All sciences. №1, 2023. International Scientific Journal

Even more surprising is that some similar systems can be created in others, so in the game "Life" itself, you can create a Turing machine in which the game "Life" is already running. David Hilbert's dream of completeness has really come true in modern computing machines. And for him the main idea was: "We need to know, and we will know," but unfortunately, the truth is that we can't know, but in trying to figure it out, we discover new things by changing our world around us, for example, Turing implemented his ideas during World War II, anticipating the algorithm of the Enigma machine of fascist Germany according to some estimates, this brought the end of the war by 2-4 years.

After the war, Turing and John von Neumann created the first programmable computer "Eniac", based on Turing's developments, although, unfortunately, he did not live up to these days. But he changed our world, he is called the most influential figure in the cybernetic world, all his ideas still work in any computer, but they arose as a result of the thought of the Turing machine, and this already needs to be said thanks to Hilbert and his questions about the solvability of mathematics, so Turing decoders and the entire computer industry are fruits amazing paradoxes in mathematics.

Therefore, there is a weak spot in the foundation of mathematics to this day, because of which it is impossible to know everything for sure and there will be statements that cannot be proved, this circumstance could drive mathematicians crazy and lead to the collapse of the discipline, but surprisingly attempts to solve this problem changed our idea of infinity, turned the course of the world War and helped to create devices that contribute to the development of technology today.

And although this is true, it still serves as an even better sign and hint for all living and thinking, but rather a statement that we need to go further, try to develop, even though the ideal is unattainable.…

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