vol 2: Synopsis
part IV: Divine dynamics
page 30: Network
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... to restore theology to the mainstream of science
The transfinite network
[Further information relevant to this page is available at Immensity and Transfinite network]
We can imagine any organisation as a filing system and a set of processes for updating the files. This businesslike idea is here expanded, using Cantor's theory of transfinite cardinal and ordinal numbers, into an infinite abstract structure we call the transfinite network. We assemble a selection of the mathematical, physical and philosophical ideas developed so far into a model large enough to talk about God, but with sufficient finesse to deal with every detail of the world, no matter how small.
We are looking for a language or space to describe God. By God we mean here the whole. We can only imagine two constraints on the nature of God. The first is consistency. God must be consistent with itself. The second is size. Cantor's theorem shows us that a consistent symbolic system as large as the natural numbers will grow without limit into the transfinite cardinal and ordinal numbers. This space, we postulate, is large enough to begin to model God. Every point in it is represented by a unique number, that is, a unique ordered set, or ordered set of ordered sets, of whatever symbols we choose to use to represent the natural numbers.
Transitions from point to point are made by reordering sets, that is by permutations. Permutations are performed by computers. Turing, one of the inventors of the computer, envisaged two types of machine which he called a (for automatic) machines and o (for oracle) machines. A-machines are deterministic, in the sense that once they are started they follow a definite course until they either halt (if their initial configuration is computable) or not (if the initial configuration is not computable).
O-machines, on the other hand, go through a certain number of steps until they come to a point where they consult an 'oracle', which tells them what to do next. In modern terms, we would call them network machines. One would expect an o-machine to be more powerful than an a-machine since it has the oracle to help it. The machines populating the transfinite network are o-machines. Most real computers are o-machines. My computer spends most of its time doing nothing, waiting for me to input another keystroke. The user is the oracle.
Since the transfinite network is taken as a model of the whole universe, every o-machine within it has, in principle, the ability to consult all the other machines, and can thus tap the power of the whole network. This is the first step in a recursive process, since we can imagine that once each machine has learnt everything all the others have to teach it, this new generation of more powerful machines can begin another round of consultation. And so on without end.
The power of an o-machine depends on its place in the recursive hierarchy of the network. The transfinite net has an infinite hierarchy, and so allows for the existence of machines of unlimited power. This abstract network provides us a huge space for modelling reality, beginning with physics.
Books
| Beal, R, Neural Computing: An Introduction, Adam Hilger 1991 Jacket: '... starts from basics and goes on to cover all the most important approaches to the subject. ... The capabilities, advantages and disadvantages of each model are discussed as are possible applications of each. The relationship of the models developed to the brain and its functions are also explored." http://www.amazon.com/exec/obidos/ASIN/0852742622/tnrp">Amazon back |
| Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' Amazon back |
| Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. ... The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' Amazon back |
| Jech, Thomas, Set Theory, Springer 1997 Jacket: 'This book covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. ... It can be used as a textbook for a graduate course in set theory and can serve as a reference book.' Amazon back |
| Tanenbaum, Andrew S, Computer Networks, Prenctice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. ... This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.' Amazon back |
Click on an "Amazon" link in the booklist at the foot of the page to buy the book, see more details or search for similar items
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