KNOT TERMINOLOGY AND DEFINITIONS

[agent_smith]

Knot terminology and working definitions are in need of a general overhaul (in my view).
The present use of terminology is problematic.
However, the chance of reaching any broad agreement is vanishingly small.
But, I am an optimist...

To my audience of one (Dan Lehman).
If you're going to cut and paste, try to ensure that the extracted text retains the original meaning.

Also note: These definitions are a work in progress... nothing is set in stone.

My definition of a tangle being:
An unintentional confused mass of twisted cord/rope - that has no distinctive geometry which can enable it to be recognised.
The confused mass is unlikely (or unable) to be repeatable/reproducible by others.
Dan Lehman reply:

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>

The use of the word 'tangle' to describe a hand tied knot is silly in my view.
Part of the definition of 'knot' is that it can be repeated by others.
That is, there is a way to draw it, and publish it, so that others my repeat the tying process and
arrive at the same (precise) outcome.
Precision is required - a change in the geometry may result in something else.
I fail to see how a confused mass of cord/rope can be precisely reproduced by others.

My broad definition of a knot:
An intentionally hand tied structure with a distinct geometric form which enables it to be recognised.
The term knot generically captures the broader aspect of hitches, bends, and self-supporting structures.
The intentionally tied structure can be repeated/reproduced by others.

In my view, intent is required.
A knot is hand tied, with either a known geometric form or a new form is created that was not
previously documented or known to exist.
NOTE: I accept and concede that a 'tangle' can be intentionally formed.
That is, a person sets out with intent to create a confused mass of cord/rope.
They might do this for artistic reasons, or simply to vent anger...

Sub-definitions to differentiate between various types of knots:

My definition of a 'bend':
A hand tied end-to-end join where the S.Parts are axially aligned and 180 degrees in opposition.
There are 2 ends (ie 2 S.Parts), and they are united to enable through loading.

My definition of a 'hitch':
A hand tied structure that requires a 'host' to form around and function under load.
The host acts as a skeleton framework to support the hitch and enable it to function.
If the 'host' is removed, the hitch loses structural integrity.
The host and hitch co-exist in a symbiotic relationship (commensalism).
Reply from Dan Lehman:

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 ...)

No.
Your cut and paste omitted a key sentence.
The host acts as a skeleton framework to support the hitch.
If the 'host' is removed, the hitch loses structural integrity.
I am modifying the first sentence to be:
The host acts as skeleton framework to support the hitch and to enable it to function.

A #206 Crossing hitch/Munter hitch; a Clove hitch; and a Prusik hitch all provide good examples:
The 'host' provides the skeleton framework (scaffold).
Removal of the skeleton framework results in structural collapse.
Load control hitches such as the #206 Munter hitch flow around their host.

My definition of a 'knot' (taking into consideration the broader definition of what a knot is):
A hand tied self-supporting structure.
No 'host' is required, and there is no union of two ends.
per Dan Lehman:

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.

A regular (#1053) Butterfly is a self-supporting structure.
It does not require a 'host' to take form and exist.
It is an 'eye knot'.
Cutting the eye of a #1053 Butterfly does not result in structural collapse.
I would point out that the act of cutting is not a part of the definition.
In the case of the class of 'knots' called hitches, these structures require a skeletal host.
We don't 'cut' the host, we imagine removal of the host - which then results in the hitch losing structural integrity.
I think of the host and hitch co-existing in a type of symbiotic relationship (commensalism).


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.

Definition of transposition:
For transposition of eye knots:
Where an S.Part changes identity with a tail end but without altering the knot core geometry.
Transposition can be likened to a reversal of polarity.
[NOTE: The 'identity' is used in lieu of 'exchange'].

For transposition of 'bends':
Where the S.Parts change identity with the tail ends but without altering the knot core geometry.
Transposition can be likened to a reversal of polarity.
per Dan Lehman:

:: one doesn't exchange
anything, but rather uses a different loading profile
(which sort of alteration could occur in practice).

I have substituted the word 'exchange' with identity.
What happens in a transposition is that there is a change of identity.

Definition of 'core':
The part of a knot that is central to its existence and character.
A centralised core may not be apparent or obvious in hitches, being dispersed or distributed.

Definition of 'eye knot':
A self-supporting structure that has a connective eye that is non-slipping.
The eye has no chirality.

...

[agent_smith]

I recently found an 1884 knot book authored by Joseph Tom Burgess.

Book title: Knots Ties and Splices
Link: https://ia601301.us.archive.org/12/items/cu31924014519940/cu31924014519940.pdf
At page 24, the author identifies a loop.
Fig 17 is identified as an underhand loop (actually 'S' chirality).
Fig 18 is identified as an overhand loop (actually 'Z' chirality).
At Fig 153 he also identifies 2 loops.

I find this very interesting because the author appears to have a concept
of what a loop is circa 1884.
We have progressed some 140 years since this book was published.
It appears that Burgess did not have a concept of chirality (handedness)
as we understand it today.
Other than to say that he understood the concepts of 'underhand' and 'overhand'.
Whether we can extrapolate his understanding to also include chirality is unclear.


Robert Birch has a useful glossary (updated to VER 1.4 2020):
Link: https://igkt.net/publications/32-recent-additions

Birch has made a solid attempt to sort out technical definitions.
Its one of the best efforts I have seen.
I think he has derived a lot of his understanding from this IGKT
forum - and he has re-stated many concepts evolved by people such
as myself, Dan Lehman, and Xarax.
I agree with at least 80% of what Birch has defined.
In my view, Birch needs to do more work on the definitions of:
[ ] Loop
[ ] Nipping loop
[ ] Turn
[ ] Hitch
[ ] Half-hitches

In the first instance, a hitch requires a host.
The hitch and the host exist in a symbiotic relationship.
There is a further subset of hitches as follows:
[ ] Slide and grip hitches
[ ] Noose hitches
[ ] Binder hitches
[ ] Load control hitches (eg Munter hitch)

Things get tricky when trying to define what a 'half-hitch' is.
Birch has made a solid attempt to try to set things in order,
including picking apart historical concepts.

The distinction between a turn and loop is a little muddled at times,
and his illustration on page 1 shows a turn and a loop.
He also shows a 'closed turn' and a 'half hitch - the distinction
appearing to be the presence of an overlap/cross-over.
But, he includes another drawing showing a Round turn and 2 half hitches.
This creates a conflict between the 2 drawings of half hitches.

My proposal is to define half hitch as follows:
A half hitch is a termination mechanism.
It is principally used to secure a loose tail end.
Primary characteristics of a half-hitch:
1. It is formed around an S.Part (or an active load segment).
2. It is formed from the loose tail end of a rope/cord.
3. A half hitch has chirality ('S' or 'Z').

Turn
Birch tackles the definition of a 'turn' - but there is ambiguity.
Birch defines that a turn requires a solid object (a host).
His drawn half-hitch around a 'solid' indicates an overlap/cross-over.
In contrast, a turn is also shown around a 'solid' but without an overlap.
My view is that this muddies the waters.

I agree that a turn forms around host (what Birch refers to as a solid).
A turn assumes the shape of its host.
A turn benefits from the capstan effect.
A loop does not require a host to take form.
I agree that both a loop and a turn have chirality.
I dont agree that a turn cannot have an overlap (eg a riding turn).
A riding turn is allowed - and indeed enables the creation of a binder hitch.
The presence of a riding turn does not disturb the definition of a turn.

I think Birch ought to have distinguished a half-hitch from a turn by declaring that
a half hitch is a termination mechanism. Half hitches always form around an
S.Part or a load segment. Half-hitches are always formed from a loose tail end.
The important concept here is that a half-hitch forms around a loaded segment (eg S.Part).

Birches drawing of a half-hitch tied around a solid host can be conceptualised
as a turn with an overlap. The turn is taken around a solid host but has an overlap
point. The presence of the overlap/crossing-point does not transform the turn into a half-hitch.
It simply a turn taken around a solid host that has an overlap/crossing point.

Birch also attempts to distinguish between a 'open turn' and a 'closed turn'.
I am unclear if such a distinction is necessary or important.
In his drawing, both form around a solid host.
Birch ought to have distinguished turns by degrees of arc traced out.
A U turn is 180 degrees, a round turn is 540 degrees.
With specific regard to Birch's drawing, I see the following:
[ ] Round turn = 540 degrees
[ ] Open turn = 360 degrees
[ ] Closed turn = 360 degrees
Birch's open turn and closed turn are simply 2 sides of the same coin.
I think he was attempting to differentiate between a turn that is splayed
apart, versus a compact turn.

Birch's drawing of 2 loops include the terms; 'overhand' and 'underhand'.
This is unnecessary. The concept of under versus over is meaningless.
All that is required to differentiate between loops is chirality.