If you were an acolyte (novice, student, whatever) at the Citadel, which three links would you first want to forge for your chain? Does the order matter? Do your choices reflect a desire to work with particular archmaesters? In the books, I'm not sure students get to choose - do the archmaesters decide who studies what at any given time? But let's assume you have a choice. Or would you rather be an alchemist? From the wiki: Maybe we need to speculate about the likely meanin