The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us

Rather than write about what he knows, Yanofsky (Quantum Computing for Computer Scientists) prefers to explore the topic of what he doesn't know%E2%80%94or rather what we as humans cannot know. In this refreshingly original and ambitious philosophical inquiry, he attempts to map the limitations of human reason by examining the established conundrums, paradoxes, impossibilities within science and technology. Divided by subject area (including language, philosophy, science, mathematics, computing), each chapter lays out an array of paradoxes and unsolvable problems, clearly and concisely guiding readers into and around the worlds of reason. The examples range in complexity and some may be more familiar than others, such as his explanations of the Liar's Paradox, "this sentence is false." The more complicated contradictions, such as George Cantor's proof that an infinite set of numbers between 0 and 1 is vastly larger than an infinite set of natural numbers (1, 2, 3, 4 . . .), the author unpacks succinctly within the framework of modern life. He writes, "It would be foolhardy to cross a modern suspension bridge if you knew that the engineer did not believe in Cantor's work." Yanofsky takes on this mindboggling subject with confidence and impressive clarity. He eases the reader into the subject matter, ending each chapter with further readings. His book is a fascinating resource for anyone who seeks a better understanding of the world through the strangeness of its own limitations and a must-read for anyone studying information science. Illus. (Sept.)