I've loved reading all the comments on this, and the mathematical geekitude, but I had another thought about the idea of us being alone: What if the universe is just far more malicious to life than we thought? We are a tiny little solar system in one arm of one moderately-sized galaxy. And our little planet in our little solar system has already had at least one extinction-level event caused by an asteroid. Recently, as our sensors have gotten better, we have seen not one, but two different extra-solar objects entering our system (RAMA I and RAMA II, according to kleinbl00), and I guarantee you that the first objects didn't just happen to show up when we build sensors strong enough to detect them... they've been whistling through our airspace (erm... space-space?) since forever. What if there is just so much shit flying around and crashing into each other, that life only has the luxury of time to develop, out here in our distant suburbs; in areas that are protected in some way from the primary debris flying out of the chaotic center of our Universe? Sure, the math says that there SHOULD be a gajillion planets out there that are habitable for things we would recognize as "life". But the practicalities of having a habitable environment, undisturbed and stable for long enough to develop intelligent human-equitable life, is a vanishingly small occurrence? Think Seveneves but on a galactic scale, rather than a planetary one... Hmmm....
Before there was Seveneves there was Lucifer's Hammer and before there was Lucifer's Hammer there was Rendezvous with Rama and before there was Rendezvous with Rama there was When Worlds Collide and really if you go back to the dawn of astronomy it's always about "the universe is just far more malicious to life than we thought." It's kind of like the whole "what if AI is evil" trope - I mean, fuckoff with that shit the first use of artificial intelligence was in RUR which was not only the first book about robots, it was literally about a robot uprising. Your discussion is literally FsubC ("the fraction of civilizations that develop a technology that releases detectable signs of their existence into space") and L ("the length of time for which such civilizations release detectable signals into space") in the Drake Equation, the veracity of which is handled eloquently in this xkcd comic. It's not entirely fair to pick on the Drake Equation as being six stacked bullshit factors we cannot begin to approximate. At the time he wrote it, those bullshit factors were complete unknowns and the intervening decades have not done much to fill in the blanks. We've got an n of one here - exactly one inhabited planet capable of transmitting into the void. But if we look at that n's historical record: - Ordovician extinction, 439m years ago - Devonian extinction, 364m years ago - Permian extinction, 251m years ago - Triassic extinction, 200m years ago - K-T extinction, 61m years ago That's an average of one extinction-level event every 94 million years. That's fifteen times as long as it took us to go from "walking erect" to "arguing about the Drake equation on the Internet." Fuckin' the discovery of radio waves is new enough that we have footage of their discoverer: So. Presume that Earth is an outlier with radically infrequent bombardment. How radical? Lascaux is probably less than 20,000 years old. So. From cave paintings to 4chan in 20,000 years. Leave everything else the same - don't give anyone a faster metabolism, don't give anyone better or worse socialization, don't give anyone any advantage or disadvantage beyond what we're looking at, and that 20,000 year period happens 4700 times, on average, between every extinction. Is the center of the galaxy 4700 times more hostile than the limbs? I'd think we'd see astronomical evidence of that.
From cave paintings to 4chan in 20k years... that's an excellent way to look at it, and makes it easier to wrap your mind around the timelines it can take a civilization to get from milestone to milestone. It's hard to conceive of the times and distances we are talking about here. Having a practical timeframe to think of, at least gives you a handhold to grab on to, as you slide down the infinite mountain of numbers... And ooli makes a good point about intelligence. I know the Drake Equation has thought of that, but breaking it down into layman-understandable pieces is a valuable exercise for me.
On the other hand, Arthropods in 500m years never managed to create 4chan Dinosaur in their 40m years span didn't get a radio wave out Mammal in 200m years only managed to get some primate out, 100m years ago, any extinction event in that time frame, and Adios 4chan, Telescope, and bipedal walk Not only the step from life to multi-cellular life took 4 billions years (1/4 of the universe life). But even after that the progression to intelligence life was long: In all the species around in the past 500m years, intelligence is a fluke.. we're still waiting for its 2nd coming. And Dolphins are more dumb than they look