Moore designed his pinball machine to complete the analogy with the Turing machine. The starting position of the pinball machine represents the data on the tape integrated into the Turing machine. Especially (and unrealistic), the player must be able to adjust the starting location of the ball with infinite precision, which means that the specification of the location of the ball requires a number with an endless figures after the decimal point. It is only in such a number that Moore could code data from an infinitely long turing band.
Then, the arrangement of bumpers directs the ball towards new positions in a way that corresponds to reading and writing on a band of Turing machine. Some curved bumpers move the band in one direction, which makes data stored in more significant distant decimals in a way recalling chaotic systems, while opposite curved bumpers make the opposite. The output of the ball at the bottom of the box marks the end of the calculation, with the final location accordingly.
Moore has equipped its pinball configuration with the flexibility of a computer – an arrangement of bumper could calculate the first thousand pi figures, and another could calculate the best movement in a game of chess. But in doing so, it also allowed it to an attribute that we could not generally associate with computers: unpredictability.
Some algorithms stop, generating a result. But others run forever. (Consider a program responsible for printing the final PI figure.) Is there a procedure, asked Turing, who can examine any program and determine if he stops? This question has become known as a stop problem.
Turing has shown that no procedure of this type exists by considering what it would mean if it did. If a machine could predict the behavior of another, you can easily change the first machine – the one that predicts behavior – to run forever when the other machine stops. And vice versa: it stops when the other machine works forever. Then, and here is the part that weighs the mind – following the imagination of a description of this predicted machine modified in itself. If the machine stops, it also works forever. And if it works forever, it also stops. Since none of the options can be, Turing has concluded, the prediction machine itself should not exist.
(His conclusion was intimately linked to a revolutionary result of 1931, when the logician Kurt Gödel developed a similar way of Feed an auto-referential paradox in a rigorous mathematical framework. Gödel has proven that mathematical declarations exist, the truth of which cannot be established.)
In short, Turing has proven that the resolution of the stop problem was impossible. The only general way to know if an algorithm stops is to execute it for as long as possible. If it stops, you have your answer. But if this is not the case, you will never know if it really works forever, or if it would have stopped if you had waited a little longer.
“We know that there are these kinds of initial states that we cannot predict what it will do in advance,” said Wolpert.
From Moore had designed his box To imitate any Turing machine, it could also behave unpredictable. The release of the ball marks the end of a calculation, so that the question of whether a particular arrangement of bumper will trample the ball or direct it towards the exit must also be undecidable. “Really, any question about the long -term dynamics of these more elaborate cards is undecidable,” said Moore.