When making prediction there is usually a tendency to run too fast and too far, neglecting the size of human population: the inertia is difficult to overcome, however once moved, only a simple change will be overwhelming. I don't think application convergence will happen soon. Why? There are so many small steps to go and each step by itself can be a revolution.

Lets say information portability, so far we have only taken a small step using XML. There are still a lot to go before information can flow from one end to the other. What is the point of applications convergence if everyone can only talk in vendor specific language or buying software/hardware from that vendor? It will break just like the other previous attempts.

Luckily already there are some hints that such portability is growing, but how long and in what form will that happen, it is not a few market heavy weights to decide.