We present new probabilistic forecasts of the timing of the world's population reaching 8 billion, the world's peak population, and the date at which one-third or more of the world's population would be 60+ years old. The timing of these milestones, as well as the timing of the Day of 7 Billion, is uncertain. We compute that the 60 percent prediction interval for the Day of 8 Billion is between 2024 and 2033. Our figures show that there is around a 60 percent chance that one-third of the world's population would be 60+ years old in 2100. In the UN 2010 medium variant, that proportion never reaches one-third. As in our past forecasts (Lutz et al. 2001, 2008), we find the chance that the world's population will peak in this century to be around 84 percent and the timing of that peak to be highly uncertain. Focal days, like the Day of 7 Billion, play a role in raising public awareness of population issues, but they give a false sense of the certainty of our knowledge. The uncertainty of the timing of demographic milestones is not a constant of nature. Understanding the true extent of our demographic uncertainty can help motivate governments and other agencies to make the investments necessary to reduce it.