Every scientific breakthrough has taken time to get going. Knowledge and technology needs to slowly accrue over time until a tipping point is reached. But in some cases, time just isn't a factor. Can we say that some things will never happen because they haven't happened yet?
Case in point: first contact with aliens. Wouldn't it have happened already if it was going to?
There's a famous equation, the Drake Equation, that attempts to figure out exactly how likely it is that humans will make contact with alien life. The equation is a long string of variables. Some variables represent the rate of planet formation and the rate at which life and civilizations evolve. Some variables represent the fraction of planets that can support life, and the fraction of civilizations that develop technology that can competently look for alien civilizations in the universe. The last variable represents how long those societies can last, before they collapse.
In the past, the Drake Equation has been used by doomsayers, who were worried about global nuclear war. The fact that people haven't seen anything yet had to mean, they thought, that societies which develop sufficiently high levels of technology always destroy themselves. Although the apocalyptians still make a decent argument, the fact that the globe hasn't been reduced to ash yet makes it just possible that, instead, we're just coming up against some hard physical limits.
The Odds in Space
Obviously, the equation is more a thought experiment than an actual solution. At the time that Frank Drake, a astrophysics professor at UC Santa Cruz, thought it up, the world didn't even know that there were more than nine planets (Pluto was still in play). Every single value was an estimate, and continues to be an estimate. Still, the estimates make you wonder. There have to be billions of other Earths out there. What does it mean that no one has contacted us?
There's a Catch-22 built into the equation. Because we haven't made contact, the only thing on which we can base the rate of the development of life and technology, from a single cell to SETI, is the Earth. In order to understand properly whether the Earth is slow or fast by universal standards, we have to be able to compare ourselves to other planets — which we can't do until we make contact.
The search for alien life is still in its infancy here. Let's say the Earth holds a relatively fast-developing civilization. Our planet is about four billion years old, a third as old as the universe, so if the other worlds out there are developing at a rate of less than one third Earth speed, it's doubtful they'd be able to receive Earth's signals, let alone contact us back. If, on the other hand, they're developing faster, they should have found us by now. Or we should have found them.
The only thing that could keep them doing so is if it's physically impossible, given the size of the universe, the number of worlds that can develop intelligent life, and the distance between them, to make contact contact other civilizations. Ever.
Saying that, in an infinite universe, if something can happen, it has to happen to us, is verging on lottery-ticket logic. Just because there are a lot of chances for something, doesn't mean that anyone actually has to hit it big. Random chance always plays a part. But there is a case to be made that, if we didn't find intelligent alien life waving a flag and trying to contact us soon after we started looking, we very well might never find it at all.
The Odds in Time
Space isn't the only thing we have too much of not to have noticed something by now. There's near-infinite space, but there's also a vast amount of time, and if anything it simplifies the Drake Equation. Instead of the possibility of civilization arising in the universe, we can eliminate all those variables and make it a certainty. In the place of variables such as the likelihood of that Earth-like planets will form, life will evolve on them, and scientifically minded civilizations growing from that life, we will have to substitute in how likely it is that time travel actually can happen.
Again, when we look at the world around us, we have to consider one of two outcomes; the impossibility of time travel, or the end of the world. At least this time, though, the end of the world is metaphoric. One of the biggest arguments against time travel is the fact that no one has run into any time travelers. This is a good point — except that it presumes that time travelers would want to come back and hang out with the likes of us. Some people talk about how, if there were time travelers, millions or perhaps billions of people would show up for, say, the crucifixion of Christ. Therefore there could be no time travel. Actually, it just meant there could be no Christian time travel.