ABSTRACT
This book was intended to be entirely about information and computation. More precisely it was intended to focus on large scale synthetic collections of such things in one particular system, that being the World Wide Web. The reason for this was exclusively to investigate the nature of the Web and to speculate on the underlying causes behind its various macro-level behaviours. This led us straight to the door of modern mathematics and physics to provide a comparison between the behaviours we see and understand in the everyday world and those now apparent on the man-made creation we have come to know as ‘the Web’. By doing this we actually had to be ambitious and reach beyond the Web to think about the possibility of there being fundamental laws which underlie the very notions of information and computation, perhaps even to enquire about the very stuff of digital physics itself. So the core themes of this book might appear straightforward, as being information, computing, mathematics and physics, nothing more, nothing less. But a further and unavoidable theme has been implicit throughout the text and this is all to do with language. The very notion of digital physics, the idea that the universe and everything within it might be forged from nothing more than raw information, is intrinsically dependent upon the notion of language. We are not talking about any natural language spoken by the human tongue, however. Rather we are referring to the type of language that can accurately capture the intricacies of the universe in such a way that it affords rigorous testing and absolute proof wherever possible. This may appear to be a contradiction, as we have already just stated that mathematics is a core theme of this book. But a contradiction it is not. Mathematics is both a tool with which we can probe the problems that interest us and the crucial mechanism needed to describe our findings once such probing is over. This book has primarily focused on mathematics as a tool and not as a language, but as a language its properties are particularly special. It is, literally, the binding that holds information and computation together, thereby
turning the sum of their parts into something greater than their whole. It allows us to turn the raw units and connections we discern through observation and experience – the gibbering abstract nonsense of individual bits, bytes, quarks or whatever other fundamental ‘dust’ the universe might, or might not, be made from – and turn them into communicable concepts that we can understand and trust. It is the glue that holds together the very essence of the reality we perceive and believe to be true. It is the bridge that can lead humankind from absolute nothingness to high enlightenment. And the only thing that will stop us from reaching such enlightenment will ultimately come entirely from within. The limits of our talents and the capabilities of the, no doubt, awesome computing devices we will produce in the future will be the only things holding us back. Such limits will be frustratingly finite whereas the limits of mathematics and the computational capabilities it describes may indeed flex close to infinity. For such reasons we should treat the concepts of information, computation and the very nature of universe itself with equal reverence, for in many ways they are one and the same thing.
