How and Why Knots Spontaneously Form 145
palegray.net writes "Scientists believe they have found the underlying reasons why knots are so common in the universe. This research helps us understand how knotty arrangements in various molecules lead to biological patterns, as in certain proteins. The article also provides a look at the field of topology, and how it relates to knots."
Slashdotted article text (Score:2, Informative)
Tied Up in Knots
Anything that can tangle up, will, including DNA
Davide Castelvecchi
Knotted threads secure buttons to shirts. Knots in ropes attach boats to piers. You can find knots in shoestrings, ties, ribbons, and bows. But even without Boy Scouts or sailors, knots would be everywhere.
Call it Murphy's Law of knots: If something can get tangled up, it will. "Anything that's long and flexible seems to somehow end up knotted," says Andrew Belmonte, an applied mathematician at Pennsylvania State University in University Park. Belmonte has plenty of alarming anecdotal evidence. "It certainly happens in my house, with the cords of the venetian blind." But the knot scourge is a global one, as anyone who owns a desktop computer can confirm after peeking at the mess of connection cables and power cords behind the desk.
Now, scientists think they may have found out how and why things find their way into knotty arrangements. By tumbling a string of rope inside a box, biophysicists Dorian Raymer and Douglas Smith have discovered that knots--even complex knots--form surprisingly fast and often. The string first coils up, and then its free ends swivel around the other coils, tracing a random path among them. That essentially makes the coils into a braid, producing knots, the scientists say.
The results' relevance may go well beyond explaining the epidemic of tangled venetian blind cords. That's because spontaneous knots seem to be prevalent in nature, especially in biological molecules. For example, knottiness may be crucial to the workings of certain proteins (see "Knots in Proteins"). And knots can randomly form in DNA, hampering duplication or gene expression--so much so that living cells deploy special knot-chopping enzymes.
Raymer's interest in knots began as an answer waiting for a question. Two years ago, he was an undergraduate student working in Smith's lab at the University of California, San Diego (UCSD). Raymer fancied taking a class about the abstract theory of knots, offered by UCSD's math department. Smith told him that he should take it only if he could find a practical use for it--some kind of knot experiment.
Raymer never took the class, but he and Smith did come up with a simple idea for an experiment. They put a string in a cubic container the size of a box of tissue. By tumbling the box 10 times "like a laundry dryer," as Raymer puts it, the researchers hoped to observe knots forming spontaneously on occasion. They didn't have to wait for long: Knots formed right away. "The first couple of times, it was pretty amazing," Raymer says.
The researchers repeated the procedure more than 3,000 times, and knots formed about every other time. Longer strings, or more-flexible strings, tended to knot more often.
The researchers took pictures, planning to gather precise statistics of the types of knots that were forming. Raymer soon realized that, to make sense of the mess, he'd need to teach himself the mathematics of knots after all.
Ready-made tools
The theory of knots began in earnest in the 1860s, under the stimulus of the British physicist William Thomson, later known as Lord Kelvin. Kelvin suggested that atoms of different elements were really different kinds of knotted vortices in the ether. So to lay the foundations of chemistry, he believed, it was imperative to classify knots. Ultimately, physicists discovered that the ether didn't exist. But mathematicians took an interest in knots for knots' sake, as part of the young branch of mathematics called topology.
Topology studies shapes. Specifically, it studies shapes' properties that are not affected by stretching, moving, twisting, or pulling--anything that doesn't break up the object or fuse some of its parts. The proverbial example is that, to a topologist, a coffee mug is the same as a doughnut. In your imagination,
Wrap them (Score:5, Informative)
Re:Yes, but what about shoe laces, huh? (Score:3, Informative)
Re:All knotted up for next year. (Score:1, Informative)
Re:All knotted up for next year. (Score:4, Informative)
Re:Yes, but what about shoe laces, huh? (Score:4, Informative)
[disclaimer: I maintain one of the sites]
It's true, Bush does it. (Score:2, Informative)
Re:All knotted up for next year. (Score:3, Informative)
Re:All knotted up for next year. (Score:2, Informative)
Re:All knotted up for next year. (Score:4, Informative)
It links to http://www.realsimple.com/realsimple/package/0,21861,1683690-1133623-3,00.html [realsimple.com].
Re:All knotted up for next year. (Score:3, Informative)
http://en.wikipedia.org/wiki/Over/under_cable_coiling [wikipedia.org]
(having myself wrapped probably hundreds of miles of cable with this technique.)
Re:All knotted up for next year. (Score:3, Informative)
In regards to Christmas lights though, this still may not work simply because of the nature of the wire layout and the obstacle the lights themselves create, but it's worth a shot. I wrap all my cables this way, and even in my box of 100+ cables, I almost never get any tangles (and when I do, they only take a few seconds to untangle).