131–139 of 139 posts
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What do you mean? Knot theory is a field.
knot theory is abstract- I care more about the material sciences aspect.
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Knot theory https://en.wikipedia.org/wiki/Knot_theory
I meant more like how to actually tie a knot, not just topologies.
How to actually tie knots -- in a practical sense -- would be knotcraft [1] -- not sure what kind of math that would entail? What kind of connection did have in mind between that and the math of knots and programming? (in your original statement)
If it's a mathematical treatment of the strength of knots (physics), I believe that's what the article is about, which is quite interesting.
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Sure, those might be the numbers in your use cases, with your materials, but I'd be very careful about claiming those numbers if the situation is changed even slightly. 1. Change in strength is dependent on the cord material and weave. Stiffer cord will lose more strength when tied, while more supple cord will maintain its strength better. The tradeoff is that supple cord is more susceptible to tangling. Citing one n…
> We aren't typically just tying an overhand or figure 8 midline in a knot and pulling on the ends--I can't think of ANY place where that's useful. The closest thing I can think of is a stopper knot, and neither of these knots is ideal for that application. I'll admit that I've mostly used this "useless knot" test methodology you're criticizing here. But in its defense, it is an easy to do micro-benchmark with consis…
That's fair, and it does prove that different knots affect strength differently. That's a base principle that is useful to know even if it doesn't get you far on its own.
With regards to your application: while it lacks the "finesse" of tying knots that give you just enough strength, simply getting stronger twine would solve this problem without the complexity.
In general, there's a whole lot of ways knots can fail. If you can solve the problem by just using stronger cord, that frees up mental cycles for dressing, avoiding slippage, effective communication, ease of untying, etc. If you're just tying up boxes do whatever you feel like doing. But for climbing, I'd rather have the rope be more than strong enough to do its job, and have those brain cycles for focusing on preventing other system failures.
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I meant more like how to actually tie a knot, not just topologies.
So... the math of knots is... knot theory, and you're correct that it is topology. How to actually tie knots -- in a practical sense -- would be knotcraft [1] -- not sure what kind of math that would entail? What kind of connection did have in mind between that and the math of knots and programming? (in your original statement) If it's a mathematical treatment of the strength of knots (physics), I believe that's what…
Something where I have some sort of representation of the physical knot that is much less than just a drawing of the knot, but more than just saying 'this is a reef knot'. Something you can do operations on.
Say you are trying to tie a reef knot. You can tie a reef knot many ways. Say you want to write down how to tie it one way.
So you take 2 strings. Say you represent that by the number 2.
Then you have to twist them together, so you write down something like 2T.
Then you have to pull a bite on each of the 2 strings string. So you write down 2T + 2B.
Then you have to retwist them, but the opposite way. So you write down something like 2T + 2B + 2(-T). Then you have a reef knot.
But the thing is that since there are a LOT of ways to tie a reef knot, that 'formula' should be able to be manipulated to produce the other 'formulas' that also produce a reef knot. Also, a reminder, this 'formula' thingy I just made up should not be taken as any sort of gospel.
We all know that when you pull hard on some knots, that they just decompose into a simpler knot. So this representation of knots should be able to be worked though on paper and give the right result. Or with slip knots and hitches, knots that are designed to decompose into just a string when you pull hard on them or something. So when you take the knot tying 'formula' and then work through it, it just returns a string.
I think you could then apply the physics to these 'formulae', like, each twist you do reduces the rope strength by X% and increased friction by Y%.
Some sort of thing like that is what I am thinking, I guess.
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> We aren't typically just tying an overhand or figure 8 midline in a knot and pulling on the ends--I can't think of ANY place where that's useful. The closest thing I can think of is a stopper knot, and neither of these knots is ideal for that application. I'll admit that I've mostly used this "useless knot" test methodology you're criticizing here. But in its defense, it is an easy to do micro-benchmark with consis…
> I'll admit that I've mostly used this "useless knot" test methodology you're criticizing here. But in its defense, it is an easy to do micro-benchmark with consistent results. That's fair, and it does prove that different knots affect strength differently. That's a base principle that is useful to know even if it doesn't get you far on its own. With regards to your application: while it lacks the "finesse" of tying…
That's why I asked.
For standard knots the Klutz book of knots is really excellent! https://www.amazon.com/Klutz-Book-Knots-John-Cassidy/dp/0932... The article doesn't mention fishing knots; in case anyone's curious anglers care a lot about knot strength but strength changes based on whether you lubricated the knot when tying and what kind of line you used to tie it (braid vs smooth fluorocarbon for example). My favorite fishing knot is…
Indeed. Fishing knot strength is always a hot topic of debate, particularly during the slower, off-season winter months when everyone's hunkering down and doing tackle maintenance. Here's a pretty good breakdown of the line breaking strength of various fishing knots across monofilament, fluorocarbon, and braided line: https://www.knotsforfishing.com/knot-strength-chart/ I personally prefer the Palomar Knot as it is p…
I find it surprising how many people use clinch knots vs the uni in real life. It's certainly easier to tie clinch knots but I've never found the ease worth it, since the uni is so much stronger and can be used for more things. Once I got fast at uni the clinch knots went out the window.
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Been using bowlines for safety(fire dept) and sailing 35yrs. Never ever ever seen a proper bowline "shake loose". Can tie it weakside one-handed, upside down, behind my back, in the dark, underwater, while brushing my teeth.
You use a bowline for life-safety in rescue operations? That's really unusual, in my experience (firefighter/rescue tech in upstate New York)
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Been using bowlines for safety(fire dept) and sailing 35yrs. Never ever ever seen a proper bowline "shake loose". Can tie it weakside one-handed, upside down, behind my back, in the dark, underwater, while brushing my teeth.
It's the "proper" part that's the problem. Even the Yosemite finish is problematic. Google for "deaths from climbing with bowline" and you'll find lots of veteran climbers who have died or been seriously injured from their bowline coming undone, either because they did it messily and it capsized, or they screwed it up and didn't realize it until they took a fall.