yChan,
Thanks for all your work.
However, have you ever pondered why you don't seem to be getting any replies or interaction from anyone?
Surely you must be asking yourself this question.
Even Xarax has not commented (privately) - and this is saying something.
...
Okay - here is my opinion.
Your work constitutes big data - and big data can get lost in translation very easily.
The human brain is a complex and remarkable organ - but the human brain needs to find order and patterns to make sense of the information it sees/hears/feels.
Solutions:
1. Forget about the various tying methods that induce deliberate instability - which simply arrive at the same end result anyway.
For example, the Zeppelin bend boils down to two (2) superposed loops of opposite chirality.
And with this fact, you can either arrive at a Zeppelin bend that is S/Z chirality or in Z/S chirality.
In your pdf file titled "OTZeppelinBendop.pdf" - you show the final S/Z form (front and back) - but offer nothing beyond that?
All 3 of the tying methods you show to arrive at a Zeppelin bend induce deliberate instability - yet all arrive at the same end result.
You should simply show the two superposed loops (with opposite chirality) - with one base pair arriving at the S/Z form and the other base pair arriving at the Z/S form.
In my view, your work on the Zeppelin bend is not a full and proper presentation of the Zeppelin bend - because you presume that there is only the S/Z form.
And you do not show the arrangement of the two superposed loops - with their chirality reversed - to arrive at the S/Z and Z/S final forms.
Another example is the #1053 Butterfly eye knot (TIB version).
There are multiple ways of tying this knot - but all arrive at the same finish line...which is the #1053 Butterfly.
Do any of these tying methods tell us about the geometry of the knot and how it works?
It actually all comes down to two (2) loops - which are inter-linked and of opposite chirality.
There is a close relationship between #1425A and #1053...and this is best seen via examining the base pair loops for each knot.
The various tying methods don't reveal this or provide insight into the underlying geometry...
2. With all of your end-to-end joining knots (ie 'bends') - you show no relationship to corresponding eye knots.
All end-to-end joining knots have four (4) possible corresponding eye knots.
EDIT NOTE: 6 if you take into account chirality...for example, there are a total of six (6) possible eye knots that correspond to the Zeppelin bend in all of its Z/S and S/Z forms. And there are 6 possible corresponding eye knots derived from the Butterfly bend (when accounting for both Z/S and S/Z geometries).
This can be confusing though...because it is the general convention to show a bend in one geometric form (eg Z/S) and then derive the corresponding eye knots from that form.
But, if you take into account all of the possible chiralities, it turns out there are six (6) corresponding eye knot to a bend.
You'll see this is virtually all knot books...in that the author will only show a bend in one chirality - and not show its opposite chirality.
You should have a closer look at your latest presentation of 'Crossing knot South and North'.
In reality, your presented 'eye knots' correspond to the #1439 Carrick bend.
3. I believe that you should show end-to-end joining knots and their corresponding eye knots in the same view/page of your document.
This would make your data more meaningful.
In any case, several experienced IGKT members have already discussed at length the correspondence between end-to-end joining knots and their related eye knots.
Why not venture down this path?
I even recall Xarax (years ago) declaring that if you had tied a 'bend' - you had also (by definition) also tied its corresponding eye knot!
I am not 100% with him on this - as it can get rather complicated - and I think it is best to just tie them and show the direct correspondence (in side-by-side imagery).
This is also in part due to the fact that some of the time, one of the corresponding eye knots can be weird looking - eg one of the corresponding Zeppelin eye knots is very close the #1062 (per Ashley).
4. With all of your loop diagrams that create an end-to-end joining knot, it seems pointless to show arrangements that deliberately induce instability.
Fact - all end-to-end joining knots have their SParts (standing parts) axially aligned (ie 180 degrees in opposition). They are never aligned at right angles...
Many of your loop base pairs are rotated out of axial alignment - which simply induces an instability as soon as load is applied - and the knot will automatically (by default) try to axially align itself.
It therefore makes no sense to show this? I think you should only present your loops in base pairs with the SParts in axial alignment.
5. I think you need to reconsider your understanding of what a 'loop' is.
A loop has chirality, an eye does not.
All of your base pair loops (for tying bends) will have a particular chirality - which is either S or Z.
What you describe as a 'loop knot' is really a 'fixed eye knot'. The resulting fixed eye has no chirality, its simply a round eye (like an eye bolt from a hardware store).
Now, if the 'eye' was not fixed - ie its was slipping...then it would be a noose.
For example, the simple #1010 Bowline is a fixed eye knot (the eye is non slipping).
6. You offer no information about jamming or security.
For example, the Zeppelin bend is totally jam resistant while the #1425A Riggers bend jams.
#1053 derived Butterfly bend is jam resistant when through loaded from SPart to SPart (ie axially loaded) but its corresponding eye knot (#1053) jams when eye loaded.
Again, the Butterfly bend has 4 corresponding eye knots - only one of which is 'TIB' (#1053).
I would also suggest investigating which corresponding eye knots are 'TIB'. Is there a rule for TIB eye knots... ie why are some TIB and others not?
7. You offer nothing about symmetry.
For example, the Zeppelin bend has point inversion symmetry.
How would you describe #1452 Ashley bend in terms of symmetry?
Does the type of symmetry play a role in security or jam resistance?
None of this is investigated.
Jam resistance is certainly a measure of a particular knots 'efficiency' - and is a desirable quality.
...
There are some typo errors in the naming of one or two of your pdf files - and a few other errors - but I wont go into further details...
