The long-term prospects of civilization here on Earth are very uncertain. Many say it is a matter of when, not if, disaster will strike. By that prediction, the only sure way for humans to survive in the long run is to spread beyond the Earth and explore the galaxy.
The problem is that our chances of doing that, before our errant ways or some sort of catastrophe wipes us out, appear to be rather bleak. The probability for a civilization to survive the existential challenges and colonize its galaxy may be small, however, it is still above zero; the so-called ‘large civilizations’ of theoretical physics.
By extension there are ‘small civilizations’ too, but these die out before they spread much beyond their native planets. For the sake of the argument, let us assume that small civilizations do not grow much larger than ours currently; and die soon after they reach their maximum size.
Then, the total number of individuals who lived in such a civilization throughout its entire history, is comparable to the number of people who ever lived on Earth; which is about 400 billion people, 60 times the present Earth population. Although, we logically accept that a large civilization contains a much greater number of individuals.
Moving on...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 in our galaxy (give or take, what’s a million here or there!).
Assuming that each planet will reach a population similar to that of the Earth, we get 4 trillion individuals. (For our purposes lets focus on human-like civilizations, disregarding the planets inhabited by little green people). Of course, the numbers can be much higher if the civilization spreads well beyond its galaxy.
The crucial question of this thought experiment is: “What is the probability 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, individuals likely live predominantly in large civilizations.
That, then, is 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 that 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. However, based on the numbers above, both of these options are very unlikely - which indicates that the original assumption is probably wrong.
If, indeed, we are typical observers in the universe; then we have to conclude that the probability 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".
However, 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, it proposes that some rare civilizations do beat the odds.
What would distinguish these exceptional civilizations? Apart from pure luck, apparently, civilizations that dedicate a substantial part of their resources to space colonization i.e. 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; and one of the reasons why large civilizations are so rare. On top of that, there is no guarantee either. 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. 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, therefore, it should take much less than a billion years to colonize the entire galaxy.
Which probably means we are solely 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, which blinks in and out of existence, and a civilization that transforms itself.