We all know that irritating feeling when your neat computer cables get turned into a thick weave of plastic dreadlocks. Ultimately, the reason this happens is due to one of the most important laws in all of Science: the second law of thermodynamics. The second law states that "the change in entropy of a closed system is greater than or equal to zero with respect to time". It's a beautiful law. I have a tie with the equation on it, and Ludwig Boltzmann has it on his tombstone. There's a lot of subtley going on in that definition but for our purposes we can state it pretty simply: things are more likely to get disordered.
A pile of sand will spread out rather than jump into a neat column, bedrooms become messier, cars get rusty and a pencil balanced on its tip will fall over. The same thing applies to cables and strings. Given a tiny amount of movement energy, they will gradually get tangled up (if you think about it this is quite logical because if they start out in perfect alignment and you move them about...there's only one way for them to rearrange...into a messier configuration!)
That's why a bunch of cables given even a small amount of agitation will quickly become knotted together. But DNA doesn't. And this is actually a pretty deep puzzle. A single thread of DNA is somehwere between 1 and 3 meters long when stretched out (depending on which chromosome you pick) and you have enough of those strands in your body to reach the Sun and back several times. That's a lot of thread, and it doesn't get knotted up. At the moment, nobody has a clue why, but mathematicians and biologists are hot on the case.
There is a particular branch of mathematics called topology which deals with the shapes of objects and how deforming them changes their properties. And, within topology, there are three sub-sets of ideas called (I'm not making this up) braid theory, knot theory and tangle theory. The idea is that if you solve some simple equations for a knot made of string, the same equations can be modified to describe a knot in a piece of hair, or a piece of marshmallow. The same mathematics should underpin everything. So if we can find out what makes something more/less lilkely to tangle, we might be able to answer the DNA question.
A study conducted by Robert Matthews at Aston University in 2004 (who also carried out research on whether flipping buttered toast is more likely to land butter side down) was able to show that having loops in your thread makes it less likely to get completely tangled. His research even involved recruiting students from a school in my hometown of Coventry and getting them to tie over 12,000 knots in different types of looped string. It turns out that strings with loops in them are less likely to get tangled.
Then there's the research of Dorian Raymer from Chicago Univestiry in 2006, who measured how likely a string is to get tangled depending on how much it's being jiggled about. It turns out that the length of string actually has more to do with whether it gets tangled than how much it's being agitated.
Some people have suggested that by having loops in the DNA, nature has found the perfect way to minimise tanlging, while others have suggested that DNA is made of chemicals which are less likely to fold around each other. The simple answer is that we just don't know. A helix of string or wire would get horribly knotted (slinkies anyone?) but DNA is somehow able to avoid this curse. Answer unknown...for now at least.
P.S. This has nothing to do with string theory.