Intergenerational impartiality requires putting the welfare of future generations at par with that of our own. However, rational choice requires weighting all welfare values by the respective probabilities of realization. As the risk of non-survival of mankind is strictly positive for all time periods and as the probability of non-survival is cumulative, the probability weights operate like discount factors, though justified on a morally justifiable and completely different ground. Impartial intertemporal welfare maximization is acceptable, though the welfare of people in (...) the very far future has lower effects as the probabilities of their existence are also lower. However, the effective discount rate on future welfare values justified on this ground is likely to be less than 0.1 per annum. Such discounting does not compromise environmental protection and sustainability unduly. The finiteness of our universe implies that the sum of our expected welfare to infinity remains finite, solving the paradox of having to compare different infinite values in optimal growth/conservation theories. (shrink)