"In the past two centuries, we have witnessed an unparalleled expansion in scientific and technical horizons. But with our longer view of things, the horizon is now interrupted, here and there, by walls. With our newfound knowledge and technical abilities has come an understanding of the limitations of science and technology. Beyond Reason provides a mind-bending exploration not into what is doable and knowable - but what is undoable and unknowable." "Temporary barriers to understanding are sometimes swept away by knowledge, each advance revealing new vistas. But some barriers appear to be permanent. Author A. K. Dewdney explores these grand limitations that stand like granite walls around our scientific and technological enterprise. These are not the barriers of ignorance, but knowledge. It is perhaps only ignorance that prevents us from traveling through time; certainly no theory yet prohibits the possibility. Yet the presence of chaos in our atmospheric system implies rather strongly that we shall never predict the weather much better than we do now." "Beyond Reason explores these barriers and the theories that give them form and substance. We shall apparently never travel faster than the speed of light, nor shall we ever build a perpetual motion machine that performs useful work. After laying the foundations of each theory, illuminated by stories of the scientists who discovered them, A. K. Dewdney then goes on to ask "What if?" Is there a way out? Are there no secret passages through these walls?"--BOOK JACKET.… (more)
Introduction -- Where Reason Cannot Go -- We all live with limitations -- some natural, some rule-based. We cannot fly unaided, nor can we beat the ace of spades with the deuce. This book is about the grander limitations that stand like granite walls around our scientific and technological enterprise. "This far and no farther," they seem to say, an ancient prohibition from sacred ground. I locate these barriers "beyond reason" because reason, even though it found them, sees no way around them.
Unless and until we stumble upon a completely new paradigm for what it means to compute, many of our more important problems will be solved only by forcing them through the big-O bottleneck. The bottleneck, like the other barriers to knowledge or action in this book, challenges us to the very limits of our competence. Will we ever break through? Don't bet on it.