Minimum number of known practical knots

General Discussion
1

The Ashley Book of Knots has more than 3000 knots, and I assume they all have practical uses. But since knot uses overlap than maybe if you already know a subset of all known practical knots, then learning the other known practical knots will not give better results for any use cases. If so how large is this subset ? I don’t expect exact numbers so estimates are fine.

2

Hello roobee,

The Ashley Book of Knots has more than 3000 knots, and I assume they all have [b]practical [/b]uses.
Depends on your definition of 'practical'. Ashley Book of Knots (ABoK) also includes a significant number of decorative knots. One could advance an argument that decorative knots have a 'practical' application - one of which is art and another is to generate an income from the purchase of such knots by customers. Art has therapeutic value - which can lead to healing and personal growth (which has practical value).

Decorative knots can also have mathematical and geometric applications.

In the ordinary interpretation of the word ‘practical’ - it likely means doing or use of something (eg a joining knot to tow something, yet does not jam). Or for ropes sports (such as climbing) - there are several knots that are commonly used.

ABoK isn’t the only source of knots…

But since knot uses overlap than maybe if you already know a subset of all known practical knots, then learning the other known practical knots will not give better results for any use cases. If so how large is this subset ? I don't expect exact numbers so estimates are fine.
I'mm comment that no one knows a 'subset' of all known [i]practical [/i]knots. I think this question will likely never have a definitive answer. For example, people are still finding new ways to do things.

The average Joe likely knows only a small number of knots.
The regular contributors to this IGKT forum are a special case - because knots is their hobby and/or passion.
Sailors of non-motorised vessels are a class of users that likely know more ‘practical’ knots than the average person.

May I ask the reason for your question?
Is there a particular fundamental truth or idea you are pursuing or trying to evolve?

3

Hi. I realized that there is no good theoretical model of knots, aside from maybe one about hitches. There’s knot theory but that doesn’t talk much about practicalities of knots. So I wanted to learn about the field, to see what centuries of empirical work was able to accomplish that scientists and mathematicians couldn’t. I figured the number of knots could give a good idea of how far advanced the field is, and was surprised at the overwhelmingly large amount of knots in ABoK. Then I became curious whether all those knots are really necessary, or whether a small subset of them would work just as well for all use cases. I’m more interested in practical knots which is why I ignore decorational knots. Also without the practical constraint I imagine a computer could just iterate possible knot configurations long enough to discover all known knots, and discover a few new ones in the process. Which wouldn’t be an example where empirical knowledge beats modern mathematics/brute forcing.

4
I realized that there is no good theoretical model of knots
Hmmm, there are theoretical models of knots... but work appears to be advanced in isolation. That is, theories and papers dont appear to be a collaborative effort between different groups.
and was surprised at the overwhelmingly large amount of knots in ABoK. Then I became curious whether all those knots are really necessary
ABoK isn't the only source of knots. This IGKT forum is an example of another source. [b]Xarax [/b]is a prolific knot tyer and innovator - he has discovered a huge array of 'new' knots. If you want to even more [i]overwhelmed [/i]- have a read of yChan's paper!

Why are so many knots “necessary”?
Indeed, we could ask; Why are so many different cars (automobiles) necessary?
Or, why are so many different types of aircraft or boats necessary?
Humans are creative by nature - its part of our DNA. We like to improve and control our environment - so we build/make things.
Knots help us to control things that we make.
For example, knots help sailors control their ocean going vessels.
Knots help mountaineers climb mountains.
And my favorite class of users - Arborists. They like to think that they invented an entire suite of slide and grip hitches…the need being to improve their tree work.
Different classes of humans and users had different needs…and knots were invented to fulfill a need - which improved or made their lives easier.
And so on…

I imagine a computer could just iterate possible knot configurations long enough to discover all known knots, and discover a few new ones in the process.
Computers lack the things that makes us human... imagination and inspiration. Humans have imagination and ideas...a computer has to be programmed by a human. The computer simply follows a set of pre-defined instructions. [b]Xarax [/b]would be able to weigh-in with how humans conceptualize and invent new knots.

I suggest you read ‘The History and Science of Knots’ - it might help shed some useful background on knots.
Link: https://www.worldscientific.com/worldscibooks/10.1142/2940

Here are some more links: (some of these sources are quite interesting)
https://www.researchgate.net/publication/2136300_History_of_Knot_Theory
https://www.dc.fi.udc.es/ai/~cabalar/knots19.pdf
http://www.marindustrial.com.au/documents/knots%20splices%20and%20rope%20work.pdf
http://ceur-ws.org/Vol-1007/invited1.pdf

EDIT: Added this link (surgical knots): The field of medicine has created the need for practical applications of knots…
http://www.uphs.upenn.edu/surgery/education/facilities/measey/Knot_Tying_Manual.pdf

5

.
And what is the hitch theory please?
.
i think working knots are as a pulley set; the power and magic are in the 180 arcs that both ends pull in same direction, not the nonArcs who’s ends pull in opposing directions, and are just extensions to the arcs.
A hitch to me is a clean linear rope part/nonArc called Standing Part, feeding force into a nodeDeformity of controlling arcs ; and the nodeDeformity forms a termination of that forceLine. Bend is same, only a continuance of the interrupted force line. Whether the controlling arcs are hosted on nonRope parts (as typical in hitches) or hosted on ropeParts (bends) is not of consequence to this view. So between the 2 cover all linear force to radial control, terminating or not.
Thus, a Hitch definition to me would explain Bends as well, as simply double ended hitch to each other.
Working Hitches and Bends are mechanic in rope, ruled by cosine and its non of sine.
Arcs can capitalize on the cosine and sine together to control more so than the nonArc extensions.

Rope is a material, that we keep trying to innovate in; just as metal, wood or even rock etc. How much is real innovation, and how much is fluff around i think is real question. And good to seek pivotal works, clean of fluff. Free form empirical work as turtle can outrun scientific focus rabbit many times, and should be respected so. Plant medicinal usage is fave example of following senses rather than instruments to sometimes surprising innovations and understandings.

6

?? Really? Why do you assert this?
Do you have this book?

... and I assume they all have practical uses.
No.
if you already know a subset of all known practical knots, then learning the other known practical knots will not give better results for any use cases. If so how large is this subset ? I don't expect exact numbers so estimates are fine.
Really, it's better made less about some supposed quantity than the *quality* of knots (i.e., knowledge of their workings) and with that knowledge one can adapt known structures to fit one's needs.

To the top assertion, it’s pure BS. Here’s a bit on that
from a recent KM (Knotting Matters, IGKT’s 1/4ly publication) ::

Why are the facts about knots in such a confused state? Des Pawson's article "A History of Knot Tying Works" (km138:22-30) exposes a dubious history of our the western, supposed knotting record. Just consider what is regarded as "the knot tyer's bible", [u][i]Ashley's Book of Knots[/i][/u]. Des's article shows many different covers for this major knots work, each of which carries some variation --why the variety?-- of the publishers' nonsense claim about the book having "Uber 3,800 Knotten," "3.900 nudos," "3800 noueds," "over 3900 knots", ... or maybe exactly "3854 Nodi"!?? (Perhaps these are only valid numbers at the current international exchange rates for knots? :o) These are all simplistic exaggerations based on Ashley's image #s, which reach that exact "3,854". Anyone concerned with accuracy should quickly see that many #'d images are not of knots, and many knots have multiple image #s. The actual number is more nearly a third, and well less if practical knotting is wanted.

(One might hope that the world’s most authoritative body on knotting
would have an answer; some of us have made private estimates.)

–dl*