POZNAN, Poland, April 9 (UPI) -- A Polish physicist and a Swiss biologist may be the first to have untangled the mysteries of a legendary knot dating back to Alexander the Great.

Piotr Pieranski, of the Poznan University of Technology in Poland, and Andrzej Stasiak, of the University of Lausanne in Switzerland, claim to have discovered the mysterious and complex structure of the so-called Gordian knot, which bound the yoke and beam of the chariot of Gordius, king of Phrygia.

According to legend, whoever untied the knot would become the ruler of Asia. For centuries, pretenders to the throne tried in vain to untie the thick rope, which became a popular tourist attraction housed in its own temple. In 333 BC Alexander the Great is said to have cut the knot with his sword. In so doing, Alexander defined the Gordian knot as a knot that must be cut to be untied.

The Gordian knot has never been fully described, Pieranski told United Press International, though rumors have existed for centuries about its nature. The knot was either a loop of rope with spliced ends, or a straight length of rope with free ends, Pieranski explained.

Pieranski told UPI that modern knot theory, a branch of mathematics called topology, predicts that any knot tied from a straight length of rope with free ends can be untied, regardless how complex the knot. With this prediction in mind, Pieranski and his colleagues knew the Gordian knot must be an "unknot," which is another name for the simplest knot, a circular loop of rope with spliced ends.

History supported their hypothesis. Pieranski said reports describing the original Gordian knot, dating to 150 AD, said the ends of the rope were not visible and so must have been spliced together.

Starting with a loop of rope, Pieranski set out to prove his team could construct a knot that could only be untied by cutting.

"We answered the apparently simple question to which the answer was not previously known: Is it possible to tie an unknot in such a way that it is impossible to untie it and restore it back to its circular form?" Pieranski said, adding that the simple answer is yes.

Mathematicians view the Gordian knot problem as purely physical. University of Massachusetts professor Rob Kusner told UPI that rope knots are very different than their mathematical counterparts. "Mathematically, we can't prove you can or cannot make a Gordian knot," he said from his Amherst office.

Eric Rawdon, assistant professor of mathematics at the University of Pittsburgh, agreed.

"In normal topology, knots have only one dimension and no thickness" Rawdon told UPI. "Ropes have three dimensions, so forming a Gordian knot from a piece of rope may be possible."

To tie their Gordian knot, Pieranski and Stasiak used a computer algorithm called SONO (Shrink-On-No-Overlap). SONO constructed a complicated knot by looping and shrinking a circular piece of rope.

Shrinking was necessary, according to Pieranski, because a loose-fitting knot can be untied without cutting. The rope used to make the Gordian knot was tied and then shrunk, Pieranski said, possibly using a brine solution.

"We propose then that the Gordian knot was a shrunken loop of rope entangled in such a way that it could not be converted back to its original circular form by simple manipulations," Pieranski said. Rawdon said he has never seen such a complete description of the Gordian knot, and that Pieranski and Stasiak have reached sound conclusions.

Kusner agrees, though he is quick to emphasize the difference between theory and practice.

"The real test is to prove, mathematically, that you can or cannot construct a Gordian knot," Kusner said. "I'm not sure a Gordian knot made of rope rises to that standard, although I will say that Pieranski and Stasiak have constructed an algorithm that gets stuck when it tries to untie a rope without cutting."

Pieranski and Stasiak are presenting their findings later this month to the American Mathematical Society.

(Reported by UPI Science Correspondent Mike Martin in Columbia, Mo.)

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