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
