The Doomsday argument is a probabilistic argument that claims to predict the future lifetime of the human species given only an estimate of the total number of humans born so far. Simply put, it says that supposing the humans alive today are in a random place in the whole human history timeline, chances are we are about halfway through it.
Denoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that we are equally likely (along with the other N − 1 humans) to find ourselves at any position n, so we assume that our fractional position f = n/N is uniformly distributed on the interval (0, 1] prior to learning our absolute position.
Let us further assume that our fractional position f is uniformly distributed on (0, 1] even after we learn of our absolute position n. (This is equivalent to the assumption that we have no prior information about the total number of humans, N.) That is, for example, there is 95% chance that f is in the interval (0.05, 1], that is f > 0.05. In other words we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies[dubious – discuss] an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n.
If we take that 60 billion humans have been born so far, then we can estimate that there is a 95% chance that the total number of humans N will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1140 billion humans will be born in 9120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live.
the doomsday clock
The Doomsday clock shows the expected time to nuclear doomsday. If the twelve hours of the clock symbolize the lifespan of the human species, its current time of 11:55 implies that we are among the last 1% of people who will ever be born.
The Doomsday clock specifically estimates the proximity of atomic self-destruction – which has only been possible for sixty years.
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