Not sure why this occurred to me, but don't you think that since there are about 400 billion stars in the Milky Way, and there are an estimated 125 billion galaxies in the known universe, that the chance that more than one star has a planet which harbors life is nearly infinity-to-one?
Warning: dubious calculations appear in the following text. If you're a nit-picking astronomer-type, either skip it, or correct me gently. Thanks.
Ok, maybe I sound like Carl Sagan here, but really -- assuming that our galaxy is of roughly average size, there are about 500 trillion stars in the universe. That's a 5 with 14 zeros after it, or 500,000,000,000,000 stars. If the universe is 15 billion years old, that means that there are, on average, about one new star for every 15 minutes of all of existence(!) -- 33,000 new stars for every Earth-year.
Doesn't it seem inevitible that, at least at one time, there was intelligent life somewhere else? The trick, I suppose, is whether it was there at the "right time" for us to see them.
I think it's pretty easy to run the numbers... Let's assume that human beings will be around for a total of 10 million years. Not all that long a time in astronomical terms, but a pretty long time as far as I'm concerned, and pretty conservative if things don't get too far out of hand in Kashmir.
Let's also assume that humans are roughly average as far as intelligent life is concerned (at least in terms of life forms that we might have a chance of detecting at astronomical distances).
That means that our exposure to potential extra-terrestrial life, as a species, is about 300 billion star-years, where a star-year is a year of existence of a star in the universe, which exists during the life-span of our species. That's more than twice the number of galaxies in the universe!
Now 10 million years is about 0.066% of the total age of the universe. If we assume that other intelligent species last for about the same amount of time, then we can extrapolate the likelyhood that we'll ever see them. It's about 0.000044%. Multiply that by the number of star-years that we're exposed to as a species, and we get the likelyhood that if every star were to develop intelligent (and detectible) life, that't we'd be exposed to them over the lifetime of our species. It's a very large number: 133,333.
Here's the rub. Let's say that only one in 100,000 stars ever has a planet which develops intelligent life. That leaves us with odds of about 1.3-to-one, that if we were paying very close attention to every star in the universe all the time, that we'd see signs of intelligent life elsewhere in the universe.
Then consider that we have a very hard time detecting even the existence of an entire planet orbiting a nearby star. I have no way to assign a value to this factor, but let's say for sake of example, that we could detect planets orbiting one-in-a-million stars in the universe. (Probably optimistic.) That puts us in the 13-to-one range for detecting extra-terrestrial life for the entire life of our species. Factor in Moore's Law, and you can probably change 13:1 to 100-to-one.
That gives us about one chance in 100,000 for success per year, which is -- very roughly -- one in two-thousand in my lifetime.
Since our powers of observation are astronomically speaking, pretty limited (at least for now), it should come as little surprise that we haven't heard much from our universal co-habitants.
However it's also pretty clear from the archeological record here on Earth, that life is extremely resilliant and adaptible. It might not be unreasonable to think that the number of stars in the universe which have habitable planets is much larger than the 1-in-100,000 number I used above. Maybe it's more like 1-in-10? We are, after all, already theorizing about the possibility of (non-intelligent) life existing on at least four large bodies right here in our own soalr system. (These theories are not without reason, btw.)
Perhaps the reason we haven't heard from them is that their envoronments aren't conducive to inventing technologies which we could detect from here on Earth. I personally think that it's quite likely that we're not alone, but that our roommates are so quiet or so distant, that we haven't even noticed that they're there... yet...