a different way to you.
In my view, the term 'correspondence' is a geometric character (you appear to disagree - and that's fine).
Per my attached image below - I can see the geometric correspondence between the #1043 'bend' and the #1043 eye knot.
Now - loading is another matter - which (in my view) adds complications.
For now, I am proceeding on the basis of a direct geometric correspondence.
I think you are declaring something else - and I think it again comes down to ones definitions and interpretation of language.
I would say that you are positing a different geometric arrangement for the F8+Loop bend - perhaps with the inclusion of a U fold of sorts?
All I can state is that I am confining myself to a direct geometric correspondence - because to do otherwise complicates matters and opens up an array of possible derivatives.
You might argue that all possible geometries must be accounted for - and add loading profiles to the mix - and try to define it all.
Outliers do need to be examined and accounted for - I agree - but I prefer to start with simple/basic forms, and tease out the theory from that starting point.

With regard to the generic form of an eye knot tied end-of-line, with a distinct non-loaded tail end.
Take #1047 F8 eye knot as an example.
This 'eye knot' has 4 segments exiting from the core.
In terms of pure loading profile, there are only 3 loaded segments (1 S.Part in opposition to 2 eye legs).
Again - you may wish to disagree - but I think if there is disagreement - it comes down to definitions and interpretations.
I am confining myself to the geometric form of #1047 F8 eye knot, tied end-of-line (with a non loaded tail).

With regard to an end-to-end joining knot formed from 2 singular rope ends:
I see this arrangement as generically consisting of 2 opposing 'S.Parts' and 2 non loaded tail ends.
I included the word 'generically' because I accept that there will be bends that don't conform to this rule.
It gets complicated when 'U folds' (bights) are present (eg #1074 / #1016 derived bends)
I don't claim to have all the answers (and I never made such a claim).
#1074 Bowline with a bight is an example of a structure that has a U fold/bight.

Anyhow, for now, I am confining myself to a strict geometric correlation (or correspondence) between a parent bend and its 'offspring' eye knots.
Lets try not to snip out pull quotes to try to advance an argument to denigrate or slander ones perceived opponent.

I really think you need to get your camera out and try to use high quality images to support your arguments - rather than using a myriad of typed words to describe a geometric arrangement.

Also, can we try to keep the ship steered with a good tack - with a view to finding safe passage through the rough seas of language complexity :)
« Last Edit: December 08, 2023, 07:53:15 AM by agent_smith »

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #22 on: December 09, 2023, 05:52:00 PM »

All I can state is that I am confining myself to a direct geometric correspondence
--because to do otherwise complicates matters and opens up an array of possible derivatives.
//
Anyhow, for now, I am confining myself to a strict geometric correlation (or correspondence) between a parent bend and its 'offspring' eye knots.
We differ on the use of "correspondence" : you want it to apply
with the precision & limits of my *tangle* --for which I've yet
to try any particular names/IDs for the various loadings--;
I want to leave it a general connotation (which can take
qualifiers), accommodating of practical concerns and reflecting
loading.  (Another e.g. :: if one ties the U-fold legs qua a single
"end" to a truly single end in the manner of the Thrun's Bend
(aka "zeppelin"), arguably one has been well more faithful
to preserving e2e joint knottedness than if one loads the
S.Part's Tail as Outgoing Eye Leg and has then only a 50%
loading in the path of the completion of that knot --which
might make a fine EK (seems to) and all, but is arguably
more of a departure from the e2e joint.)

Also, you are focused on a particular *direction* :: e2e -> EK.
Going the opposite direction one has immediately an single
S.Part to convert, and "primary" l00ks appealing as its
descriptor (though we might resist)!


--dl*
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agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #23 on: December 11, 2023, 08:54:34 AM »
I've uploaded the 'U Fold' bend and corresponding eye knots.

I am defining correspondence to be of a geometric character.
That is, the geometry of the parent bend core is congruent with the the cores of all the corresponding eye knots.
I am also defining some of the corresponding eye knots to be 'primary'.
The primary eye knots are closest to the parent bend in terms of loading profile.
A good example of a 'primary eye knot' is the Zeppelin eye knot found on this webpage: https://knots.neocities.org/zeppelinloop
The content creator of this webpage has presented what I refer to as a primary corresponding eye knot.
(there are in fact 2 'primary' corresponding Zeppelin eye knots).

In my view, it is more logical to use a 'bend' as a starting base.
From this parent bend - you can then derive corresponding eye knots.
I am also stating that there are 4 possible 'linkages' with all bends.
These 'linkages' enable corresponding eye knots to be derived.
If loading profile is taken into consideration, then there are a total of 8 possible corresponding eye knots that can be derived from a 'bend'.
Not all of these corresponding eye knots will be stable (or viable).
For example; the Reef/Square bend produces no stable/viable corresponding eye knots.

I am of the view that to do it in reverse - ie to start with an eye knot, and then try to derive the bend is also possible but is illogical.
I'm not saying you cant do it that way!
I'm simply stating that it makes more sense (to me) to start with a 'parent bend' - and then try to derive the corresponding eye knots.

...

The 'U Fold' bend was sent to me by Xarax in June 2022 (correction; June 2020).
He might have discovered it prior to that date - he simply sent it to on that particular date.
At the time it was sent to me, Xarax did not assign a name to it. EDIT: I have since discovered that Xarax did assign 'Bingo' bend.
'U Fold' bend is a name that I have assigned (for now) - it is a placeholder name.
I like it (interesting structure)... note however that I have not investigated jam resistance.

EDIT NOTE:
Xarax might provide further details about this interesting bend (I hope).
I have not tested any properties of the corresponding eye knots.
Agaion, I have assigned a placeholder name for now - because Xarax did not reveal a name back in June 2020.
« Last Edit: December 14, 2023, 11:29:25 AM by agent_smith »

siriuso

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Re: The relationship between 'bends' and eye knots
« Reply #24 on: December 11, 2023, 01:25:23 PM »
Hi Mark,

What you say the U-fold Bend is named Heart Bend by Xarax.

yChan

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #25 on: December 11, 2023, 01:43:57 PM »
Quote
What you say the U-fold Bend is named Heart Bend by Xarax.
yChan

When Xarax sent me the 'bend' in June 2020 - he didn't assign a name to it.
In other words, when he sent it to me (via email in 2020) - he didn't reveal a name to me personally (at that time).
EDIT: In fact, Xarax did assign a name - it was identified as a 'Bingo' bend!

It seems that you have information about the 'bend' that I didn't have at the time.
Thank you for updating the information about the bend!
(The image you uploaded is a dressing state - it is not energy stable.
The dressing geometry depicted in my images are energy stable).
[presumably Xarax wanted to present the knot in a heart shape - but he knows as soon as load is applied, it wont remain in that configuration].
« Last Edit: December 14, 2023, 11:28:24 AM by agent_smith »

alana

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Re: The relationship between 'bends' and eye knots
« Reply #26 on: December 15, 2023, 12:14:00 AM »
... a high quality image is better than a thousand typed words attempting to describe that image).
Please examine the attached images below...

these fig's and pics are great  :)

DerekSmith

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Re: The relationship between 'bends' and eye knots
« Reply #27 on: January 02, 2024, 01:11:19 PM »
"Re: The relationship between 'bends' and eye knots"

The relationship is that all knots are bends and that some groups such as Loops and  hitches, tend to feature a single cord bent to itself.

My professional fields - Chemistry, Math and Programming, have well established lexicons, while my preferred hobby subject is, shall we be generous and say, fluid, and as such leads to a great propensity to steer us away from the challenge of conceptualising and understanding the inner functionality of KNOTS...

The IGKT is probably the nearest thing the world of knotting has to an International Reference Body, so perhaps it is up to the members here to try (once again) to distil some fundamentals of a lexicon for our field?

Derek

Dan_Lehman

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Re: The relationship between 'bends' and eye knots
« Reply #28 on: January 02, 2024, 10:48:40 PM »
The IGKT is probably the nearest thing the world of knotting has to an International Reference Body,
Boy, is this ever a sad joke!  Many people who might have
been constituents to such a group have left.
(Consider that Book Review at km160:15 --basically,
"There's a Budworth book with spiral binding and modern
images; I recommend it."
--a now 10yr-old **title**
on a then a 10yr-old prior title (which was rebuked in a
2002? KM for having Ten Errors! (actually, more)).
And this got into KM!)

Knots are a deceptively hard thing to get a good grip on!
--even with entangled "simple" OH knots.  Look at yChan's
tranformation of the #1425a SmitHunter's Bend into a
more-like-#1425 shaping (and quick jamming), quite
stable these two distinct dressings & settings of one
entanglement!!  Egadz!  <sigh>


--dl*
====

agent_smith

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Re: The relationship between 'bends' and eye knots
« Reply #29 on: January 03, 2024, 02:23:13 AM »
First of all - Happy new year to all :)
Hopefully 2024 will be a year of many advances in scientific discovery.

...

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 had advanced that there are 4 possible linkages between the Tail(s) and S.Part(s) of a 'bend'.
NOTE: If 2 different colour ropes are used to form a 'bend' - linkages can only be made between segments of opposite colour (refer to attached image).
And here I am defining a 'bend' to be a union between 2 ends of [a] rope.
It may be 2 independent ropes... or; it may be 2 ends of a singular rope to form a round sling.
Essentially, I define a 'bend' to be an end-to-end join.

With reference to the attached Butterfly image below:
Extraordinary claims require extraordinary evidence (Carl Sagan).
I am making a claim that #1053 Butterfly eye knot corresponds to the parent Butterfly bend.
Is this claim 'extraordinary'?
Claim 1: Both knots are through loadable.
Claim 2: Both knots respond identically to a through-loading profile.
Claim 3: The tail segments in the 'bend' experience no load
Claim 4: Both legs of the 'eye' of the #1053 Butterfly experience no load
Claim 5: The core of both knots are geometrically identical.


Lexicon / Epistemology
I am using the term 'eye knot' - because the 'eye' of an eye knot has no chirality.
One must first have a robust definition of what a loop is.
A loop is formed by the overlap of one rope segment over the other to circularise with a distinct chirality (either S or Z) - no host object is required.
In my view, the 'eye' in an eye knot has no particular chirality.
Ashley did not conceptualise this clearly - although there are hints that he understood the concept of chirality - but in his classic publication, he chose to describe eye knots as 'loop knots'.
Ashley was not particularly clear on the distinction between a turn and a loop...
I define a turn as a wrap around a host object - for example: A round turn and 2 half hitches; the 'turn' is performed around a host object.
And a turn can be further defined in terms of degrees - eg a 180 U turn, a 360 degree turn, a 540 degree turn, etc (540 degrees is in fact the 'turn' in a round turn & 2 half hitches).
I am 100% confident that some IGKT members will vehemently disagree on the use of the term eye knot in lieu of loop knot. For me, it is a question of defining what we actually mean by the word 'loop'.
For some, I am of the view that tradition and culture strongly influences how a person defines something - and Ashley is regarded as a primary source - and it may be counter-culture to challenge the long held views of such sources. I think the word 'change' sounds alarm bells in the minds of traditionalists. Change can be frightening for some (and fear can induce anger and/or outrage).

To Dan:
#1425 has a very interesting derived Offset joining knot - only partially offset but morphs a little under load into... see below.
I'll photograph and upload it...
[HINT]: #1425 is topologically equivalent to the 'False Zeppelin bend' (with crossed tail segments).

Also, just to be clear...
I find it logical to begin with a 'bend' - and then try to derive the corresponding eye knots.
Obviously, you can work in the opposite direction - that is, start with an 'eye knot' and then try to derive the 'bend'.
In my view, this is not a question of 'right' Vs 'wrong'... rather, it is matter of the logical ease of deriving and classifying possible eye knots.
It seems to me that to begin with an eye knot - and then attempt to derive the 'bend' - is more complicated particularly since you need to define which segments will become the 'S.Parts' (which opens up a branching chain of possible bends based on choice of tails and S.Parts).

I also am of the view that this whole subject matter is best dealt with in terms of geometric correspondence - that is; the core structure of the corresponding eye knots must match the core structure of the 'parent bend'.
Dan - you may choose to disagree with these basic premises - and because of free speech and the freedom to express ones ideas in a democracy, you are perfectly entitled to disagree.
The ability to make scientific advancements is best achieved in an environment where there is freedom to express ones ideas/concepts without fear of cancellation, reputation destruction or retribution. If you have alternative competing ideas - please publish (preferably with quality images to convey your concepts).
« Last Edit: January 03, 2024, 06:55:06 AM by agent_smith »