Scientists Are Mapping the Boundaries of What Is Knowable and Unknowable

Moore designed his pinball machine to complete the analogy to the Turing machine. The starting position of the pinball represents the data on the tape being fed into the Turing machine. Crucially (and unrealistically), the player must be able to adjust the ball’s starting location with infinite precision, meaning that specifying the ball’s location requires a number with an endless procession of numerals after the decimal point. Only in such a number could Moore encode the data of an infinitely long Turing tape. Then the arrangement of bumpers steers the ball to new positions in a way that corresponds to reading and writing on some Turing machine’s tape. Certain curved bumpers shift the tape one way, making the data stored in distant decimal places more significant in a way reminiscent of chaotic systems, while oppositely curved bumpers do the reverse. The ball’s exit from the bottom of the box marks the end of the computation, with the final location as the result. Moore equipped hi ... Read full article.