Peer review needed: How Knots Work - draft

[dionzand]

Hi all!

I have recently started taking an interest in knot tying. I have a strong science background, and my way of learning has always been: "understanding how and why something works". For me, simply following a step-by-step guide on how to tie a know does not stick. I want to understand why that specific knot "works" and another one, that looks similar, does not.

So that's why I have been working on a book/reference called "How Knots Work" ( How Knots Work – Google Drive ). It is not a tying manual, or a "best knots" list. I barely use a dozen knots in the whole book. I basically want to explain the actual mechanics of why a knot holds/slips/jams/fails: topology, geometry, friction, the capstan effect, self-locking, etc...

Attached you will find a text-only draft, 36 chapters, ~50k words. I have not taken any photos yet, because I wanted to have the framework ready first.

I'd love to have your feedback on:

• Anywhere the mechanics are just wrong, or I'm overstating something I shouldn't be that confident about
• If a knot doesn't actually behave the way I describe it
• Terminology that doesn't match how you'd actually talk about this stuff
• Bits where it sounds like an explanation but is really just describing something without saying why

Don't hold back, tell me what's broken.

Hopefully this can become a nice introduction into the principles behind knot tying for people that have the same learning preference as I have

Cheers, and thanks to anyone who gives it a read.

Dion

Link to the docs: How Knots Work – Google Drive

[agent_smith]

Greeting Dion,

Thanks for your work (in draft form).

I would make many changes - only because I have tackled this topic many years ago - and still keep refining it.

Many of the definitions you use need to remove ambiguity and variation in interpretation by readers.

Go to this link and download my 'PACI protocols' document. Most of the knot related definitions have already been defined.

Link: PACI (at #2 in the table).

...

Here is my definition of what a 'knot' is: (extracted from my protocols document).

NOTE: Dan Lehman and I have been engaging in open lively debate about this subject for many years. Dan appears to prefer the use of the word 'tangle' in his definition of what a 'knot' is. I prefer to avoid this word - because it implies randomness. On this forum, all knots presented are intentionally tied and have a specific geometric form that enables it to be recognised.

Having said that, I accept Dan's viewpoint that knots can also form via a random pathway. I have differentiated this by use of the words; intentional and unintentional. Dan is correct in stating that knots can also form unintentionally. Some great discoveries have been made by accident... where a person (a human) has attempted to tie a known/existing knot - but inadvertently arrived at something else - which turned out to be significant and/or better, in and of itself.

A knot could also form by accident due to random motion - eg Dan has pointed out that a 'knot' can accidentally form in ones trouser pocket via jostling and cyclic motion. I conceptualise this outcome as unintentional.

Anyhow - here is my current definition of what a 'knot' is:

- Means an intentional fastening of rope (or cordage) possessing a distinctive geometric form that enables it to be recognised and repeated by others.

Knots are rope made machines that perform a function in response to a defined magnitude and direction of load.

Knots may also form unintentionally – either as a result of careless rope handling – or, via a mistake in tying. Some remarkable discoveries have been made via a tying mistake – that resulted in a better/improved knot, or a completely new knot!

..................................................................................................................................................................

Your definition of what an 'eye' versus 'loop' also needs work.

A loop has chirality, an eye does not.

A loop can be formed with 'S' chirality or 'Z' chirality - this being heavily influenced by the 'handedness' of the person (human).

[Dan_Lehman]

Congratulations !! --you're writing a book that I hope
to write. Maybe now I can cheap out and just kabitz
(er, contribute).

1. "kernmantle" : I believe that this is defined
   in (USA-based?) Cordage institute to cover
   --essentially, seems the intent-- those ropes
   much made for rockclimbing, caving, & SAR.
   Which is a use-based definition rather than
   a structural one.
   IMO, a "kernmantle" rope is one in which the
   mantle (sheath) is needed in order for the rope
   to have integrity --i.e., absent the mantle, the
   kern can't function. In climbing (and to my
   surprise, caving also), the core is a multiple
   of laid cords, and not --as in "Dbl. Braid"--
   a potential stand-alone structure.
   IMO, this is a reasonable definition/distinction,
   and should be adopted. But then there is I
   think some further distinctions between cores
   --some just "parallel fibre" multitudes, others
   in other arrangements.

"tangle" means what one would define it to mean,
and it's silly to grab your only misguided sense of
this and cling to it into a technical discussion that
uses the given technical definition --which in this
case, as already seen light in topology via the late
John Horton CONWAY and a method of analysis
he developed.

For me, it's simply shorthand for "entanglement"
--six characters shorter--, which denotes the
knot's structure devoid of any particular loading.
You might see it as much for what you mean by "core".
Alas, there is a can of worms in dealing with some
tangles and loading and ... wanting some more
boundaries to deal with shape/geometry changes
that should lead one to ask (or one loading of the
"same" tangle vs. another) "Is this the same tangle?!".
.:. very tough issue.

But I find it nonsense to presume/require that
intent be a determinant in "knot" :: that shoots
away most field research --finding Knots In The
Wild and being clueless (but for presumption!)
about any tyer (vs. nautural entanglement & loading)
and intention. (I have mis-tied knots into unintended ones.)

"working end" = "tail" No, it well might not --after it has well knotted!
Putting on a snood to a ground line might well entail working from
the tail-side outwards, and, well, one would be working (in one odd
sense of terms) with the standing part, per definition.
I've long sensed a problem using terms who stand in best
definition only during the tying, but have no real bearing
upon the tied knot. I want to refer to the tied knot, but
must admit then that my use of the terms is having
a finish already --for loading-- that isn't manifest at
tying time & term usage! (I.e., to be accurate, I'd need
to say "the to-become Tail is then ..." --not appealing.

"bitter end" was defined --not sure if first?-- in Ashley to be
the part of the rope ending at the bitts --and not some
sort of right-at-or-nigh the physical end of the material.
And I'd rather keep w/Ashley and see for the most part
"b.e." go away. There is anyway a challenge in precise
meaning of "end" --that last-of-it-all sense or the "over
in that part" sense (like "West End" of a city).

"crossing" Ack, topology hurts my head re this.
if I hold my arms up facing you and have each
one inclined so to make an "X" at you,
someone looking from our side might see no
"crossing" --say I'm not pressing arms together.
In knots, the same is true often enough : the
visual crossing is of parts that will NOT touch
--and by another perspective not cross, either.
(Consider the case of a capsized-form Carrick bend.)

"bight" is pretty sharply defined to mean opposite
things, so please do away with this as you've defined
it and use "U-fold" --which is precise & perspicuous.
The between-ends sense can be picked up with
"noue' sans extremites (NSE)" (vice "TIB"), or "endless".
Really, trying to work with a contradictorily defined
IN THE KNOTS FIELD term is a frustration well worth avoiding.

"Loop" should be e.g. the "central nipping loop" of the Bwl,
et cetera; eye is that extended U-fold from the knot,
legs crossing or not, who cares. The essence of "loop"
is surrounding, emphasis "round".
BEWARE of having things defined by behavior --that
might want then to see your eye change to a noose
and so on. (See a Bwl suppsed "fixed" loop(eye)
draw down around some machine anchor pin
in break testing! Is the Bwl not an eye knot,
maybe not a knot at all? !!)

Btw, I find the supposed lookalikeness of Reef/Granny
to be over done : properly dress & set, these knots well
enough differ visually --the former fitting nicely into
a planar state, the latter not. (Yes, there is an MIT article
making a big fuss of this, and humans' inability to assess
knot strength (which turns out mostly to be security).

"bend" ::Ashley and some others go overboard on this,
as historical names show --and VERBS : "bending" isn't
restricted to joining two ends; why then "bend"?!
IMO, use "JOINT".

"knot" in its narrow sense :: please, NO, no narrow sense
--this is our catch-all term; and the distinction given in
traditional knots books isn't all so natural/seemly.

"can be transformed into each other" :: hmm, there is
the case of having the same tangle, but this doesn't
allow transformation but for a re-shaping that keeps
the tangles ends out as ends; whereas e.,g. in transforming
a Bwl one might collapse the Returning & Outgoing eye
legs (thanks to Mark for these terms!) into the knot and
then getting dressed around.

OK, that's my quick take.
Again, THIS is just the sort of book/discussion NEEDED !

One more thing : webbing is much knotted, but it's
excluded from things "cordage" in current jargon;
well, it would be nice to broaden "cordage" to be
"knottable materials" --ha, and then face various
boundary cases ... !

Cheers,
--dl*

[agent_smith]

The following is presented for open debate on what constitutes a 'knot'.

Thought experiment:

If I submitted 'Exhibit A' to this forum, there would be no way to recognise it or to repeat it. I intentionally tied this random form - to represent a 'tangle' (or entanglement). There is no way to predict how this random entanglement will respond to load.

On the other hand, 'Exhibit B' can be recognised and repeated by others. It has an intentional geometric form and response to load can be tested and predicted. It could be submitted to this forum for identification.

EDIT NOTE:

With regard to the random tangle 'Exhibit A' - there is no way to describe the knot in any meaningful way. It is not possible to explain the tying sequence.
In contrast, it is possible to describe 'Exhibit B' - an explanation (or instructions) could be given to tie the knot.

[Dan_Lehman]

Exhibit A & B are both knots.

Ah, there's a nice start.
And from a knot one can abstract a tangle
--though Good Luck at doing so for knot-A !
(And also have fun counting its X-ings!!)

I can see intention in Knot-A. Consider yourself
a forensic knots examiner looking at this in some
case of a fallen rockclimber :: you would have to
believe that the massive entanglement Knot-A
was intentionally --i.e., not accidentally-- created,
as its formation requires (I think) a continual
reeving of a "working end" to build the mass
(perhaps with the purpose being to have a
large rope safety stopper/block to the abseil
device. (I was thinking of a Fig.8 device but
it has a pretty large opening, so maybe it
was guarded by a not-so-open 'biner to
catch this big stopper knot).
.:. You would see no way that such a tangle
could arise from some natural process,
from the fall or some shaking about prior
to it of a less-knotted tail. (Oh, I'm thinking
of abseil essentially of single, larger dia. rope
with a 6-7mm haul line joined to it, for full-length
abseil & then pull-down of the joined lines.)
I think that one might have reasonable confidence
in how such a big knot would behave, and
"Could it be repeated?"
even some repeatability with the general back'n'forth
reeving tying to make another like-performing
albeit probably not exactly the same knot.
(Hey, one can see various forms of the common
Fig.8 Eye knot per dressing & setting --not exactly same).

I will be thankful not to have to illustrate it
--though I did try to follow a path through Mark's
image ... , so far w/o success.

Knot-B is a lesser tangle to consider. One can see
that it arises from the same (enough) tangle that
yields --on a different load_profile-- the Butterfly,
a slightly asymmetric 2-tangle that thus has 8
Eye Knots, 4 End-2-end Joints, 4 structure hitches
(think "becket bend" : end-1 opposed to ends-B&A
with end-2 the Tail), 4 1-vs-3 spreads (out of names;
but round, plastic drum-top conch-pot bridles can be
A-B stoppered into pot, and 1-2 ties to mid-point of
A-B & 2 is stoppered into drum too (1 vs. 3 bridle legs)),
2 Net knots (an articulation I'm unsure of, but think
of 1-2 in W & N positions opposed by A-B in E & South
ones; then 1-2 in W&E, A-B N&S
--both orientations making a right-angle "+").

I'm still unsure how to deal with such a Tangle :
if one loads qua e2e Joint 1-v-A
. . . . ("through loading" of the Butterfly,
. . . . . aka "Straight Bend" per BToss),
the S.Parts pull holds their collars open;
but absent the load on 1 or A and say ring-loading
with B & 2, the collars collapse --possibly to capsize
into the original state but w/new ends as S.Parts !
So, how to see this as a single Tangle amonst
the geometric results of the various loadings
--of having obvious collars vs. collapsed ones!?

... hoping that there is a way to abstract a Tangle
from a submitted-to-TheKnotsRegistry knot so
that an image search can be done. (So, one would
want "front"/"back" & both hands ... which is a lot
but then computers are powerful.)

<sigh>

[agent_smith]

Dan,

If you carefully read my definition of what a 'knot' is, I have captured intentional and unintentional within the definition.

Thought experiment:-

Please consider the following questions:

1. Could I submit 'Exhibit A' to this forum for identification?

2. Could I submit 'Exhibit A' to this forum as a claim for a new knot? That is, could I claim 'Exhibit A' as a new knot?

3. Could a person reproduce 'Exhibit A' from a photo?

4. Could I write down a set of instructions for tying 'Exhibit A' (so a person could tie it from written instructions)?

...

Now contrast your answers with 'Exhibit B'.

Would your answers be different if the questions were intended for 'Exhibit B'?

...

Another thought experiment:

Imagine a 'Lehman8' eye knot.

Could I make the claim that a 'Lehman8' is a type of 'Bowline'?

Could I make the claim that I personally discovered it - and that I should receive credit for its discovery? Would my claim hold up to public scrutiny?

Does the 'Lehman8' possess a defined geometry that allows it to be recognised by others?

Could others tie a 'Lehman8' from a supplied photo template? (by studying the photo, could they reproduce a "Lehman8'?).

[dionzand]

First of all, thank you both, Mark and Dan, for taking the time to engage with this and for the very thoughtful comments! You both have far more experience with knots and knot theory than I do, and I find the discussion extremely useful for clarifying what I am actually trying to do with this book.

I think we may be using the word “knot” at two different levels, and I think it would help me to distinguish them explicitly in the book.

I look at it primarily as a “physical knot”: the physical configuration of a flexible body. I want to describe and analyse that object in terms of geometry, topology, material properties, contact, friction, loading, deformation, mechanics…

From that perspective, I don’t think intention, recognisability, reproducibility, naming, or usefulness should be part of the definition. A rope can accidentally assume a particular configuration, and that physical configuration exists and can be analysed regardless of whether anybody intended to create it, recognises it as a particular knot, or has a method for reproducing it. Agree?

I believe you two approach the “knot” more from a practical standpoint: the way we, as humans, identify and work with particular knot configurations. At that level, questions such as whether a configuration can be recognised, communicated, reproduced, given a name, tied by a particular method, or regarded as a variant of another knot become relevant.

I now think Mark’s A/B example is a very good illustration of this distinction. The questions it raises (whether the configurations can be identified, reproduced, described, or regarded as distinct knots) are important questions about our practical classification of knots. But I don’t think they need to become requirements for the physical configuration itself. Or do you see this differently?

This also resolves the question of intention for me. An accidentally formed configuration and an intentionally formed configuration are physically on exactly the same footing. Their origins may be relevant to how humans discover, name, or use them, but intention is not a physical property of the configuration.

So, at least for the purposes of my book, I am leaning towards something along these lines:

Physical knot: a physical configuration of a flexible body, describable through its geometry, topology, and physical/mechanical properties.

Practical knot: a human concept used to identify, classify, communicate, reproduce, name, and/or use particular physical knot configurations.

Only thing I am still struggling with is the load profile: is/should the (intended/unintended) load profile be part of the knot definition? My feeling is: no, it is not part of the physical knot, but it is part of a particular physical “state” of a knot. So there is a difference between a knot itself and a knot under load (configuration vs state). (But then again, as Dan points out, loading can change the configuration itself…)

Thanks again for your valuable feedback and ongoing useful discussion! I will work on it further and will let you know if I have a revision ready.

Best,

Dion

[Dan_Lehman]

@dionzand

I am leaning towards something along these lines:

Physical knot: a physical configuration of a flexible body, describable through its geometry, topology, and physical/mechanical properties.

Practical knot: a human concept used to identify, classify, communicate, reproduce, name, and/or use particular physical knot configurations.

But you really aren't looking at a physical anything,
but at an ideal abstracted from some physical thing
or --in our case, more likely-- thingS. Instantiated tokens
especially in a collection will enlighten one about the
ideal; but individual physical entities are going to be
shapes in some range of geometries.

.:. A knot is an ideal of entanglement of knottable material
that will endure tension to produce attachments of the
material ... [bailing out here, at the moment]

Only thing I am still struggling with is the load profile: is/should the (intended/unintended) load profile be part of the knot definition?

Though loading is implicit in one's classifying a knot
as a Joint, Hitch, Eye Knot, Net Knot, ... . --and then
comes awkwardness when loading of that knot changes;
or e.g. how to describe the Loading_Profile for a mid-line
Eye Knot --which might see in the course of actual use
a variety of profiles ("directional" such knots imply the
absence of one case, but have still EK, e2e, and both).

I want to describe and analyse that object in terms of geometry, topology,

I think that "topology", in some mathematical sense,
is problematic --too used to ignoring those aspects
of real/physical knots. (If a topological examination
wants a "closed curve", how does one close a Tail-Inside
(#1010) Bwl? --one way yields amphicheirality, the other not.

--dl*
====

[Dan_Lehman]

[9/28 edit re one question --oops]

The answers re both sets of quetions --or one set
as asked of each knot-- are from me "yes".
EXCEPT for

Could I make the claim that a 'Lehman8' is a type of 'Bowline'?

to which I say "no" --not a nipping loop.
[END EDIT]
I will (again?) note that there are ample cases of known
knots that aren't recognized. It is somewhat comical
that among my list of "Indiscernible Images in EKFRW
("Hensel & Gretel") are several in which the book gives
"... can be tied easily following the picture" (or the like) !!
--things that even I, well-practised in knot discernment,
cannot figure out (and from photos --which don't lie )

Claims of discovery/invention can be made however.
And as I've said previously, were a child of say 4 to
be given some play rope and she tied several known
knots, we'd consider that quite an achievement
--much more so than if Alan-Dan-X-yChan comes
up with their N^^2 th discovery!
And re origin, well, the Lineman's Loop seems to fit
the case where a later-dated discovery (1928, Alpine
Journal, Wright & Magowan) is rightly recognized as
the origin of that knot to modern knowledge in at
least some considerable reach, though AA Berger's
1915(?) presentation of the knot precedes it --maybe
few paid much attention and it went nowhere?!
Well, no, it went to H&G, Ashley, Day. But, still,
it seems right to note two points of origin;
and less important to hand out a prize.

yChan has a gazillion e2e Joints, presented or noted here:
how many have seen other hands tie & try them?

--dl*
====

[agent_smith]

Can a 'knot' exist absent a human mind?

In quantum mechanics, some argue that a human mind is a requirement for an event to manifest itself in what we call reality - ie a particle that is detected by equipment. Prior to detection, some argue that there is no particle - its just a probability that spreads out. When we turn our detectors on, and contact is made with the detector - we see the particle as an event within out spacetime reality.

So what is a 'knot'.

My previous random tangle 'A' is a 'knot' - few would argue that.

And exhibit 'B' is also a 'knot' - few would argue that.

What do they have in common?

1. They are both formed from flexible material (rope/cord).

2. They are both formed into a structure - the original material is no longer a straight line - the material is intertwined to occupy a physical volume.

As an abstract concept - we can define a knot as follows:

"An intertwined structure formed from flexible material to occupy a physical volume or space."

I don't find this definition meaningful or satisfying - but it is accurate.

For me, its like describing a wave or a particle in quantum mechanics.

Is light a wave, a particle, or a probabilistic manifestation of hidden reality?

What we see as reality is simply the outcome of a transaction by an 'absorber' (the detector... which can be human eye receptor cells, or a detector screen).

As humans, we need to find meaning in things.

...

To Dion,

I have to be very careful with my typed words because there are some who believe words can cause harm - and can be interpreted as 'hate speech'. Mere disagreement can be conceptualised as a form of hate speech. It is a manifestation of what is happening in the 'West'.

I am saying that I largely disagree with your conceptualisations. It is risky for me to say that I disagree with you.

Since you are intending to write your own book - you will exercise your own free will and your book will reflect your personal preference. If you publish my or Dan's conceptualisations, then its our preferences, not your own.

All book authors want to express their personal preference.

I have been on a 'journey' for well over a decade - trying to make sense of knots and knotting. Most knotting terms and concepts have epistemological foundations from ancient sailors and age of maritime exploration. Many terms that you see in knot books have not been accurately defined - because it was assumed by the author.

Terms such as 'bend', 'loop', 'turn', 'bight', 'elbow', have ambiguity because the various authors did not require a strict definition to write their books - it was assumed knowledge.

When I started writing technical papers on knots (eg 'Analysis of Bowlines') - I found that I had to define concepts that had not existed in mainstream consciousness.

I can now define what a 'loop' is, and what a 'twist' is (a twist being what some prefer to call an 'elbow').

For example, to tie a 'Butterfly' knot - one tying method is to form a 'twist' - which can be a Z twist, or an S twist. And so a Butterfly knot has chirality.

To Dan:

I don't believe that you can describe knot 'A' in any meaningful way. I also don't believe that you could submit it to this forum for identification.

[Dan_Lehman]

@agent_smith

So what is a 'knot'.

My previous random tangle 'A' is a 'knot' - few would argue that.

And exhibit 'B' is also a 'knot' - few would argue that.

?! I believe the natural reading of "few would argue that"
means "most will NOT argue that" or "few ... argue WITHat".
To which point we note that previously you argued against
the claim of "knot" for Knot-A.

[SS369]

Good day Dion. I must say that I am impressed with your shared document! I have read through it and have not found any glaring mistakes. But, it does deserve rereading. Will you be adding pictures? Thank you for sharing and asking for the review.

[agent_smith]

@Dan_Lehman

To which point we note that previously you argued against
the claim of "knot" for Knot-A.

No - Knot 'A' and 'B' are both knots... few would argue that

That is, the random tangle that is 'A' - is by definition - a 'knot'. I never - even for a picosecond - doubted that 'A' is a 'knot' !

To Scott:

Yep - photos/images are essential - being necessary to convey complex ideas and concepts. Particularly to illustrate the concepts of; chirality, what a 'loop' is, what an 'eye' is, and what a 'turn' is.

To Dion:

I doubt that you'll ever reach unanimous agreement about the definitions of knots and knotting concepts. Be that as it may, this fact should not stop you!

I personally thrive on challenges - and if you're like me in that regard, it will fuel and drive your engines...

[dionzand]

@SS369 Thank you for your kind words! Yes, I am planning on taking and adding pictures and diagrams. As Mark said, they are essential for explaining complex concepts. This will likely take a while, so I ask for your patience on an updates version

To Mark, yes, I find the discussion incredibly interesting and useful! I am trying to take all nuances into account when updating my manuscript, and indicate where there exist different viewpoints/interpretations. I will have to work with a definition that works in the context and framework that I want to use it in.

Thanks again, and will keep you posted on any updates!

ps. Mark, if you have any tips for taking high quality pictures of knots, would love to hear. Your images are always great.

[dionzand]

Haha, everytime I think I am a step closer to a good "working definition" of a knot, I find a way to immediately knock it down. Here my thought process:

My first definition of a "functional knot" compared to a "snarl" was based on reproducibility. But this was shaky, because a snarl can be reproduced just as well. Next, I thought the difference had to be in purposefulness: a snarl is random, unintentional, without purpose; a functional knot is intentional and purposeful. Both are "knots" in the loose sense, but with a hierarchy: "all snarls are knots, but not all knots are snarls."

But that also does not hold: a rope that randomly knots itself into a working bowline has to be classified as a snarl using this definition.

So then I thought: maybe "snarl" and "functional knot" answer different questions (sit on different axis): origin (how did this come to exist) and capability (what can this structure do). Occasionally a random tangle lands in a reproducibly structure, and when that happens, both labels apply at once.

But then I immediatly found a case that broke this compromise again: someone sets out to tie one knot, errs, and ties a different one that still works - intentional (they were trying to tie something) but the outcome was unintended. So intent does not distinguish a snarl from a functional knot: an intentional, purposeful attempt can still collapse into a structureless snarl, and an unintentional accident can still produce a functional knot.

There are four combinations:

1. Intentional, and hits the target = functional knot (already established)
2. Intentional, misses the target but lands on a different, still-reproducible structure = nobody would call this a snarl. You'd say
   "oh, that's actually a [different knot]," not "that's a mess." It's a functional knot, purpose and all, just not the one that was meant.
3. Intentional, but the attempt genuinely falls apart into a structureless tangle; someone fumbling a knot and getting nothing but a mess.
   Everyone calls this a snarl too, despite full intent being present the entire time.
4. Unintentional, but happens to land on a reproducible structure = a functional knot.

At this point I might just use the dictionary definition of knot: "an interlacement of the parts of one or more flexible bodies forming a lump or knob", and leave reproducibility, intent, purpose, function, recognizability, etc out of it (or rephrase it as a more philosophical discussion).

Best,

Dion

[KC1]

TY for your dedication, passion and energy on this huge undertaking! I have dove into your fine works deeply but not totally to now offer own view.

My view, facet of understanding to the same central jewel/cosmos we all look at, is that it is bound by the same rules as all other rigidities(in it's working form). For to me slack rope is as if it is in it's molten form in plastic or metal etc. terminology. Whereby only when has 'tensioned rigidity' has if/then logic of being able to rigidly displace against a Load. Just as a circuitry can only display a working logic when loaded with electrical force. This i believe parallels the magnificent ship's heritage view of loading only but rope(molten form) onto a great ship, that became a line in actual usage. This extends to another factor/view i hold that this and all mechanics are about Dimensionality. Whereby in yin:yang as non's of each other , has 2 extreme opposing states of IS:IS NOT of in the SAME Dimension as Force OR NOT. The shifting gray region between defined by cos:sin ratio of values. This is shown best in the simpler linear functionalities of a single S.Part(Standing Part as a Lehman-ism) form of Hitch or opposing S.Parts form of Bend.

For there is only a finite amount of Force fed into the system from the input, that then is parted out inside the system. But another factor input is the Direction of the input, that then inherently carries Dimensionality.

In the simpler form of linear rope parts, where the input and outputs of the rope part are in opposing Directions, only the parts in SAME Dimension as input can work against the Load. Other parts cannot and are simply byproducts, but are usable byproducts to power frictions, nips and grips. Non-linear parts are more evolved and can work against the Load as also provide the functions of what are byproducts in the linear form verbiage. Premium example being a 180arc that can use BOTH cos+sine forces at once for fictions, nips, grips etc.

I break all working/loaded knot forms into but 3 components: linear(even if not purely), and 90/180 arc forms. An RT(Round Turn as yet another Lehman-ism ) then is but 3x arc 180s. arc180 in this model is the most evolved rope form as a simple component. I say arc0,90,180 are the component names, with arc0 being the non of arc. Just as arc90 is the non of input/outputs being in the SAME Dimension. These are basics and not always pure forms. I remove first the highest evolved arc180 components, then the arc90s. Thus remaining are the non's of arc, arc0s. Even if some impure deformity from pure linear such as commonly seen in S.Parts on round host. The key factor is that the endpoints of input/outputs are tensioned in opposing directions. For me Dimensionality reigns thru all these things.

Decoding Half Hitch vs. Anchor Hitch by this model:

Peace and roping knowledge to all !

[Dan_Lehman]

@dionzand

At this point I might just use the dictionary definition of knot: "an interlacement of the parts of one or more flexible bodies forming a lump or knob", and leave reproducibility, intent, purpose, function, recognizability, etc out of it (or rephrase it as a more philosophical discussion).

One still needs to use both the ideal & ideal-manifested senses
of "knot". E.g., you might put a child into a summer camp where
students will be instructed on the tying & use of a dozen "knots"
(oh, the usual suspects). Then consider a test where children
are to look around a room and count how many knots there
are. With one sense in mind, instructors might have in mind
the answer "7", but some count only "4" --and explain their
count as "3 bowlines, 2 clove hitches, and overhand in the
middle of a line, and a sheet bend (=4 knot ideals in tokens).

The above dictionary definition I think doesn't accommodate
hitches & binders which incorporate an object.

--dl*
====

[agent_smith]

@Dan_Lehman

With one sense in mind, instructors might have in mind
the answer "7", but some count only "4" --and explain their
count as "3 bowlines, 2 clove hitches, and overhand in the
middle of a line, and a sheet bend (=5 knot ideals in tokens).

This requires a human mind - in order to be able to recognise thing 'XYZ'. A human can recognise geometric patterns, and assign a name to thing 'XYZ'.

Absent a human mind - thing 'XYZ' still exists - but there is no language to assign names, or to recognise geometric patterns, or to assign a category.

And so absent a human mind, thing 'XYZ' is fundamentally an intertwining of flexible material that occupies a physical space or volume.

Add a human mind, and thing 'XYZ' can now be recognised, classified into a category, and documented, so others may repeat it.

The presence of a human enables thing 'XYZ' to be intentionally tied with a practical purpose in mind, or to exist as an artistic expression.