might think that we could find a Turing machine to churn out all the successive digits, 3, 1, 4, 1, 5, 9, . . ., of the above expansion for π one after the other on the output tape, where we simply allow the machine to run on forever. But this is not allowed for a Turing machine. We must wait for the machine to halt (indicated by the bell ringing!) before we are allowed to examine the output.
