New Books In Mathematics

Math has a complicated relationship with the counterintuitive: Rigorous logic, calculation, and simulation can both help us wrap our minds around phenomena that defy our intuition, and thrust upon us whole new worlds of counterintuitive results. In his new book, Jim Stein introduces readers to several unexpected and sometimes astonishing examples, while demanding a minimal mathematical background. The Fate of Schrodinger's Cat: Using Math and Computers to Explore the Counterintuitive (World Scientific, 2020) takes the reader along a journey in three segments. The first, through only by-hand calculations, builds up to a variation on Schrödinger's notorious thought experiment in which an observer can use an unrelated random process to predict the outcome of a 50/50 trial more than half the time. The kernel of this setup is Blackwell's Bet, a simple yet extraordinary illustration of what Stein calls "probabilistic entanglement". The second section uses computer simulation to get a handle on several paradoxical e