Scientists plan the limits of what is known and unknown

Moore designed the ball and pins to complete the measurement of the Torring machine. The place of the beginning of the ball and pins is the data on the tape that is fed in the Torring machine. Decally (and unrealistic), the player must be able to adjust the start of the ball with countless accuracy, which means that the location of the ball requires a number with an endless procession of numbers after the decimal point. Only in such a number, Moore can encrypt the long -term Turning strip data.

Then arrange the fenders directing the ball to new sites in a way that corresponds to reading and writing on the Torring machine tape. Some curved fenders turn the tape in one direction, which makes the data stored in ten days far more important in a way that reminds us of chaotic systems, while the curved bumps in the opposite do the opposite. The ball’s exit from the bottom of the box is the end of the account, with the final location as a result.

Moore has prepared the preparation of the ball and pins machine with computer flexibility – one may calculate the arrangement of the first thousand number of PI, and the last best step may be calculated in the chess game. But when doing this, he also installed it with features that we may not usually connect to computers: the inability to predict.

In prominent works in 1936, Alan Turing has identified the arithmetic boundaries by describing the main features of the global computing device, now known as the Torring machine.

Photo: Archive Generation/Albus Photo album

Some algorithms stop, and out of the result. But others run forever. (Consider a program in charge of printing the PI.) This question has become known as the problem of stopping.

Turning showed that there is no such procedure by looking at the meaning of this if it happens. If one of the device is able to predict another behavior, you can easily adjust the first device – the device that predicts the behavior – forever when the other machine stops. And the opposite is true: it stops when the other device is operated forever. After that-here is the part that bends the mind-imagine feeding a description of the predictive machine that has been modified itself. If the device stops, it also works forever. And if it works forever, it also stops. Since there can be no choice, there should be no prediction machine itself.

(His discovery was closely related to a pioneering result from 1931, when logic Kort Godel developed a similar method Feeding the self -reference paradox In a strict sports framework. Godel has proven that the sports data exists cannot be proven.)

In short, Turning has proven that the solution to the stopping problem is impossible. The only general way to see if the algorithm stops is running for as long as possible. If you stop, you have your answer. But if not, you will never know if he is really working forever, or whether it will stop if you have been waiting for a little longer.

“We know that there are these types of initial cases that we cannot predict early on what you will do,” said Wolbert.

since Moore designed his box To imitate any Torring machine, it can act in an unpredictable way. The ball’s director represents the end of the account, and therefore the issue of whether any specific arrangement of the fenders will wear the ball or direct it to the director must be not collapsed. “Really, any question about the long -term dynamics of these most detailed maps is not subject to healing,” Moore said.