This is assuming, of course, that these aliens are exactly like us and send dumb, inflexible machines that will run out of power and can’t draw attention to themselves. And, for that matter, that they would want to draw attention to themselves.

We’ll probably have some form of strong AI within a generation, and one that will be ready to act as our ambassador to an alien race within three. Allow it to replicate itself when it has the chance (the von Newmann “universal constructor” idea), and even if each one only makes two copies in its lifetime, we’re all but guaranteed to find any other civilizations that might exist out there sooner or later. There are problems to that idea, of course — given what’s happening right now to the Russian Mars mission, I really wouldn’t trust our race to make something with that much raw potential for disaster, but presumably strong AI will help greatly reduce that problem.

Of course, once we do have that capability, there’s a very good chance we’ll want our ambassador to simply study the races it finds and let us know about them, rather than blindly trying to contact them. After all, knowing our own history, would you trust a newly-discovered race to be peaceful and interested only in commerce and exchanging ideas? There could be intelligent probes from dozens of races sitting in our solar system right now, trying to determine whether our race is mature enough to approach, as posited by the popular Star Trek series and many other works of science fiction. If I were them, I certainly couldn’t think that we’re ready, taken as a whole.

I guess we’ll find out if and when the hypothetical aliens deem us grown up enough.

(I have my own ideas on the subject, but even if they’re correct, there’s no way to prove them.)