In the field of computer science, everyone knows that this is an outstanding masterpiece of scientific popularization. It introduces many difficult theories in the fields of mathematical logic, computability theory, artificial intelligence and so on in a simple way with carefully designed clever strokes. However, when you read it, the first things that jump into your eyes are Eisele's famous paintings with strange ideas and Bach's well-known music scores. Finally, when you close the book, you will see "printed on the cover". (quoted by translator)

There is an unusual Canon in Bach's "Dedicated to Music", which is only marked with the words "Canon per Tonos". In this cannon, Bach gave us the first example of the concept of "strange circle". The so-called "strange circle" phenomenon is that when we go up (or down) through some levels of a certain level system (the system here is the tune of music), we accidentally find ourselves back to the starting point.

Aysil's paintings are usually based on mathematical principles, such as symmetry or patterns. How did he realize the "strange circle" phenomenon with his works? There are six independent stages in the working waterfall, and the water can flow endlessly. So the concept of "strange circle" implies an infinite concept. Isn't cycle a way to express endless process in a limited way? Off-topic: the visual illusion created by the works is our automatic elevation in consciousness.

In the example of Bach and Eisele's strange circle, there is an illusion between infinity and infinity, which gives people a strong sense of paradox.

The "strange circle" phenomenon in the mathematical system is transformed from an ancient paradox, which is the "liar paradox". Epiman Nittis, a Crete, once said an immortal sentence: "All Crete people are liars". This sentence can be divided into two declarative sentences:

Note: If 1 is true, it can be inferred that 2 is false. If 1 is false, it cannot be inferred that 2 is true.

The statement made by Epstein-Nittis grossly violates the dichotomy of dividing the statement into truth and falsehood, because if we assume that it is true, it will immediately produce an opposite result, which makes us think it is false. Conversely, if we assume that it is false, it will also produce an opposite result, which brings us back to the point that it must be true.

The "Epstein-Nitis Paradox" is a strange circle step by step, just like a gallery in Eisele.

Whether it is Epstein's Nitis Paradox, Russell Paradox or Eisele's Gallery, there is a common curse, that is, the strange circle phenomenon, or self-reference. For example:

If you look at it together, you will find it contradictory, but if you look at it separately, there is nothing wrong with these two sentences. This strange circle phenomenon cannot be attributed to any sentence, but to the way they "refer" to each other.

Existing problems:

How does 1. godel theorem eliminate these paradoxes?

2. How did it produce computers and artificial intelligence?

3.bach? Eisele? Godel?