A STRING OF LIGHTS PRESENTS A KNOTTY HOLIDAY PROBLEM
Knot theory and its ramifications for the holidays
It’s a knotty problem unfurling those Christmas and Hanukah lights. But progress is being made: Between 1926 and 1927 several mathematicians found that de-knotting involves applying just three different “moves” – and they’re called Reidemeister moves after the first mathematician to discover them:
1. Twist and untwist in either direction;
2. Move one loop completely over another; or
3. Move a string completely over or under a crossing
To make a nice knotless string, we need to know which part of the knot to operate on and which Reidemeister move to use. In other words, we need an algorithm.
It’s called the “Unknotting problem”: Mathematicians continue to search but have yet to find an efficient algorithm (they have found several very slow and inefficient algorithms). Mathematicians do know that the algorithm has complexity NP, which means that no efficient algorithm is known. But if you could show that any complexity NP problem – such as the unknotting problem – does have an efficient algorithm, you’ll earn $1,000,000 from the Clay Mathematics Institute.
Just something to think about as you figure out how to de-knot your holiday lights…
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