This paper takes an integrated history and philosophy of science approach to the topic of "simplicity out of complexity". The reflex theory was a framework within early twentieth century psychology and neuroscience which aimed to decompose complex behaviours and neural responses into simple reflexes. It was controversial in its time, and did not live up to its own theoretical and empirical ambitions. Examination of this episode poses important questions about the limitations of simplifying strategies, and the relationship between simplification and (...) the engineering approach to biology. (shrink)