The definition of a loop

[agent_smith]

per Dan Lehman:

Discussion carried from this link: https://igkt.net/sm/index.php?topic=6748.msg44365#msg44365

It might be helpful to distinguish between a loop
and a helix --though either might transform
into the other.

We have to be very careful with terminology.
 tsik_lestat did not use the term helix to describe a loop.
Rather, it is simply a loop with a helical shape (Note: This is not the same as declaring a loop to be a helix!).

I see #1013 double Bowline as having a nipping structure based on double loops.
The double loop structure has the form of a helical loop.
That is not the same as declaring the double loop to be a helix.

A rolling hitch presents a challenge to such
handedness assignment, and the multiple OHs
do as well.

I experience no such challenge.
A loop is created when one segment of rope overlaps and crosses itself.
The notional concept of 'over' or 'under' is irrelevant (or 'up' or 'down').

The notional concept of up, down, over or under can only have meaning within a carefully defined reference frame.
Such a reference frame (in the majority of cases) can only have meaning to an individual observer at a point in spacetime.

In my view, we can avoid difficulties with up/down/over/under by simply referring to chirality.

In which case, I can create a loop that has either left-handed (S) or right-handed (Z) chirality.
The chirality aspect takes the form of a helical loop (again - avoiding the word helix).

All hitches require a host.
They are all based on various geometries which involve a series of turns, riding turns and penetrations through existing turns.

One could more easily examine #1763 Prusik hitch... which consists of a numbers of turns around its host.
[ ] From one leg of the Prusik, the turns around the host are left-handed (S) chirality.
[ ] From the opposite leg, the turns around the host are right-handed (Z) chirality.
There is no 'up' or 'down' - and a mirror image makes no difference because it will still involve both S and Z chirality.
This is because #1763 Prusik is tied from dual legs (not a single leg... and is symmetric. An example of a single leg hitch is the so called 'Blakes hitch' - per Prohaska)

The Rolling hitch can have a mirror of itself too - which reverses the 'flow'
It differs significantly from #1763 on account of its creation from a single leg (not dual legs).
Maybe you are only contemplating the Rolling hitch from the direction of flow depicted per Ashley (and not in mirror image form)?
And there is also #1245 Clove hitch - which can have mirror versions being tied with S or Z chirality. At illustration #1245, he shows the Clove hitch tied with S/S chirality (not Z/Z chirality).
I would further comment that in virtually all cases, Ashley illustrates his 'Bowlines' with Z (right-handed) chirality.

I continue to advance the point that handedness
in at least these simpler bowline cases is determined
by the SPart's initial turn --which in the OP's case,
is right-handed.

This is muddying already turbulent waters.
I don't think this definition is useful or practicable (yes - I intended practicable).
Per Ashley's depiction of his Bowline at #1010 - it is shown with Z (right-handed) chirality.
The SPart's 'initial turn' could be hard to define in any reference frame. Initial turn in reference to what?
The nipping loop shown by Ashley at #1010 has the form of a helical loop (not a helix) and occurs because a rope segment overlaps/crosses itself. It matters not whether it is 'up' or 'down' (or over/under) - because these concepts are independent of chirality.

I am happy to debate these concepts with you...
I think good starting points are #1245 Clove hitch and #1763 Prusik hitch and Blakes hitch (which includes a penetration).
And for me, all loops have a particular chirality - while an 'eye' does not.
For example, the eye of #1047 Figure 8 isn't a 'loop' - it has no chirality and it is intended to attach to some object and sustain load.

EDIT: attached image should be working now...

[Dan_Lehman]

per Dan Lehman:
The SPart's 'initial turn' could be hard to define in any reference frame
 Initial turn in reference to what?

Yes, the fundamental question :: initial in reference
to the axis of tension, where the SPart's direction
is "deflected* from the straight-&-narrow.

In your illustrations, just rotate those by-the-spring/coil
BWLs arouund (eye upwards) and overlay them upon
the coil and the SPart WILL RUN OPPOSITE TO THE
CONTACTED COIL.  That is what I see as wrong;
this is where I see a key aspect of the cordage in
the knot.  (But then how do I account for the
continued, anti-direction/-deflection as the looping
continues *backwards* for a knot with multiple
turns?!)

Similar seemingly paradoxical indications come from
e.g. a multiple OH in pretzel form then set by load
into strangle form, and there the overwraps will
be contrary in helical movement to ends at entry.

Consider marling vs. half-hitch hitching of a sail
or whatever, where in both cases the movement
of the hitched line over the sail goes out and
down-around the right side :: by convention this
defines R-handed OH but ... L-hand HHitch?
(One can see at the loop-crossing point the
one torques one way, the other the other; but this
is a small point in the structure, not the initial
(principal?) turn.

.
Rather, it is simply a loop with a helical shape
(Note: This is not the same as declaring a loop to be a helix!).
//
The double loop structure has the form of a helical loop.
That is not the same as declaring the double loop to be a helix.

How is it that a *loop* is ever NOT a (minimal) helix?
--the closing, in most cordage, must lie to one side
or the other, and thereby be minimally helical; I was
thinking to just *define* away this case for the
purpose of handedness.
(Btw, the "crossing/not" distinction traditionally
offered for "loop"/"bight" (resp.) is IMO not helpful,
and mostly (in terms of frequency) irrelevant to
the physical thing : I see loops as *round*,
bights as *elongated* (and should a bight's legs
cross by some perspective, no matter.
(Though I'd find it awkward at best to refer to
all "the bights of the rug" rather than "loops" !     )


--dl*
====

[KC]

For me it is about follow the forces,
Equals forces vs. Greater over or under lesser
>>as the relevant points to understanding.
And the SPart is the force input for all this in Hitching as termination
Or multi competing SPart inputs of forces in Bending.
.
Other highlights beside force path may guide relaying how to tie better,
But force relationships and geometries  give the understanding I think.
Then once understand tying just more Natural as purposefully groom and align to equitable target.

[agent_smith]

per KC:

For me it is about follow the forces,
Equals forces vs. Greater over or under lesser
>>as the relevant points to understanding.

And how does this shed light on the chirality of a loop?
Or...what is a loop?

Hmmm.
Politicians are very clever at providing answers that don't actually answer the specific point
I know you are not a politician!

Here is very specific question for you:
With regard to Ashley's #1010 illustration of a simple Bowline, what is the chirality of the nipping loop?
Is it S or Z chirality?
Or is it something else?
Does it even qualify as a 'loop'?
What is a 'loop'?

[agent_smith]

per Dan Lehman:

Yes, the fundamental question :: initial in reference
to the axis of tension, where the SPart's direction
is "deflected* from the straight-&-narrow.

This is problematic in that it requires a reference frame to declare a 'direction'.
You appear to suggest that your reference frame is the 'axis of tension'.
The SPart is then deflected off axis - in some 'direction'.

How much of a deflection off-axis is required to determine chirality?
Is one (1) degree deflection sufficient?
Or is five (5) degrees required?
And if its 5 degrees, how do you define direction when using the axis of tension as a reference frame?

Is there an up, down, left, right, over, under?
Or a north, South, East and West direction?

I think you will struggle to define your proposition with precision.

In your illustrations, just rotate those by-the-spring/coil
BWLs arouund (eye upwards) and overlay them upon
the coil and the SPart WILL RUN OPPOSITE TO THE
CONTACTED COIL.  That is what I see as wrong;

Chirality cannot be affect by a simple rotation.
Only by viewing an image in a mirror can you get a reversal of chirality.
A left glove is always a left glove - rotating it in any axis changes nothing.
If you view a left glove in a mirror - only then can you see a virtual image of the glove with opposite chirality.

Lets start with the simple #1010 Bowline as depicted by Ashley.
I see the nipping loop with Z (right-handed) chirality.
The spatial position of the SPart and the outgoing eye leg play no role in the chirality of the loop.
I can rotate the entire knot and flip it over... its still the same chirality.
All objects can be classified as chiral or achiral, right down to and including molecules.
An object is chiral if it is not superimposable on its mirror image.
For example, your hand is a chiral object, as it not superimposable on its own mirror image.

In the case of a loop, it has a spiral/helical shape.
I am not stating that a loop is a helix.
You could state that it is the beginning of a helix - but a loop by itself isn't a helix.
A helix will be either left-handed or right-handed.
See this link: https://en.wikipedia.org/wiki/Helix

I see loops as *round*,
bights as *elongated* (and should a bight's legs
cross by some perspective, no matter.

For me, there has to be some demarcation point - a robust definition otherwise we are being nebulous.
For a loop to be formed in a rope, one segment must cross itself (overlap).
If there is no crossing point, and the legs simply approach but never actually cross, no loop is created - it remains as a 'bight'. The bight can be as elongated as one wishes.
In a perfectly round loop, each leg exits 180 degrees in opposite directions.
By degrees, one reaches a point where difficulties arise.
I presume at least a 90 degree separation... less than that is simply an overlap/crossing point (but this definition is also difficult).

When a simple #1010 Bowline is loaded, the legs of the nipping loop are in 180 degrees opposition.
In a Zeppelin bend, the legs of the loops are at 90 degrees at the point where they each cross their respective SParts. I therefore have no difficulty conceptualizing a Zeppelin bend as being built from 2 superposed loops of opposite chirality. Same with #1425A Riggers bend - which can be tied as either S/S or Z/Z chirality... and so on.

[KC]

Actually, i was trying to politely and lightly say going more with your counter-part's version of view;
as watch this, not dictate it.
As he watches the SPart as reference start, i see as same for is full force input into heart of knot, as the trail of friction degrades the force.
This includes somewhat of simple/mono helix where you say must be plural.
Rather than get caught up in what seems to my eye this constant degrading undertow of confrontation and calling others out ;
that i see, feel, shy from and watch others get turned off and out rightly leave, others would seem not join at all.
At some points hard to tell if we are building or braking/breaking as watch some of the fray go'round.
Perhaps everyone is kidding and i'm missing the locker room joking, but that is not what i honestly see, nor hear from others.
>>and when some promising first light peeks thru the din and folds in few posts; this is what i blame many times.
>>as like when some newbs start throwing in the same game in few mos. of examples brings meter more towards brash tavern than quiet library.
.
Chirality to me is more of how to tie, than understanding mechanix.
So chirality is what i try not to see/not to be blinded by as try to peer deeper into the works.
.
i think working knots are about the 180arcs and the non-arcs.
>>Arc offering both ends and apex as 3 unequal force points in same direction.
>>non-Arc as ends pulling in opposite directions, more equal forces, w/loss of the mid force point.
Then the force induction thru the once powerless rope 'wiring' (pipeline pathing for tension rather than electricity or water or air)
>>And the geometric and directional relationships between the force points formed
Without change of other factors, chirality does not change the grip, nip, strength, reach etc. of the works.
A change in force, carries more weight than a change in name.

[Dan_Lehman]

per Dan Lehman:

Yes, the fundamental question :: initial in reference
to the axis of tension, where the SPart's direction
is "deflected* from the straight-&-narrow.

This is problematic in that it requires a reference frame to declare a 'direction'.
[as does any definition].  That given for rope, e.g., takes
a similar one : rope looked at as it goes AWAY from viewer
(we could say "on the top": but viewer cannot see bottom.,)

How much of a deflection off-axis is required to determine chirality?
Is one (1) degree deflection sufficient?
Or is five (5) degrees required?

Is there an up, down, left, right, over, under?
Or a north, South, East and West direction?

I think you will struggle to define your proposition with precision.

Yes, I'm struggling ; but I don't see your method/answer,
means of assessment.

In your illustrations, just rotate those by-the-spring/coil
BWLs around (eye upwards) and overlay them upon
the coil and the SPart WILL RUN OPPOSITE TO THE
CONTACTED COIL.  That is what I see as wrong;

Chirality cannot be affect by a simple rotation.

Completely off point :: I'm making the rotations
so to put the initial turn in a  graphical position for
the likeness to show (the spring has a 2D falseness
in trying to present as the 3D entity it is).

What I want to be seen is how the SPart's curvature
FITS the R-handed helix FOR A WHILE, HERE.

(But, then, as it comes back up *behind* itself
vs. "going away" like strands of a R-handed rope,
we have our problem; the outgoing eye leg DOES
reach away in that direction, but resumes a straight
path per tension; and in the case of ITS "initial turn"
--views as it comes INTO the turNip--, we have there
a rather too-hard a turn (or is it?).)

Let's start with the simple #1010 Bowline as depicted by Ashley.

WHY THIS, vs. what we can see HERE --I don't port ABoK
around w/me, and find your images well better than Ashley's
(frankly, his "artist" credential take a hit, IMO!).

I see the nipping loop with Z (right-handed) chirality.
The spatial position of the SPart and the outgoing eye leg play no role in the chirality of the loop.
I can rotate the entire knot and flip it over... its still the same chirality.

But WHY/how do you make this judgement?
Surely you cannot ignore where the outgoing
eye leg is --if it returns on the *away* side of
the SPart it is dead-on defining a helix, and
one contrary your assessment.

All objects can be classified as chiral or achiral,
right down to and including molecules.

And I read of a difference concerning helices.
In cordage & knotting, we want "handedness" and
the helical aspects.

An object is chiral if it is not superimposable on its mirror image.

Which has no bearing on TYPE of chirality, which is our
question here.

In the case of a loop, it has a spiral/helical shape.
I am not stating that a loop is a helix.
You could state that it is the beginning of a helix - but a loop by itself isn't a helix.
A helix will be either left-handed or right-handed.
See this link: https://en.wikipedia.org/wiki/Helix

If it isn't a helix (of minimal length), why not?

I see loops as *round*,
bights as *elongated* (and should a bight's legs
cross by some perspective, no matter.

For me, there has to be some demarcation point
--a robust definition otherwise we are being nebulous.
For a loop to be formed in a rope, one segment must cross itself (overlap).

Crossing or not is a matter of perspective
--turn your crossed part sideways and now
the parts are merely adjacent.

When a simple #1010 Bowline is loaded, the legs of the nipping loop are in 180 degrees opposition.

If anything, unloaded BWLs look to have a 270deg
rotation & crossing (like a sheet bend esp. opp-sided).,
Or you mean "and flattened, but for obvious thickness
AT the crossing point"?!

In a Zeppelin bend

No need to bring in Thrun's Bend.

CONSIDER THIS :: #388 can dressed into a normal
Dbl. BWL, and you would call the latter, say,
"left-handed" but the former got by dressing this
will have a quite obvious R_handed helical SPart :
what to do?!  Wouldn't your notion of unchangeable
chirality find a problem with this and common sense?

(My test of unknotted rope --i.e., lock the SPart at
entry & exit points, untie, and then straighten out
this locked-in-place segment-- will yield a quite
obvious L-handed twisted strand.
(E.g., cast a series of HH-loops over a pencil and
then remove the pencil & pull straight; my R-handed
turNip has L-handed strand/span.  One can try to
**simulate** a matching set of marling's OHs
by closing the OH around an inserted extra strand
(so to not actually knot an OH but to capture its
effect), and then ... R-handed for I think agreed
R-handed OH.  (Tie a Dbl. Strangle and see initial
R-handed turn flow into L-handed overwraps.,
but an agreed R-handed Pretzel-form dressing)


Might be that a good paradigm to examine
is that of marling vs. HHitching, where each course
"goes away" turning to the right; yet the marling's
OHes are called R-handed and you the other L-handed.


-dl*
====

[Keystoner]

This is problematic in that it requires a reference frame to declare a 'direction'.

Is there an up, down, left, right, over, under?
Or a north, South, East and West direction?

Chirality cannot be affect by a simple rotation.

Lets start with the simple #1010 Bowline as depicted by Ashley.
I see the nipping loop with Z (right-handed) chirality.
The spatial position of the SPart and the outgoing eye leg play no role in the chirality of the loop.
I can rotate the entire knot and flip it over... its still the same chirality.
All objects can be classified as chiral or achiral, right down to and including molecules.
An object is chiral if it is not superimposable on its mirror image.
For example, your hand is a chiral object, as it not superimposable on its own mirror image.

I understand chirality and all that you wrote above but I can't quickly identify the chirality of a loop using the mnemonic letters 'Z' and 'S'.  I think I have it but I'm slow.  My reference frame is to look from above and trace the loops as the rope descends.  If it's descending clockwise, it's 'Z'; descending counterclockwise is 'S'. The letter mnemonics only work for the top half of each letter though since each letter changes direction--clockwise to counterclockwise or vice versa.  What do you do--what is your reference frame to assess 'Z' vs. 'S' and where does left-handed vs. right-handed come in?

[agent_smith]

per KC:

Actually, i was trying to politely and lightly say going more with your counter-part's version of view;
as watch this, not dictate it.

Nobody is dictating anything.
You are mistaken.
This is a technical forum where people dive deep in to the science and mechanics of knotting.
Nobody is insulting, dictating, deriding, attacking, being offensive or engaging any other form of belligerent behavior.

Your perception of dictating is way off the mark and I find the suggestion of it to be misguided.

Rather than get caught up in what seems to my eye this constant degrading undertow of confrontation and calling others out ;
that i see, feel, shy from and watch others get turned off and out rightly leave, others would seem not join at all.

This is incredibly way-off and somewhat offensive.
Don't mistake 'argument' as dictatorship, degrading, confrontational or whatever overtone you wish to apply.
Remember, people can engage in technical argument - and merely because they are engaging in such technical argument does not imply or suggest inappropriate behavior.
The scientific world operates the same way - someone discovers a theory and publishes it.
Others have the right to refute or agree with it.
If they refute it - it is not evidence of misbehavior.

Chirality to me is more of how to tie, than understanding mechanix.
So chirality is what i try not to see/not to be blinded by as try to peer deeper into the works.
.
i think working knots are about the 180arcs and the non-arcs.
>>Arc offering both ends and apex as 3 unequal force points in same direction.
>>non-Arc as ends pulling in opposite directions, more equal forces, w/loss of the mid force point.
Then the force induction thru the once powerless rope 'wiring' (pipeline pathing for tension rather than electricity or water or air)
>>And the geometric and directional relationships between the force points formed
Without change of other factors, chirality does not change the grip, nip, strength, reach etc. of the works.
A change in force, carries more weight than a change in name.

Ok - thats all fine.
Now, I'm going to ask a question - and this question is not intended to be offensive, a dictatorship, slanderous or a form of misbehavior.
Here is the question:
Q. In the case of #1010 simple Bowline as depicted by Ashley, what is the chirality of the nipping loop?

Now, you are entitled to have your own view. And thats perfectly fine.
In asking you this question, it is simply an attempt to gain insight into your understanding of 'chirality'.
Now, if you declare the nipping loop to have left-handed (S) chirality - thats perfectly fine by me.

However, I reserve the right to disagree with you - and thats not being offensive or being a dictatorship.
Its just 2 people disagreeing over a technical matter - nothing more and nothing less.

[agent_smith]

per Keystoner:

I understand chirality and all that you wrote above but I can't quickly identify the chirality of a loop using the mnemonic letters 'Z' and 'S'.

Please be aware that this is simply my view.. others may disagree.
For example, KC may form a different view - and thats perfectly fine.
Others are perfectly entitled to form their own views - and to me, this is a necessary human condition and the basis of how we progress.

Here is a link: https://en.wikipedia.org/wiki/Helix

In the first instance, one needs to define what a 'loop' is.
Knotting terminology is something that is unlikely to have universal agreement.

Be that as it may, i see a loop as being the first stage toward creating a helix.
This is NOT the same thing as stating that a loop IS a helix.

Definition extracted from Wikipedia and also generally other papers:

Helices can be either right-handed or left-handed. With the line of sight along the helix's axis, if a clockwise screwing motion moves the helix away from the observer, then it is called a right-handed helix; if towards the observer, then it is a left-handed helix. Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa.

Extract: (refer to attached image)

In a left-handed (sinistral) helix, as one moves up the helix the line moves to the left across the front face. In a right-handed (dextral) form, the line moves to the right across the front face. Historically, the two forms in plants have also been given other names. Upward movement of the helix can be related to a clock face as viewed from above. The central part of the letters S and Z reflects the slope of the line.

COMMENTARY:
This is not a dictatorship!
I am merely presenting my understanding of a helix and chirality.
I see a loop as being the first stage in creating a helix - the continuation of which creates a helix.
Others may completely disagree...and they are perfectly entitled to do do!

EDIT: Added image showing S and Z in relation to a helix.

[Keystoner]

Agent_Smith, thanks for all the time you spend with your explanations. I got it and I had it.

What I don't get is any point of contention here.  I don't understand why Agent_Smith goes to great lengths to emphasize that he's stating an opinion on issues that are glaring facts, in my opinion.  I don't get why he wastes his time with people who apparently wake up in the morning with the desired intent to find something they can take offense to.

From Wikipedia and emphasized many times by Agent_Smith: Handedness (or chirality) is a property of the helix, not of the perspective.

Do people actually find that to be open to opinion?

You have a 4-way intersection. There is a red light in the north/south direction. There is a car stopped facing north and a car stopped facing south. Agent_Smith passes through the intersection traveling east. The car facing north sees Agent_Smith pass from left to right.  The car facing south sees Agent_Smith pass from right to left. Each of those stopped cars has a unique and different perspective but still, of course, and not open to opinion, Agent_Smith was traveling east.

[Dan_Lehman]

Agent_Smith, thanks for all the time you spend with your explanations. I got it and I had it.

What I don't get is any point of contention here.
I don't understand why Agent_Smith goes to great lengths
to emphasize that he's stating an opinion on issues
that are glaring facts, in my opinion.  I don't get why
...

Clearly you are ignoring me, or greatly out of line
with your implicit rebuke that I somehow do not
take considerable effort to elucidate points of discussion.
I expressly reference all this "helix" discussion and put
my point smack ON it.  To which I'm w/o reply.

Notably, I've not seen an answer as to how handedness
is assessed by A_S except for what he has published,
to which questions were put.  My reference i.p. to #488
and a like-formed dressing of the double bowline
and to the marling-vs-hhitching series are good cases
for discussion.

From Wikipedia and emphasized many times by Agent_Smith:
Handedness (or chirality) is a property of the helix, not of the perspective.

Do people actually find that to be open to opinion?

YES, Wikipedia in its discussion of "chirality" points to circumstances
where it departs from matching that of a helix.  --which points
go beyond what I think we want here, for knot structures.
 ALSO
NO, but the issue is whether one is actually dealing with
a helix when considering a knot --as my example
with the bowline etc. illuminate.  For ME, I'm looking
at a specific and key part of the *knot* (which might or
might not lead to a helix at some point), not a helix per se.
DO READ the comments, not come here and deride them implicitly.

... Each of those stopped cars has a unique and different
perspective but still, of course, and not open to opinion,
Agent_Smith was traveling east.

Okay, I'll play :: you have this intersection and he's on a
road passing through it and at the moment of passing
he'd going one direction but
that road has its own directions, and the police
report refers to them and after the intersection's
state the road bends from east to south and the
road is overall referred to in N-S directions.

.:.  You've chosen one small section to use to make
your assessment of direction; others see a larger
picture.  I'm at the intersection of the point of
deflection from the axis of tension with the bowline
and seeing the RIGHT-handed turn;
you and A_S are standing back and assessing
handedness from a different perspective and range.

And to reiterate by pasting:

I think you will struggle to define your proposition with precision.

Yes, I'm struggling ; but I don't see your method/answer,
means of assessment.

In your illustrations, just rotate those by-the-spring/coil
BWLs around (eye upwards) and overlay them upon
the coil and the SPart WILL RUN OPPOSITE TO THE
CONTACTED COIL.  That is what I see as wrong;

Chirality cannot be affect by a simple rotation.

Completely off point :: I'm making the rotations
so to put the initial turn in a  graphical position for
the likeness to show (the spring has a 2D falseness
in trying to present as the 3D entity it is).

What I want to be seen is how the SPart's curvature
FITS the R-handed helix FOR A WHILE, HERE.

--dl*
====

[Keystoner]

you and A_S are standing back and assessing
handedness from a different perspective and range.

How do you not get this?  Handedness has NOTHING to do with perspective.

[Dan_Lehman]

you and A_S are standing back and assessing
handedness from a different perspective and range.

How do you not get this?  Handedness has NOTHING to do with perspective.

Try READING before replying : I even used your intersection illustration.
How you do not get that is becoming obvious.

--dl*
====

[KC]

I'm sorry chilarity is part of things I've so much exercised to look past in force chase etc.
That I don't have much of any comment or view of as things evolved.