Let $\gamma$ be a simple (non-self-intersecting) open curve in $\mathbb{R}^3$.
I am seeking a measure of its degree of "entangledness," some measure that accords
with the intuition one senses with a tangled fishing line.
One measure is to connect the two ends of $\gamma$ and use a measure of its degree of
knottedness, e.g., its [unknotting number][1], or, perhaps, its [writhing number][2].
But it would seem these depend on *how* the ends are connected, rather than on $\gamma$ alone.
Have other natural measures been proposed? I'd appreciate pointers. Thanks!

<hr />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;![Tangle][3]<hr />
A year later, I remain interested, especially in some type of energy
measure along the lines attempted by *Qfwfq*. It would be especially pleasing
to have a measure that somehow measures the effort it would take to straighten
a tangle.

  


  [1]: http://en.wikipedia.org/wiki/Unknotting_number
  [2]: http://en.wikipedia.org/wiki/Writhing_number
  [3]: http://www.getlineoff.com/Pics/tangle1.gif