I saw this the first time in the Science times, but was reminded of it in a link from Lou Anders' blog.
To understand Richard Gott's Copernican principle, you basically have to assume that there was even odds that you could have been any human from the beginning of our species' history to its end, whenever that is. So what are the odds that you are going to have been one of the first humans? Very small, because there were only maybe a hundred thousand people on the world then, which is not many out of the many billions that existed. Of course you weren't, you live now. But why now?
It doesn't seem so unlikely, since there are far more people on the planet now that you "could have" been than ever before. But wait a minute. If people in the future go out and colonize other stars some day, then the number of people in the inhabited stars will likely be in the hundreds of billions or trillions, or more. So the odds you would have been born now would be very small.
In this column, he argues that if we don't colonize Mars in the next 50 years or so it will probably never happen, more or less for the same reason. That's more optimistic than the way he's put it before, which gives me hope. With his usual pinpoint precision, he estimates that there is a 95% chance that the human race will last between about 6,000 and 7 million years. That's a pretty good range, and gives us some options.
Of course, the flaw with thinking this way is that if the people who had crossed the Siberian ice bridge, or Magellan, had thought the same way, they never would have bothered. So it's probably just as well those guys didn't take statistics.