Moore designed his pinball machine to supplement an analogy with Turing machine. The initial position of Pinball represents data on the tape given to the Turing machine. Most importantly (and unrealistically), the player must be able to adapt the initial location of the ball with infinite precision, which means that determining the location of the ball requires a number with an endless procession of digits after a decimal point. Only in such a number Moore could encode the infinitely long Turing tape.
Then the bumper system directs the ball to modern positions in a way that corresponds to reading and writing on Turing Machine tape. Some curved bumpers change the tape one way, thanks to which the data stored in distant decimal places are more significant in a manner resembling tumultuous systems, while the contrary curved bumpers perform the reverse. The ball outing from the bottom of the box means the end of the calculations, with the final place as a result.
Moore has equipped his configuration of a pinball machine with a computer flexibility – one bumper system can calculate the first thousands of PI digits, and another can calculate the best next move in chess game. But by doing so, he also gave it an attribute, which we usually do not associate with computers: unpredictability.
Some algorithms stop by displaying the result. But others last forever. (Consider a program whose task is to print the final number Pi.) Is there a procedure, asked which can examine any program and determine if it will stop? This question became known as the problem of stopping.
Turing has shown that such a procedure does not exist, considering what it means if it was so. If one machine could predict the behavior of the other, you can easily modify the first machine – the one that predicts behavior – to act forever when the second machine stops. And vice versa: it stops when the second machine works forever. Then-and here is a playing part-imagined passing to the description of this improved prognostic machine. If the machine stops, it also works forever. And if it works forever, it also stops. Since no option can be, summed up the Turing, the prognostic machine itself can exist.
(His discovery was closely related to a breakthrough result from 1931, when the logic Kurt Gödel developed a similar way Feeding of an autoreferential paradox in a strict mathematical framework. Gödel has proved that there are mathematical statements that cannot be determined).
In compact, Turing has proved that the solution to the problem of stopping was impossible. The only general way to find out if the algorithm stops is to run it as long as possible. If it ends, you have the answer. But if so, you will never find out if it really works forever or whether it would stop if you just waited a little longer.
“We know that there are such initial states that we cannot predict in advance what it will do,” said Wolpert.
From Moore designed his box To imitate any Turing machine, it can also behave in an unpredictable way. The ball output means the end of the calculations, so the question is whether any specific bumper system will stop the ball or direct it to the exit, it must also be dissatisfied. “Really, every question about the long-term dynamics of these more complex maps is unjustified,” said Moore.