Let's cheat. Let's say that there's another Earth out there with human beings on it. Let's say they've been producing electrical noise for 200 years like us. Where would planet Earth #2 have to be in order for us to notice it?
I like this approach, but I don't think I like the answer.
If Earth 2 has been producing noise for 200 years, that gives us an upper bound of 200 light years. However – for general terrestrial traffic – our detection range is only about 1 light year [1].
There are also no stars within that distance from Earth 1. So, at current levels of technology, Earth 2 would have to be a sad star-less frozen ball that just happens to drift into our neighbourhood within the appropriate 1 light year window on its eons-long journey.
Given that, I think we got the best deal here on Earth 1.
Exactly. Now remove the restriction that Earth #2 is active with life at the same time we are. Instead intelligent life existed 10 billion years ago. Now we've got a tiny band of space 10 billion light years away where that planet has to be located where we could have possibly detected it. It doesn't seem that unlikely that we haven't found intelligent life.
If I had to bet on the right answer it would be this. The time scales of the universe are mind-fucking and we are just naive if we think we can maneuver around them.
The point of the paradox is that if intelligent civilization is only active for 200 years out of a 10 billion year timespan, there is something seriously wrong with the survival rates of such civilizations.
Or, they became something different, not worse. For example, Victorians would have looked silly to scan the skies for aliens by looking for soot clouds in their atmospheres, because all 'civilizations' would have steam trains.
We're looking for radio waves. Radio waves! Like a million-year-old civilization wouldn't be communicating with nano-soliton-pulse masers across interstellar distances. And to receive one of those, earth's orbit would have to accidentally cross its path, and then only for an instant. The chances are trillions to one, and we wouldn't recognize it if it happened.
