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.

Comments

Unintended consequences

[Calydor]

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.

Not much practical use, yet.

[kooky45]

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.

Re:Not much practical use, yet.

[hawkinspeter]

Knots may be far more interesting and useful than just their use with ropes. There was an unexpected connection discovered between knot theory and Burnside groups: http://www.ncbi.nlm.nih.gov/pubmed/15576510/

By having a deeper understanding of knot, we may get a better handle on aspects of group theory which has very close connections to quantum mechanics and string theories. So, whilst you may argue about whether that can be considered "practical", it may lead to a deeper understanding of the matter that we're made of.

Re:Actually, they didn't learn anything new.

[Anonymous Coward]

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).

Correlation with other types of bonds in nature.

[deviated_prevert]

If we define a knot as being a configuration which simply joins strings together at a position is space then the problem of how things work and in what sequence becomes more clear. For instance if you can visualize a blood knot or a spider hitch or bimini twist in your mind then you can see the points at which the friction occurs and how the knot is lock stopped and how it works. For an experience fisherman this can become fairly easy but only with practice, for someone who never ties complex knots or conceives of how they might fail this is a very difficult task.

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.

What is a Knot?

[TapeCutter]

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