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Why do grandmothers exist?

The question is not as unfeeling as it sounds.

From the point of view of the selfish gene, creatures are supposed to drop dead as soon as they lose the power to reproduce. A man can make babies his whole life, even if the sperm of his old age lacks vigor and genetic fidelity. A woman outlives her eggs by about 20 years, which almost no other female mammals do. (Only female killer and pilot whales and orcas are known to last as long after the end of their menstrual cycles.)