Exploring mathematical paradoxes, this work delves into the complexities of mathematical expectation and its surprising contradictions. It encourages readers to rethink the validity of these applications, requiring only basic algebra. Key topics include risk and aversion in decision-making, envelope problems, Parrondo's paradox, issues of imperfect recall, non-zero-sum games, Newcomb's paradox, and the application of Benford's law in computer design and fraud detection.
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.