I suppose it is impossible to discuss this subject without mentioning UFOs. For if UFOs really are space vehicles built by intelligent extraterrestial beings (I'll use the term "alien" as a convenient shorthand from here on), then of course the question of aliens (see) is immediately answered in the affirmative. I don't want to get into a long discussion of UFOs here. I'm certainly not going to resolve that debate in a couple of paragraphs. So suffice it to say this:
There are, of course, plenty of eyewitness reports, which is certainly interesting. But there is little corroboration, little supporting circumstantial evidence, and no physical evidence. Suppose you were on a jury hearing such testimony in court: Someone claims to be an eyewitness to a murder. But the person he accuses has a plausible (though not ironclad) alibi, the conditions under which he claims to have seen the person were not ideal, and the police are unable to find a murder weapon or even a body. The witness may be telling the truth. But would you convict on such evidence? I would not. There is much more than a "reasonable doubt".
Which leaves us with exactly zero direct evidence for extraterrestials.
That doesn't prove there are none, of course. I've never met anyone from Rumania, but that hardly proves there is no such country.
So how strong is the absence of evidence for aliens? It all depends on how likely one thinks we should be to have some solid evidence by this time. That, in turn, depends on how many alien races one expects to find out there.
("*" indicates multiply -- a typical convention in programming.)
"N" is the number of alien races with sufficient technology to communicate with us, if not physically travel to our planet.
"s" is the number of stars in the galaxy.
"p" is the average number of planets orbiting each star which are suitable for intelligent life. Note that this number might be less than 1, if most stars do not have such planets.
"t" is the percentage of these planets on which aliens achieve a sufficient level of technology to communicate with us in a given period of time. A planet on which there is no intelligent life, never was and never will be, will contribute zero to this number. A planet on which there is intelligent life will contribute an amount dependent on how long it takes that intelligence to reach the specified level of technology. If some civilizations destroy themselves and then rebuild, their numerator in this calculation would be more than one, but see the next parameter.
"l" is the average length of time, in units of the time period used for "t", that such a technological civilization survives.
We have at least ball-park estimates of "s": I've seen a low of 40 billion and a high of 1 trillion. Let's take 100 billion as a working guess.
Unfortunately, values for the rest of the parameters in this equation range from debatable to outright guesses. For example, "p". In terms of empirical evidence, we of course know that the Earth is suitable for intelligent life. (Pause here for the jokes about whether or not there is really intelligent life on Earth ...) Arguably Mars could support some sort of intelligent life. And that's all we know of in the entire universe: maybe two. There is some indirect evidence of a large planet orbiting Barnard's Star. (Maybe it's more solid by now, or similar evidence has been found for other stars. I haven't kept up on this.) Even if that holds up, that was a super-Jovian planet, not likely to be suitable for intelligent life. It's possible that the average star out there has several habitable planets circling it. It's also possible that our Solar System is the only such in the universe. We just don't know.
So here is my contribution to the discussion: Using an equation such as the above, an evolutionist has far more reason to doubt the existence of aliens than a creationist. Let me explain.
s = 100 billion (The low end of the estimates.)
p = 1 / 1000 (Simply a guess, but seems very conservative.)
t = 1 / 10 billion (Assuming it's taken 4 billion years for intelligent life to evolve on Earth, and that this is less than half the time for the average planet, factoring in that some never evolve intelligence at all.)
l = 10 million (If something resembling humanity has already survived for 100 millions years, it's fair to assume we have at least 10% of that left. Indeed that seems pretty pessimistic. High technology combined with space travel would seem likely to make a species very durable. Even if we abuse the technology at that point and destroy a planet or two, we've got plenty more to spare.)
This gives N = 100,000.
That's an awful lot. Why haven't we picked up any of their radio signals, or detected their spaceships for that matter? Okay, it's a big galaxy, but if we're all evenly distributed, then we're about 1,400 light-years apart. A long haul, but if they've been broadcasting radio waves for a million years, they've had plenty of time to get here.
Let's put it in less mathematical terms. Let's be pessimistic and suppose that there is no way around the old light-speed barrier. Nevertheless, surely at least some of these hundreds of thousands of civilizations will decide to explore the galaxy at sub-light speeds. The galaxy is about 100,000 light-years across. A long trip, but if a civilization has been traveling in space for millions of years, all the little steps will add up eventually. Even one such civilization should have filled the galaxy by now. And there should be tens or hundreds of thousands of them! Seeing one of their spaceships buzzing about our Solar System should be a sight as familiar as seeing a car go by in the street or a plane pass overhead. So ... where are they?
The only possible conclusion is that there is something dreadfully wrong with our assumptions.
s = 100 billion (Same as above.)
p = 1 / 1000 (Same as above.)
t = 1 / 20,000 (Assuming it's taken humans 10,000 years from creation to the requisite technology, and that this is about half average.)
l = 50 (Humans have had the requisite technology for somewhat over fifty years.) This gives N = 250,000.
Now at first glance this looks to be even more pessimistic than the evolutionary scenario. But wait! Even with this larger number of alien races, we're still about 1,000 light-years apart. And if the average race has only been broadcasting for 50 to 100 years, we wouldn't expect to have received any transmissions yet. It's no surprise.
Let's look at it less mathematically. If the universe is only 10,000 or so years old, then obviously no alien race can be older that. Even if some of them achieved the necessary technology much much faster than we did, still, they cannot have had it for more than a couple of thousand years. And given the distances between the stars, unless one of these rapidly advancing technological races just happened to much nearer to us than one would possibly expect to happen by chance, there just hasn't been enough time -- on a young-universe time scale -- for those radio signals to have reached us.
And for them to have physically reached us? I mean, in spaceships? Forget it. Even if a race was thousands of years ahead of us and has been travelling between the stars for centuries, that's nowhere near enough time to get very far on a galactic scale.
So to the question, Where are they?, the advocate of creation theory has an easy answer: Most of them are still planet-bound just like us. Perhaps a few hundred have reached the stage of puttering about their own solar systems. And if a few have managed to travel between the stars, the chances that one of them would have gotten here by now are very small.