A task is impossible only in the relative point of view of the person describing it as impossible.
Most of the time people come to the conclusion that a task is impossible with this bad induction: "X number of people try to do this and failed. This task must then be impossible."
To me, complex problems are like mountains: Most people attack them head first in a straight line using known and proven methods. Personally, I prefer walking around it and see it from the other angles. Nature as a tendency of creating natural steps here and there. There's nothing worst than reaching the top only to find the ski lift that was on the other face.