Roth's theorem says that irrational real algebraic numbers have measure of irrationality 1. Modernity aimed towards "a progressive force promising to liberate humankind from ignorance and irrationality" . Madness herself sees the irrationality and senselessness in Hera's vengeance. Rorty begins this chapter by addressing critics who accuse him of irrationality and moral relativism. Chinese liberals such as Hu Shih often condemned the Boxers for their irrationality and barbarity. Below are listed some of these theories and their relation to rational irrationality. This atmosphere of apparently logical irrationality pervades the book. Dada rejected reason and logic, prizing nonsense, irrationality and intuition. Thus, even a rational investor may bank on others' irrationality. Dada rejected reason and logic, prizing nonsense, irrationality, and intuition. He challenged the dominant notion of crowd as site of irrationality and deindividuation. Dada works featured deliberate irrationality and the rejection of the prevailing standards of art. He put the emphasis on the irrationality of this sentiment. The Liouville numbers are precisely those numbers having infinite irrationality measure. A Liouville number is defined to have infinite measure of irrationality.