Predictably Irrational Predictably Irrational Predictably Irrational: The Hidden Forces That Shape Our Decisions is a 2008 book by Dan Ariely, in which he challenges readers' assumptions about making decisions based on rational thought. Ariely explains, "My goal, by the end of this book, is to help you fundamentally rethink what makes you and the people around you tick. I hope to lead you there by presenting a wide range of scientific experiments, findings, and anecdotes that are in many cases quite amusing. Once you see how systematic certain mistakes are—how we repeat them again and again—I think you will begin to learn
Irrational rotation between the additive and multiplicative notations is the group isomorphism It can be shown that is an isometry. There is a strong distinction in circle rotations that depends on whether is rational or irrational. Rational rotations are less interesting examples of dynamical systems because if formula_4 and formula_5, then formula_6 when formula_7. It can also be shown that formula_8 when formula_9. Irrational rotations form a fundamental example in the theory of dynamical systems. According to the Denjoy theorem, every orientation-preserving -diffeomorphism of the circle with an irrational rotation number is topologically conjugate to . An irrational rotation is a measure-preserving