Universe is infinite large, how to build an infinite society?

A system measured large in one system can be measured small in another system. For example, universe is not as important as earth for human beings. So, in society, expected happiness for universe can be smaller than expected happiness for earth. Universe is infinite when measured by expected negative action; society is infinite when measured by expected happiness; research is infinite when measured by expected knowledge.

In universe, a particle can not reach a border. In a perfect pursuit system, every pursuer's speed has upper limit c, which is the speed for electromagnetic field to propagate, so that any two pursuers can exchange with each other(or field could not catch up with pursuer). From Feedback mechanism and three principles, this is a good method to get larger feedback of negative action.

From Theorem 4 in "Axioms and Theorems for a Perfect Pursuit System", a perfect pursuit system keeps expanding. Suppose the speed is a constant H(Hubble constant in physics). For two pursuers with distance R, the distance grows at the speed HR. So c must be larger than HR to ensure that any two pursuers can exchange with each other(electromagnetic field from a particle can reach particles at the border of universe). On the other hand, c must be smaller than HR so that field will not propagate out of the pursuit system(light will not propagate out of universe). So c must equals to HR.

So, if society develops and is measured by expected happiness, and information is propagated to pursue happiness the best, then radius of society will be infinite when measured by information propagation. The society measured in this way will expand with invariant life time 1/H, similar to universe.

Mathematics is Relative relation

More generally, any relation between two quantities is relative.

When two quantities are continuous relative to each other, it is called relative continuity. In fact, continuity and discrete is always relative. Any quantity can be continuous or discrete if its relative quantity is chosen correctly. For example, space continuity and field propagation continuity are relative continuity, but continuity of space and continuity of economic market are not relative continuity.

When we say ˇ°a large quantityˇ°, we must appoint a method to measure the quantity. Expected negative action is not the unique way to measure the scale of a pursuit system. For the same reason, developing velocity, system expansion in unit time, is not the unique way to measure development.

A quantity can be measured as any function if measured correctly.

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