Do you know what continuous means?

ars · on June 12, 2009

Yes, a function which has no large jumps.

Wind has no such constraint.

On top of that this only applies to "nonvanishing vectors", and again wind has no such constraint.

  -------| | | | | |------
  -------| | | | | |------
  -------| | | | | |------
  -------| | | | | |------
  -------| | | | | |------

Assume the lines wrap left/right and up/down.

Wind can do this, and you have no pole.

(This graph is really bad, the lines are actually curved where the points meet the lines. Imagine drawing circles around the earth for 2/3 of it. Then perpendicular half circles on the rest.)

Applying a pure function like this to real life wind which is not so constrained is about as right as applying the http://en.wikipedia.org/wiki/Banach-Tarski_paradox to a real life object, even if mathematically it's correct.