This Element presents the usual material taught in a yearlong course of theoretical computer science using the intuitive language and methodology of category theory. Perfect for students or professionals working in computers or physics, or mathematics.
Many books explain what is known about the universe, but this work investigates what cannot be known. It studies the limits of science, mathematics, and reason, focusing on what cannot be predicted, described, or understood. The author considers the limitations of computers, physics, logic, and human thought processes. He highlights tasks that would take computers trillions of centuries to complete and problems they can never solve, as well as perfectly formed English sentences that lack meaning. The exploration includes different levels of infinity, the peculiarities of quantum mechanics, the implications of relativity theory, chaos theory, and math problems unsolvable by conventional methods. Yanofsky also addresses true statements that cannot be proven and the limitations of our intuitions regarding space, time, and motion. By moving from concrete examples to abstract concepts, he uncovers a variety of unsolvable problems and paradoxes. He reveals that many limitations share a common pattern, suggesting that by examining these patterns, we can gain insight into the structure and limitations of reason itself. Yanofsky even attempts to look beyond the confines of reason to explore what may lie beyond.