In this classic work, one of the greatest mathematicians of the twentieth century explores the analogies between computing machines and the living human brain. John von Neumann, whose many contributions to science, mathematics, and engineering include the basic organizational framework at the heart of today's computers, concludes that the brain operates both digitally and analogically, but also has its own peculiar statistical language.

In his foreword to this new edition, Ray Kurzweil, a futurist famous in part for his own reflections on the relationship between technology and...