Another way of looking at it: instead of imagining you're at a random time in humanity, imagine you're a random human. The number of humans on earth has been increasing exponentially, so if you pick one at random they are most likely going to be from the last two centuries. This skews the results by making it more likely that the prediction is being made at this particular point in time (or a bit later if the population continues growing), which means that it is a non-uniform sample.