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MIT Physicists Have Finally Cracked Overhand Knots
An anonymous reader writes: Knots are indeed a relatively ancient art, a technology developed across centuries of trial and error and some very old, intuitive notions of symmetry and elegance. (The more 'ugly' or random a knot looks, the less likely it is to function well.) The basic physics and mechanics of knots are, however, relatively unstudied scientifically. If a knot works then it works—what more is there to ask? Quite a bit, it turns out. In a study recently accepted for publication in the Physical Review Letters, engineers at MIT and Pierre et Marie Curie University in Paris offer a new fundamental theory of knots based on relationships between topology, the mathematics of spatial relationships, and the basic mechanics of friction and pliability.
now they can tie their own damn shoelaces!
And to think this research project started when a college undergrad typed, "How to get married" into Google and learned that he had to tie the knot.
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He could equally be stupid.
It was certainly on university courses 20 years ago, because I knew someone who took it.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Note that this does not concern the mathematical term "Knot", which means something entirely different.
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They've studied how much force it takes to tighten a very simple overhand knot with various numbers of turns and developed mathematical theory that is good at predictions. Whilst it's interesting, most knot use is probably more interested in the opposite case of how much force is necessary to untie a knot, or how much force a knotted rope can withstand, or which knot configurations are comparable in strength. That'll take a much bigger leap in research but this is a good start.
are you joking or just ignorant?
Probably the latter - this is one of the usual, vapid glossies that are too often posted here as 'relevant'; they always contain a sensationalised write-up of something well-known, if not trivial, with loads of enormous illustrations and smalltalk-like text. They are sort of the homoeopathic version of science articles: diluted in the extreme, but believed to be much more powerful than the real thing.
There is one, small grain of interesting news, that somehow snuck in, presumably by mistake: physicists may now have made some progress towards combining topological knot-theory and friction to characterise physical properties of physical knots; I'm guessing this from the subject line, as I couldn't bear reading through the article. I'm sure this wasn't supposed to happen - they will have to amend it by adding at least 10GB of inconsequential chit-chat.
>If a knot works then it works—what more is there to ask? Quite a bit, it turns out.
People -have- collected empirical data on many knot types with many different materials, compared relative knot strengths, susceptibility to jamming, ease of untying, seaworthiness, suitability for climbing/rescue/lashing/towing/packaging, etc. Why know why certain knots are weaker than others (e.g. sharp bends).
It's not as if people don't study this stuff.
I was just talking to the wife about how I learned knotting and how to use knots to pull two threads together with minimal effort (the simple start-from-the-middle-and-work-towards-the-ends method) as I was tying a cabin case onto a flatbed bike truck (don't ask). Basically I learned by trial and error, where threads had to go for the best knot for a given situation. Now I can tie just about any knot you show me a photo of, but I'm buggered if I could actually *name* many.
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The researches just couldn't be arsed to look up The Ashley Book of Knots. I used to teach Abseiling, and we had to know the strengths and attributes of various knots.
.. but I'm a bit tied up at the moment.
It will be really interesting to see the mathematical advances that come from the study of more complex knots. It is altogether possible that new algorithms that will apply to other disciplines will emerge from the study being undertaken. We might even discover insights into the knotting of proteins and other chains that produce strings that knot. What works at the microscopic scale down to the molecular level will work completely differently on the larger scale and that difference should be something that can be quantified. Knots are a fascinating study and even the primitive human was fascinated by them, they were one of the first essential skills that the human race developed. Without the study of knots we would not have clothing is the first thing that comes to my mind. Who knows where the study of knots on a mathematical level can lead us.
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It was certainly on university courses 20 years ago
Mine too (circa 1990), but the summary is correct. 20yrs is a long time, the detail you have forgotten is that mathematical knots do not have loose ends and are typically useless in the real world. TFA is talking about the mechanical properties of open knots, these are knots with loose ends, the useful kind found on shoelaces, climbing ropes, fishing hooks, sailing ships, flat-bed trucks, etc. Of course I haven't RTFA but I'm tempted because at first glance it appears they have used the same branch of math that studies closed knots (topology) to describe the mechanical properties of open knots
What is a Knot? - Numberphile
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
It is well understood in math, because it is not physics or engineering, but knot theory is a mathematically field.. Seriously.
Oh wait, he said *knots*
For instance if you can visualize a blood knot [animatedknots.com]or a spider hitch or bimini twist [netknots.com]i
Woah, someone in those links is already using Live Photos. Wild!
"First they came for the slanderers and i said nothing."
Whilst it's interesting, most knot use is probably more interested in the opposite case of how much force is necessary to untie a knot, or how much force a knotted rope can withstand, or which knot configurations are comparable in strength.
I use knots for rock climbing a combination of strength + ease to untie + safety are important to me. The annoying thing with a figure of eight (the standard climbing knot for attaching a rope to a harness) is that it can be quite hard to untie after falling on it. If you do any sports climbing - and push your limit, you will do lots of falling, so i use bowline.
The issue with a bowline is it can be unsafe if not tied correctly and with some extra redundancy, even then some people still consider it too dangerous given it's bad history of climbing related deaths. Safety and over tightening might seem inevitable but i'm interested if it's possible to find a better knot with both of these properties with a more scientific method - perhaps this is a good start toward those kind of useful discoveries.
1 knot = 1.852 km/hr
Have gnu, will travel.
There seem to be very few combinations that meet all three criteria. I wonder if these folks can take their theories and let their computers search for some new, good combinations.
More likely what they'll find is that the well known and simple knots in use are optimal - bowline, cleat hitch, square knot, and clove hitch meet all of the criteria quite well, and cover most needs.
Even more importantly, maybe they'll discover why headphone cables get so tangled up, and learn how to design new tangle-resistant headphones.
Another fisherman put it best. There are basically two types of knots. Stop knots, where loops press up against each other to prevent slippage. These always break at less than the line's breaking strength due to the stresses at the sharp angles in and around the loops. The blood knot is a stop knot.
And friction knots - like a Chinese finger trap where increased friction from tension in the line keeps the knot from slipping. These usually have higher breaking strength than the line. The Bimini twist is a friction knot. Probably the best example of a pure friction "knot" is when you splice hollow braid. There is no knot per se. The friction of the weave in the hollow braid against the line inside it holds everything in place - exactly like a Chinese finger trap.
I think mathematicians and topologists are only interested in the first kind of knot, whereas the second kind is actually functionally superior especially when connecting lines of different diameter. All the best braid to mono knots are friction knots using multiple wraps to create the friction.
I see they tied themselves in knots over this.
turns out i've been tying my pretzels all wrong, that's why they all turn into crullers.
Star Trek transporters are just 3d printers.
Yet another waste of time and money. Seriously - study knots. Only idiots who could never tie a know would study the physics of them.
and don't get me started on those idiots who try to study the movement of heavenly bodies. Obviously, they travel as God wants them to. Duh.
Star Trek transporters are just 3d printers.
Note that this does not concern the mathematical term "Knot", which means something entirely different.
And I'm guessing it has no relation to String Theory either?
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