The Gordian knot
was a famously intricate knot attached to a sacred ox cart in the ancient city of Gordium
, near Ankara in modern-day Turkey.
In 333 BC, Alexander the Great
attempted to untie the knot, but was unable to find the ends of the knot in order to do so. Instead, he is said to have undone the knot using what is now called the Alexandrian solution
, which was to cut the knot in half with his sword.
Although there is good historical evidence that Alexander undid the Gordian knot, sources differ on how he accomplished this. According to some accounts, a more plausible theory is that he undid the knot by first removing the pin around which the knot was tied. This might have exposed the two ends of the knot, making it much easier to untie.
Another possibility is that the Gordian knot did not have
ends, and was a knotted loop instead of a knotted open piece of rope (or, in this case, bark). In other words, the Gordian knot might have been what mathematicians refer to as an unknot
More precisely, an unknot
is a (possibly knotted) closed loop that can be disentangled (i.e., continuously deformed) into a closed loop with no knot in it, without cutting the knot in the process. The branch of mathematics that deals with concepts like these is known as knot theory
. Knot theory can cast light on scientific applications, for example the ways in which long organic molecules such as DNA can form tight coils.
The animation shows a good example of an unknot. However, the knot in the picture is made out of a very stretchy and almost frictionless material, unlike any material that a physical knot would likely be made out of.
What this means is that there may exist “Gordian” unknots
which can be disentangled to the unknot in theory, but which cannot be disentangled in practice because of physical limitations of the material. Cutting the knot, or altering it in other ways (for example by soaking it) is considered cheating. The unknot in the animation is thought to be an example of such a Gordian unknot, but it seems that nobody has yet proved this rigorously.Relevant links
Wikipedia on the Gordian knot: http://en.wikipedia.org/wiki/Gordian_Knot
Wikipedia on the unknot: http://en.wikipedia.org/wiki/UnknotGordian unknots,
a paper from 2001 by P. Pieranski, S.Przybyl and A. Stasiak: http://arxiv.org/abs/physics/0103080
Animation credit: based on a gif from Piotr Pieranski's
web page: http://etacar.put.poznan.pl/piotr.pieranski/GordianUnknots.html#mathematics #scienceeveryday