This chapter interprets the myth of Oedipus in light of interpersonal neurobiology and second-order cybernetics, where observers are self-referentially implicated within the observed. The riddle of the Sphinx, “What walks on four legs in the morning, two legs at noon, and three legs in the evening?” is understood as a paradox of self-reference in apparent contradiction with all known laws of science. From a developmental perspective, traumatic residues from King Laius’ attempted infanticide uniquely prepare Oedipus to solve the Sphinx’s riddle. Oedipus’ capacity for full self-reference is equated with the operation of the most powerful universal Turing machine with both implicit and explicit memory of its past. That Oedipus could move beyond literal thought to interpret morning, noon, and evening as stages of human life proves pivotal. Oedipus’ use of metaphor and abstraction to solve a paradox of self-reference signals humankind’s transition to greater levels of internal complexity, including more fully self-reflective consciousness.