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Iitakas philosophy claims that whenever we have a theorem for proper varieties,we should have a counter-theorem for open varieties.In this talk,I will introduce this philosophy with examples and evidence.Then I will report the recent progress on the theory of "log rational curves" on log pairs.As another piece of evidence of Iitakas philosophy,this theory generalizes the classical theory of rational curves on proper varieties.This is a joint work with Qile Chen.