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Human societies are collective brains. People within every society have cultural brains—brains that have evolved to selectively seek out adaptive knowledge and socially transmit solutions. Innovations emerge at a population level through the transmission of serendipitous mistakes, incremental improvements and novel recombinations. The rate of innovation through these mechanisms is a function of (1) a society's size and interconnectedness (sociality), which affects the number of models available for learning; (2) fidelity of information transmission, which affects how much information is lost during social learning; and (3) cultural trait diversity, which affects the range of possible solutions available for recombination. In general, and perhaps surprisingly, all three levers can increase and harm innovation by creating challenges around coordination, conformity and communication. Here, we focus on the ‘paradox of …