The long-term prospects of our civilization here on Earth are very uncertain. We can be destroyed by an asteroid impact or a nearby supernova explosion, or we can self-destruct in a nuclear or bacteriological war. It is a matter of not if but when the disaster will strike, and the only sure way for humans to survive in the long run is to spread beyond the Earth and colonize the Galaxy. The problem is that our chances of doing that before we are wiped out by some sort of catastrophe appear to be rather bleak.
The Doomsday argument
The probability for a civilization to survive the existential challenges and colonize its galaxy may be small, but it is non-zero, and in a vast universe such civilizations should certainly exist. We shall call them large civilizations. There will also be small civilizations which die out before they spread much beyond their native planets.
For the sake of argument, let us assume that small civilizations do not grow much larger than ours and die soon after they reach their maximum size. The total number of individuals who lived in such a civilization throughout its entire history is then comparable to the number of people who ever lived on Earth, which is about 400 billion people, 60 times the present Earth population.
A large civilization contains a much greater number of individuals. A galaxy like ours has about 100 billion stars. We don't know what fraction of stars have planets suitable for colonization, but with a conservative estimate of 0.01% we would still have about 10 million habitable planets per galaxy. Assuming that each planet will reach a population similar to that of the Earth, we get 4 million trillion individuals. (For definiteness, we focus on human-like civilizations, disregarding the planets inhabited by little green people with 1000 people per square inch.) The numbers can be much higher if the civilization spreads well beyond its galaxy. The crucial question is: what is the probability P for a civilization to become large?
It takes 10 million (or more) small civilizations to provide the same number of individuals as a single large civilization. Thus, unless P is extremely small (less than one in 10 million), individuals live predominantly in large civilizations. That's where we should expect to find ourselves if we are typical inhabitants of the universe. Furthermore, a typical member of a large civilization should expect to live at a time when the civilization is close to its maximum size, since that is when most of its inhabitants are going to live. These expectations are in a glaring conflict with what we actually observe: we either live in a small civilization or at the very beginning of a large civilization. With the assumption that P is not very small, both of these options are very unlikely – which indicates that the assumption is probably wrong.
If indeed we are typical observers in the universe, then we have to conclude that the probability P for a civilization to survive long enough to become large must be very tiny. In our example, it cannot be much more than one in 10 million.
This is the notorious "Doomsday argument". First suggested by Brandon Carter about 35 years ago, it inspired much heated debate and has often been misinterpreted. In the form given here it was discussed by Ken Olum, Joshua Knobe, and me.
Beating the odds
The Doomsday argument is statistical in nature. It does not predict anything about our civilization in particular. All it says is that the odds for any given civilization to grow large are very low. At the same time, some rare civilizations do beat the odds.
What distinguishes these exceptional civilizations? Apart from pure luck, civilizations that dedicate a substantial part of their resources to space colonization, start the colonization process early, and do not stop, stand a better chance of long-term survival.
With many other diverse and pressing needs, this strategy may be difficult to implement, but this may be one of the reasons why large civilizations are so rare. And then, there is no guarantee. Only when the colonization is well underway, and the number of colonies grows faster than they are dying out, can one declare a victory. But if we ever reach this stage in colonization of our Galaxy, this would truly be a turning point in the history of our civilization.
Where are they?
One question that needs to be addressed is: why is our Galaxy not yet colonized? There are stars in the Galaxy that are billions of years older than our Sun, and it should take much less than a billion years to colonize the entire Galaxy. So, we are faced with Enrico Fermi's famous question: Where are they? The most probable answer, in my view, is that we may be the only intelligent civilization in the entire observable universe.
Our cosmic horizon is set by the distance that light has traveled since the big bang. It sets the absolute limit to space colonization, since no civilization can spread faster than the speed of light. There is a large number of habitable planets within our horizon, but are these planets actually inhabited? Evolution of life and intelligence require some extremely improbable events. Theoretical estimates (admittedly rather speculative) suggest that their probability is so low that the nearest planet with intelligent life may be far beyond the horizon. If this is really so, then we are responsible for a huge chunk of real estate, 80 billion light years in diameter. Our crossing the threshold to a space-colonizing civilization would then really change everything. It will make a difference between a "flicker" civilization that blinks in and out of existence and a civilization that spreads through much of the observable universe, and possibly transforms it.