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Why did Liu Cixin write about the three-body problem?

The main reasons introduced in the book are as follows:

“The first element of civilization is survival.” Without the earth’s innately favorable living environment, the survival of the Trisolaran Galaxy has been enduring the chaos of the times. In the cruel alternation with the Eternal Era, there is always the danger of being destroyed. In order to survive, they must find a new home, and the earth, whose coordinates are exposed, becomes their first goal.

The Trisolaran Galaxy once had twelve planets, eleven of which were swallowed up by three suns. The last planet will also be swallowed up in 150 to 2 million years. After countless destructions and rebirths, the only way out for the Trisolaran civilization is to fly out of the Trisolaran galaxy and find a new home. Intercepting the earth's signals gave them the opportunity to begin the process of cosmic colonization. The use of the Trisolaran civilization surpassed human civilization. The scientific and technological means locked up the earth science, and monitored every move of everyone on the earth, obtaining all the information on the earth, and then dispatched the Trisolaran fleet to set out for the solar system in order to survive-invading the earth!