“A Knotty Problem Solved” on NPR

This brief, interesting feature appeared on npr.org today. It looks at knots, although it doesn’t go into depth or analyze strengths of specific knots.

"Twist is quite important in how knots behave," says Patil, who explains that having lots of twists going in opposite directions along the knot can kind of lock it. "But if lots of twists are going in the same direction, then the whole thing can roll out."

The basic example of this was a comparison of two very similar but different knots:  the granny knot and the reef knot (a.k.a. square knot).

I haven't delved further than the NPR paper, but the analysis they describe, if accurate, is about knots slipping under load (like the granny).  Knots have other failure modes too.  For example, bowlines that don't incorporate some kind of backup or locking structure are subject to loosening under intermittent loading, the EDK rolls or capsizes, and the question of slipping is different from the question of breaking.

Knot science, for lack of another term, surfaced in the study of... just how do chromosomes pack so much material into such a small space? Galletas! 

https://academic.oup.com/nar/article/46/W1/W17/5037726

A perfect allegory 

"He notes that inventing knots seems to be a uniquely human activity and that such **complicated knots don't appear in nature.** WHAT?! Maybe he's a creationist :)  

See this MIT news article for more info, including some cool photos of rope strands that change color under stress.

I'd be curious to see individual knot data that comes out of the study, sounds like it will be different that eg pull tests.

In comparing the diagrams of knots of various strengths, the researchers were able to identify general “counting rules,” or characteristics that determine a knot’s stability. Basically, a knot is stronger if it has more strand crossings, as well as more “twist fluctuations” — changes in the direction of rotation from one strand segment to another.
For instance, if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot. If, however, the segment is rotated in the same direction at two neighboring crossing, there is no twist fluctuation, and the strand is more likely to rotate and slip, producing a weaker knot.
They also found that a knot can be made stronger if it has more “circulations,” which they define as a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow.
By taking into account these simple counting rules, the team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has a higher number of twist fluctuations, making it a more stable configuration. Likewise, the zeppelin knot, because of its slightly higher circulations and twist fluctuations, is stronger, though possibly harder to untie, than the Alpine butterfly — a knot that is commonly used in climbing. 

Cue the perp' Mark Gompers in 3, 2, 1

Aidan Raviv wrote: Cue the perp' Mark Gompers in 3, 2, 1

I doubt it, they call in question almost all of the knot tyers guilds theories about knots by creating a provable scientific method of identifying what happens in a knot and producing a matching computer model. Take the knot tyers years to digest it.