Well, more food obviously lets you have more people. But it also lets those people stop worrying about where their next meal is coming from, freeing them up to start worrying about different, more productive things: why stars seem to move across the sky or how come things fall down instead of up. Farming also formalizes the idea of an economy in your civilization, since now farmers can regularly trade their food with others. With an economy comes specialization: instead of each human having to do everything necessary to survive (or splitting it among a family group), now someone who’s
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