How to Understand the Mathematical Basis of Two Basic Types of Computational Behavior

What is it about?

The method steps are as follows: On the basis of Lvs’ research on continuum hypothesis, a new theory of natural number and real number coding is proposed. Between natural numbers and real numbers, it is also possible to construct an infinite number of hierarchical topology numbers with different sizes. They are all infinite sequences of incompleteness. Then, it analyzes the calculation behavior of the Turing machine as a complete sequence, and defines a new Gödel machine, which is the computational behavior on the incomplete sequence. Next, it is illustrated that the neural network and quantum computing are Gödel machines. The result is the discovery that an interesting finding is that quantum mechanical description of the trajectory of electrons and the internal connection state of neural networks are similar or isomorphic with the topological number structure of real continuums, and are related to the choice of set theory of axiom.

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Why is it important?

The significance lies in: it proves that Lv derives two basic types of computational behavior from the most basic mathematical principles: the Turing machine and the Gödel machine. This may have some inspiring new ideas for the future research of artificial intelligence.

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