What are the limits to what a computer can do? Must all computers be composed of Boolean logic and registers, or might there be other kinds, even more powerful? These questions take us to the most philosophically interesting topics in this book: Turing machines, computability, chaotic systems, Goedel’s incompleteness theorem, and quantum computing—topics at the center of most discussions about what computers can and cannot do.
Because computers can do some things that seem very much like human thinking, people often worry that they threaten our unique position as rational beings, and there are some who seek reassurance in mathematical proofs of the limits of computers. There have been analogous controversies in human history. It was once considered important that the Earth be at the center of the universe, and our imagined position at the center was emblematic of our worth. The discovery that we occupied no central position—that our planet was just one of a number of planets in orbit around the Sun—was deeply disturbing to many people at the time, and the philosophical implications of astronomy became a topic of heated debate. A similar controversy arose over evolutionary theory, which also appeared as a threat to humankind’s uniqueness. At the root of these earlier philosophical crises was a misplaced judgment of the source of human worth. I am convinced that most of the current philosophical discussions about the limits of computers are based on a similar misjudgment.