Many books explain what is kwn about the universe. This book investigates what cant be kwn. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cant be revealed. In The Outer Limits of Reason, Noson Yafsky considers what cant be predicted, described, or kwn, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yafsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cant be solved by rmal means; and statements that are true but cant be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the kwer and the kwn. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yafsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our kwledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yafsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Noson S. Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City University of New York. He is a coauthor of Quantum Computing for Computer Scientists.
Winner of PROSE Awards: Popular Science & Popular Mathematics 2013.