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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.
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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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.
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.
Scientific knowledge proceeds from the particular to the general. Empirical data is important, but having a general theoy with predictive power even moreso. So no, what these researchers are doing is definitely a novelty. The work goes way beyond just cataloging the different kinds of knots (and their mechanical properties).
.. 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.
Oh wait, he said *knots*
It is well understood in math, because it is not physics or engineering, but knot theory is a mathematically field.. Seriously.
Topological knots are closed and not generally useful for understanding characteristics of physical knots. For one thing, it's impossible even to talk about the strength of a closed knot because there are no ends to pull on. This work is mathematical modeling of physical, open, knots and their useful characteristics.
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I learned, at age 47, I'd been tying my shoelaces wrong, so I'm amazed at what we can find out in mundane things like studying knots.
In case anyone cares - I learned if the starter knot goes left over right, the finishing part needs to go right over left. If you do left over right again, it's not strong and comes untied. As soon as I learned this and switched, I never had a shoelace come undone.
Stupid sexy Flanders.
Did you really use Velcro or just some cheap hook and look fastener?
Sleep your way to a whiter smile...date a dentist!
Did you really use Velcro or just some cheap hook and look fastener?
<hangs head sheepishly> ... cheap hook and fastener...
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