That’s the question that New Statesman put to a range of folks, including me. My answer was truncated in the magazine, which is fair enough but somewhat gave the impression that I fully bought into Richard Gott’s Copernican principle. In fact I consider it to be an amusing as well as a thought-provoking idea, but not obviously more than what I depict it as in the second paragraph of my full answer below. So here, for what it’s worth, is the complete answer.
There is a statistical answer to this. If you assume, as common sense suggests you should, that there is nothing special about us as humans, then it is unlikely we are among the first or last people ever to exist. A conservative guess at the trajectory of future population growth then implies that humanity has between 5,000 and 8 million years left. Whether that’s a sentence of doom or a reprieve is a matter of taste.
Alternatively, you might choose to say that we know absolutely nothing about our ‘specialness’ in this respect, and so this is just an argument that manufactures apparent knowledge out of ignorance. If you prefer this point of view, it forces us to confront our current apocalyptic nightmares. Will nuclear war, global warming, superbugs, or a rogue asteroid finish us off within the century? The last of these, at least, can be assigned fairly secure (and long) odds. As for the others, prediction is a mug’s game (which isn’t to say that all those who’ve played are mugs). I’d recommend enough pessimism to take seriously the tremendous challenges we face today, and enough optimism to think it’s worth the effort.