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.

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 ... :: 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. [i]The host acts as a skeleton framework to support the hitch. If the 'host' is removed, the hitch loses structural integrity.[/i] I am modifying the first sentence to be: [i]The host acts as skeleton framework to support the hitch and to enable it to function.[/i]

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 [i]cutting [/i]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 [i]identity[/i]. What happens in a transposition is that there is a change of [u]identity[/u].

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 [i]chirality /i
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.

---

[agent_smith]

Continuing on with definitions…

Focussing on the definition of a knot.

In my view a knot is defined as follows:

A fastening of material into a distinct geometric form that enables it to recognised and repeated by others. There is implied intent with respect to the geometric form (the knot tier intended to create the geometric form).

Some argue that a knot (at its most fundamental level) is simply a tangle.

However, a ‘tangle’ implies a random mass that possesses no distinctive form, and therefore is unlikely to be repeatable by others. There is implied randomness - an example being a ball of string being agitated and jostled to the extent that it forms into a random knotted mass.

A knot could also be defined as: Material arranged into a geometric form.

This definition avoids intent.

All knot books generally show geometrically distinctive arrangements of material that enables recognition. The geometric forms depicted in books can be repeated by others.

Knot books rarely (if ever) show random geometric forms that have no distinctiveness. If a knot book author intended to publish a bunch of random tangled masses of material with no distinctive form, I don’t think it would be regarded as a knot book - it might be an art book?

People who experiment to discover new geometric knot forms and publish them, arguably hope that others will repeat and use their creations. They hope that their creations will find practical use and be adopted by others (as opposed to their creations being rejected by others and never adopted).

Summary of my position/claim:

A tangle implies a random mass - and may not involve a human (ie wind, agitation, jostling, water, etc could have formed material into a random knotted mass). Some argue that the definition of a knot should not require human involvement. That is, a knot can form without human input. While this is true, this definition must include randomness, and therefore be without distinctiveness.

Dictionary definitions of knot often include the word “fastening”. That is, a knot is a fastening of material into a geometric form.

If the definition includes human intent, obviously a human can make a mistake when tying a knot - and the result is not what was intended (or the result is under a mistaken belief of being the intended outcome).

Whether the intended outcome is correct or not, should not alter the fact of the matter that a geometric arrangement was created. That is, the human had intent - but the outcome may be something else. That “something else” has led to new discoveries (ie a ‘new’ knot was discovered by mistake). But, it still has a geometric form, and it can be recognised.

I’m in favour of a definition that captures human intent (the knot tier’s actions created the knot rather than some random act of nature). Although I concede that two definitions could co-exist… one involving human action and the other disconnected from human intent.

[Dan_Lehman]

A fastening of material into a distinct geometric form that enables it to recognised and repeated by others. There is implied intent with respect to the geometric form (the knot tier intended to create the geometric form).

I’ve defined “knot” to be an intertwining of some
“piece(s) of flexible material (possibly with an
object) [<- as w/a hitch] that holds tension.”
… and given common-sense definitions for “eye
knot”, “end-2-end joint” (or just “joint”), “hitch”,
“stopper”, and then “binder”. Hmmm, on all but the
last, one can see the tension coming from at least one
end of the PoFM (vs. an object or eye legs); but for
the binder, this required tension exists …?! --IN
the intertwined material but not outside via an end.
–which then put the question to me "well, what of each
of those other defined knots : when left w/o tension on
their ends, might they yet have this binder-like inner
tension!?

I see no reason to presume intent; indeed, strictly taken
it would preclude one from surveying knots in the field
except at the point where they are tied --where one SEES
that a tyer has put things just so. Observing the bulk
of already tied knots, one must make some leap of faith
that they came via intent. I see no reason to do this;
I find the intertwined structure and call it for what it
is, intended or otherwise.

There also comes the question of what sort of required
tension is needed --full loading through to rupture;
or perhaps SOME holding but they likely transformation
via slippage or capsizing?! (I’ve used intertwined
structures that I had confidence in their holding so
to do the job I needed, while realizing that they’d
collapse with a greater (even if not so great) load.)

More recently, I came to call the intertwinement
–i.e., that part of what might be a “knot” in a
book excluding the eye of an Eye Knot, e.g.–
a “tangle”; “intertwinement” & “entanglement”
being over-long words, and “tangle” already
established in a sense in topological discourse.

But, then How to treat e.g. the basic sheepshank ::
it seems to have two intertwined parts, and yet these
are barely intertwined --just one strand’s
looping/HHitching a U-fold which runs straight!!

Knot books rarely (if ever) show random geometric forms that have no distinctiveness.

?! I’m failing to even imagine what an image
would be if having no distinctiveness? The most
I can see is that the Hensel&Gretel Ency.Knots…
tome of rubbish typically has both ends of their
presented structures the same length and devoid
of indication of loading --text usually of no value!!
(And yet this massive book has run through 4 editions
–differing almost completely only by the addition of
items to the Appendix (hardly the promoted “completely
revised … by Raoul Graumont”!!). Some of the images
are indiscernible. But in a sense they are yet “distinct
geometric forms”, albeit ambiguous (one can regard these
then as TWO knots per which loading one gives to them).

A tangle implies a random mass.

How would you call the intertwinedness of a knot
–that “nub” of an Eye Knot, say. When you take
the various connections and loadings of a Joint
to make your “principal” & other “corresponding”
eye knots, I see you applying Loading Profiles to
the Joint’s tangle. This is my way of speaking.

But I’m also bumping into challenges with this notion
of “tangle” where there comes (too) much transformation
from one Loading Profile to another.
And rather than the tangle being the foundation for
a knot via the Loading Profile, I’ve come to regard
knots as primary entities from which one can abstract
their tangle and see where Loading Profiles might go
–allowing for going nowhere or nowhere desirable.

–dl*
/===