{"id":14660,"date":"2025-04-06T12:05:48","date_gmt":"2025-04-06T12:05:48","guid":{"rendered":"https:\/\/topat10.com\/?p=14660"},"modified":"2025-04-06T12:05:48","modified_gmt":"2025-04-06T12:05:48","slug":"scientists-are-mapping-the-boundaries-of-what-is-knowable-and-unknowable","status":"publish","type":"post","link":"https:\/\/topat10.com\/?p=14660","title":{"rendered":"Scientists Are Mapping the Boundaries of What Is Knowable and Unknowable"},"content":{"rendered":"


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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\u2019s starting location with infinite precision, meaning that specifying the ball\u2019s 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.<\/p>\n

Then the arrangement of bumpers steers the ball to new positions in a way that corresponds to reading and writing on some Turing machine\u2019s 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\u2019s exit from the bottom of the box marks the end of the computation, with the final location as the result.<\/p>\n

Moore equipped his pinball machine setup with the flexibility of a computer\u2014one arrangement of bumpers might calculate the first thousand digits of pi, and another might compute the best next move in a game of chess. But in doing so, he also infused it with an attribute that we might not typically associate with computers: unpredictability.<\/p>\n

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