Populations are ageing because people live longer and because families are smaller, and the second of these matters more than the first. A country where each generation is smaller than the last will have a high proportion of older people even if nobody's lifespan changes at all. This is why the transition is not reversible by improving health: healthier old age is desirable in itself, but the shape of the population is set by births that happened decades ago. Demographers have known the arithmetic for years; the politics of it are newer.