Moore has designed its battery to complete the same with the Turing machine. Pinball's starting position represents the data on the tape that is put into the turing machine. In particular (and unrealistic), players must be able to adjust the starting position of the ball with infinite accuracy, which means that the location of the ball requires a number with an endless procession after the decimal point. Only in such a number, Moore can encrypt the data of an infinite long tape.
After that, the arrangement of the ball to the new positions in the way corresponds to the reading and writing on some tape of the turing machine. Some of the curved cars are certain to change the tape, making the data stored in distant decimal positions are more meaningful in the way that reminds of chaotic systems, while the bumpers are the opposite. The exit of the ball from the bottom of the box marks the end of the calculation, with the final position is the result.
Moore has equipped its Pinball machine with the flexibility of the computer, once the arrangement of the car can calculate the first thousands of Pi's first digits and another letter that can calculate the best step in a chess game. But when doing so, he also transmitted it to an attribute that we often do not link to the computer: Unpredictable.
Some algorithms stop, output a result. But others run forever. (Consider a program assigned to print Pi's last digit.) Is there any procedure, Turing ask, which can check any program and determine whether it will stop? This question is called a pause issue.
Turing shows that there is no such procedure that exists by considering its meaning if it has done. If a machine can predict the behavior of another machine, you can easily modify the first machine, a behavior prediction machine to run forever when another machine stops. And vice versa: it stops when another machine runs forever. Then, and this is the bend of the mind, imagine the feeding of a description of this adjusted prediction machine into itself. If the device stops, it also runs forever. And if it runs forever, it stops. Because no options can, Turing concluded, the machine itself predicted not to exist.
. Feed a self -reference paradox into a strict math frame. Gödel has proven that mathematical claims exist that the truth cannot be set.)
In short, Turing proved that the problem of temporary suspension was impossible. The only common way to know if an algorithm stops is to run it as long as possible. If it stops, you have your answer. But if not, you will never know whether it really runs forever or whether it stops if you just wait a bit longer.
We know that there are initial states that we cannot predict what it will do, Mr. Wol Wolpert said.
From Moore designed his box To imitate any turing machine, it can also behave in unpredictable ways. The exit of the ball marks the end of a calculation, so the question of whether there is any specific arrangement of the blocker will trap the ball or direct it to the exit can not be resolved. In fact, any questions about the long -term motivation of these more complex maps are not solved, Mr. Moore Moore said.