Chapter 1 Reason and Belief
Human beings have all sorts of beliefs. The way in which they arrive at them varies from reasoned argument to blind faith. Some beliefs are based on personal experience, others on education, and others on indoctrination. Many beliefs are no doubt innate: we are born with them as a result of evolutionary factors. Some beliefs we feel we can justify, others we hold because of "gut feelings."
Obviously many of our beliefs are wrong, either because they are incoherent, or because they conflict with other beliefs, or with the facts. Two and a half thousand years ago, in ancient Greece, the first systematic attempt was made to establish some sort of common grounds for belief. The Greek philosophers sought a means to formalize human reasoning by providing unassailable rules of logical deduction. By adhering to agreed procedures of rational argument, these philosophers hoped to remove the muddle, misunderstanding, and dispute that so characterize human affairs. The ultimate goal of this scheme was to arrive at a set of assumptions, or axioms, which all reasonable men and women would accept, and from which the resolution of all conflicts would flow.
It has to be said that this goal has never been attained, even if it were possible. The modern world is plagued by a greater diversity of beliefs than ever, many of them eccentric or even dangerous, and rational argument is regarded by a lot of ordinary people as pointless sophistry. Only in science, and especially mathematics, have the ideals of the Greek philosophers been upheld (and in philosophy itself, of course). When it comes to addressing the really deep issues of existence, such as the origin and meaning of the universe, the place of human beings in the world, and the structure and organization of nature, there is a strong temptation to retreat into unreasoned belief. Even scientists are not immune from this. Yet there is a long and respectable history of attempts to confront such issues by rational and dispassionate analysis. Just how far can reasoned argument take us? Can we really hope to answer the ultimate questions of existence through science and rational inquiry, or will we always encounter impenetrable mystery at some stage? And just what is human rationality anyway?
The Scientific Miracle
Throughout the ages all cultures have extolled the beauty, majesty, and ingenuity of the physical universe. It is only the modern scientific culture, however, that has made any systematic attempt to study the nature of the universe and our place within it. The success of the scientific method at unlocking the secrets of nature is so dazzling it can blind us to the greatest scientific miracle of all: science works. Scientists themselves normally take it for granted that we live in a rational, ordered cosmos subject to precise laws that can be uncovered by human reasoning. Yet why this should be so remains a tantalizing mystery. Why should human beings have the ability to discover and understand the principles on which the universe runs?
In recent years more and more scientists and philosophers have begun to study this puzzle. Is our success in explaining the world using science and mathematics just a lucky fluke, or is it inevitable that biological organisms that have emerged from the cosmic order should reflect that order in their cognitive capabilities? Is the spectacular progress of our science just an incidental quirk of history, or does it point to a deep and meaningful resonance between the human mind and the underlying organization of the natural world?
Four hundred years ago science came into conflict with religion because it seemed to threaten Mankind's cozy place within a purpose-built cosmos designed by God. The revolution begun by Copernicus and finished by Darwin had the effect of marginalizing, even trivializing, human beings. People were no longer cast at the center of the great scheme, but were relegated to an incidental and seemingly pointless role in an indifferent cosmic drama, like unscripted extras that have accidentally stumbled onto a vast movie set. This existentialist ethos -- that there is no significance in human life beyond what humans themselves invest in it -- has become the leitmotif of science. It is for this reason that ordinary people see science as threatening and debasing: it has alienated them from the universe in which they live.
In the chapters that follow I shall present a completely different view of science. Far from exposing human beings as incidental products of blind physical forces, science suggests that the existence of conscious organisms is a fundamental feature of the universe. We have been written into the laws of nature in a deep and, I believe, meaningful way. Nor do I regard science as an alienating activity. Far from it. Science is a noble and enriching quest that helps us to make sense of the world in an objective and methodical manner. It does not deny a meaning behind existence. On the contrary. As I have stressed, the fact that science Works, and works so well, points to something profoundly significant about the organization of the cosmos. Any attempt to understand the nature of reality and the place of human beings in the universe must proceed from a sound scientific base. Science is not, of course, the only scheme of thought to command our attention. Religion flourishes even in our so-called scientific age. But as Einstein once remarked, religion without science is lame.
The scientific quest is a journey into the unknown. Each advance brings new and unexpected discoveries, and challenges our minds with unusual and sometimes difficult concepts. But through it all runs the familiar thread of rationality and order. We shall see that this cosmic order is underpinned by definite mathematical laws that interweave each other to form a subtle and harmonious unity. The laws are possessed of an elegant simplicity, and have often commended themselves to scientists on grounds of beauty alone. Yet these same simple laws permit matter and energy to self-organize into an enormous variety of complex states, including those that have the quality of consciousness, and can in turn reflect upon the very cosmic order that has produced them.
Among the more ambitious goals of such reflection is the possibility that we might be able to formulate a "Theory of Everything" -- a complete description of the world in terms of a closed system of logical truths. The search for such a TOE has become something of a holy grail for physicists. And the idea is undoubtedly beguiling. After all, if the universe is a manifestation of rational order, then we might be able to deduce the nature of the world from "pure thought" alone, without the need for observation or experiment. Most scientists reject this philosophy utterly, of course, hailing the empirical route to knowledge as the only dependable path. But as we shall see, the demands of rationality and logic certainly do impose at least some restrictions on the sort of world that we can know. On the other hand, that same logical structure contains within itself its own paradoxical limitations that ensure we can never grasp the totality of existence from deduction alone.
History has thrown up many physical images for the underlying rational order of the world: the universe as a manifestation of perfect geometrical forms, as a living organism, as a vast clockwork mechanism, and, most recently, as a gigantic computer. All of these images capture some key aspect of reality, though each is incomplete on its own. We shall examine some of the latest thinking about these metaphors, and the nature of the mathematics that describes them. This will lead us to confront the questions: What is mathematics? And why does it work so well in describing the laws of nature? And where do these laws come from anyway? In m