While teaching how to implement FSMs using synchronous logical circuits, I noticed an intriguing coincidence: in both the theoretical CS world, and in the electrical engineering world, state is typically denoted $q$ (and the state space $Q$). I first asked on EE.sx, but then while researching a bit this topic, I found that even Turing's original 1936 paper uses $q_1..q_n$ to denote the states of the Turing machine. So I wonder: When does this convention go back to, and why would a state be denoted $q$ ? 
Why is the state of a FSM traditionally denoted $q$?
automata theory;ho.history overview
In his 1936 paper ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM, Alan Turing wrote : We may compare a man in the process of computing a real number to  machine which is only capable of a finite number of conditions q1, q2,  .... qR which will be called  m-configurationsSo he stressed the fact that the machine has a finite, discrete (not continuous) number of states or quantities. For me, it is a reference to the term Quanta used in physics to denote phenomena variating not continuously but by leaps or quanta. In his 1950 article Computing Machinery and Intelligence Alan Turing is more explicit about leaps speaking of sudden jumps: The digital computers considered in the last section may be  classified amongst the discrete-state machines. These are the  machines which move by sudden jumps or clicks from one quite definite  state to another.So I think that Alan Turing used q instead of s to denote a machine state to stress the fact that the state machine can be only in a set of discrete and finite values like the quanta in physics. And since then, the same notation is generally used.