Nornagest comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 116 - Less Wrong Discussion
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Elevating all of mankind to a posthuman level will be difficult. He'll have to use the Stone around twice per second.
Perhaps he could use some kind of portkey system, where portkeys are set to take people to the Stone and then immediately away, and you need to use transfiguration right before that.
Indeed, one of the stories at qntm features discovering something like the Fountain of Youth, and describes the organizational nightmare of letting a large enough proportion of mankind use it.
Harry Potter, however, if he makes himself immortal, will have a lot of time. Even if a lot of people die of old age or illness before he can reach them, he can still reach a lot of people given enough time. He would also need to figure out some efficient way of space travel and terraforming, otherwise he could cause overpopulation.