What Is Computable?
—RICHARD FEYNMAN (1965 Nobel Prize in physics)
We've now seen quite a number of clever, powerful, and beautiful algorithms—algorithms that turn the bare metal of a computer into a genius at your fingertips. In fact, it would be natural to wonder, based on the rhapsodic rhetoric in the preceding chapters, if there is anything that computers cannot do for us. The answer is absolutely clear if we limit ourselves to what computers can do today: there are plenty of useful tasks (mostly involving some form of artificial intelligence) that computers can't, at present, perform well. Examples include high-quality translation between languages like English and Chinese, ...