As Tony Gardiner says in at the beginning of this book, "the last ten years or so has seen a remarkable blossoming of public interest in mathematics [but] most of the books produced have been for adults, rather than for students. Moreover, most are in prose format - for those who want to 'read about' mathematics, rather than those who want to get their hands dirty solving problems."
If you watch a steam engine, you may not know how it works but you can soon get a fairly good idea of its behaviour, and you can predict its future behaviour accurately. Even though you don't understand its workings, you can see it's a pretty simple machine, so you can trust it to behave in a simple way: you have confidence in your predictions based on a short sample of its behaviour.
This book attempts to take a firm grip on a corner of the slippery issue of consciousness. It is directly related to Roger Penrose's earlier, hugely successful work, The Emperor's New Mind. Although much space is devoted to painstaking replies to the criticisms made of the earlier book, this is not simply a sequel. It contains a number of new ideas, some of which are still being actively debated seven years after the book was first published.
Research on the Universe leads to many such startling conclusions and this book attempts to describe some of the surprising phenomena which occupy astronomers and cosmologists. Our Universe, Martin Rees' laboratory, allows its natural laws to be cleverly interpreted at arm's length, by observing the 'extreme' physics which we could never replicate in a laboratory. The biggest questions have an almost philosophical tenor.
What is the nature of the universe that we live in? This is a question that has exercised philosophers and scientists for as long as people have been able to think. Almost everyone has asked it at one time or another, in one form or another. It is hard to imagine a more fundamental question.
Ever since Watson and Crick worked out the double helix structure of DNA in 1953, the role of genetics in biology has grown and grown. Genetic determinism - the belief that we are controlled by our genes and that no other factor is significant - is now all-pervasive.
Over the last decade, the discipline of neuropsychology has shed light on many aspects of human thought. Brain scans, carefully structured behavioural experiments, and the study of individuals who have suffered brain damage, have taught us much about which abilities are native to humans and which learned; which abilities can be lost and what happens when they are.
"I am certain, absolutely certain that...these theories will be recognized as fundamental at some point in the future." Sophus Lie said these words more than hundred years ago. We know now that he was right, absolutely right. The notions of "Lie groups" and "Lie algebras" are in the vocabulary of every mathematician and physicist today. Lie's theories are indispensable tools for understanding the physical laws of Nature.
ver the last hundred years, human understanding of the nature of the universe has expanded at a mind-boggling rate; and over the last forty, Kip Thorne, along with Stephen Hawking, who wrote the foreword to this book, have been among the group of people shining most light into the darkness. But, aware that his research is carried out on behalf of us all, Thorne has not neglected the task of explaining its results to the rest of us.