vol 3: Development
chapter 2: Model
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... to restore theology to the mainstream of science
Table of contents
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4. Computation | ||
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1. God |
9, Selection | |
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2. Immensity |
6. Simplicity |
10. Entropy |
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7. Constraint |
11. Knowledge | |
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12. Mathematics |
Here we set out to develop models to help us understand the world and plan successful action. The ancient religions teach that a successful life is the result of pleasing an invisible god. Locally, his god is often an abstract version of the reigning political power. Here, given our assumption that 'universe' and 'divinity' mean the same thing, we seek a model which embraces all the physical and spiritual features of the the world.
page 1: God
A brief history of my personal god from ancient times until the present. My starting point is the traditional Christian model of God. My purpose is to develop and test a new model of god. The most important feature of this model is that it brings us close to god. If the universe is divine, every experience in life is an experience of god.
page 2: Immensity
All agree that god is big. Physics has already taught us that natural language is too small to describe the universe, and must be augmented with mathematics. To model god, therefore, we look for the biggest mathematical structures. Our starting point is the Cantor Universe, the space of transfinite numbers discovered by Georg Cantor in his efforts to understand the relationship between continuous and discrete quantities.
page 3: Logical continuity
We distinguish two types of continuity, the physical continuity suggested by smooth motion through space, and the continuity of logical argument. We suggest that the universe of logically consistent functions is much bigger than the universe of continuous functions, and so more appropriate for modelling the whole.
page 4: Computation
Hilbert thought there was no limit to the possibilities of formal mathematics. Goedel and Turing showed that this was not so. Regions of completeness and computability in mathematics are relatively tiny. Computability is a scarce and valuable resource in the mathematical realm.
page 5 A transfinite computer network
A communication network can model a permutation group. We interpret a Cantor universe populated with Turing machines as a network, whose layers are measured by the transfinite numbers. The hardware level of this network, represented by the natural numbers, has a high degree of symmetry, and is studied by arithmetic and physics. Higher levels, which may represent things like bacteria or politics, are much more complex, but still exhibit useful symmetries which may be traced to the theory of communication and the structure of the network.
page 6: Simplicity
The structure we have imagined on pages 1, 2 , 3 and 4 is exceedingly complex. The ancient view, however, is that God is simple. How to we reconcile or model with tradition? The answer chosen is that our formal mathematical structure simply describes certain stationary points in the life of the universe, ie the life of god. Dynamically, the universe is a seamless whole.
page 7: Constraint
So far we have learnt nothing, since the model is just the biggest symbolic system I can imagine, a transfinite network. Such a network looks rather like chaos, in which every possible event is equally likely. The world is nothing like this. Some things happen frequently, some rarely, some, perhaps, never. We propose that constraint responsible for this structure is the limited power of a Turing machine in a transfinite context
page 8: Complexification
The amount of information carried by a point in a space is equal to the entropy of that space. The space of our universeis expanding and it has a strong tendency to increase its entropy . What is the source of this increase? The answer lies in the Cantor force, a consequence of Cantor's proof that beyond every transfinite number lies a greater number.
page 9: Selection
The maintenance of stable structure requires computing power, which is limited. As a result there is strong competition for the physical resources that make computation possible. This competition selects for organisms which are best able to maintain themselves, which is tantamount to election for the most efficient algorithms for life in each environment.
page 10: Entropy
The ancients imagined a gulf between the spiritual world of human imagination and communication and the physical world. This led to the idea that we are immortal spirits somehow trapped in a temporary material environment. Here, in contrast, we espouse Landauer's conjecture that information in physical. Landauer. The spiritual element of the world resides in the real relationships between the physical elements of the universe. Entropy measures the amount of information embodied in these relationships.
page 11: Knowledge
None of this discussion would be happening without knowledge. We know things and we can talk about them. Knowledge is part of the world which represents some other part of the world in a simplified and compressed form. Organisms share knowledge by communication. Such sharing is the foundation of creation and fitness.
page 12: Is the transfinite network isomorphic with mathematics?
Since we assume that the universe is God, we assume that the only constraint on the existence of the universe is that it be consistent. Since we have already noticed that this is the only constraint on mathematics, we are led to an important assumption: that the visible universe is effectively mathematics incarnate. (= made dynamic) Mathematical theology, 46.
(revised 17 November 2007)
Further reading
Books
| Brillouin, Leon, Science and Information Theory, Academic 1962 Introduction: 'A new territory was conquered for the sciences when the theory of information was recently developed. ... Physics enters the picture when we discover a remarkable likeness between information and entropy. ... The efficiency of an experiment can be defined as the ratio of information obtained to the associated increase in entropy. This efficiency is always smaller than unity, according to the generalised Carnot principle. ... ' Amazon back |
| Church, Alonzo, Introduction to Mathematical Logic, Princeton UP 1996 Amazon back |
| Hallett, Michael, Cantorian set theory and limitation of size, Oxford UP 1984 Jacket: 'This book will be of use to a wide audience, from beginning students of set theory (who can gain from it a sense of how the subject reached its present form), to mathematical set theorists (who will find an expert guide to the early literature), and for anyone concerned with the philosophy of mathematics (who will be interested by the extensive and perceptive discussion of the set concept).' Daniel Isaacson. Amazon back |
Papers
| Landauer, Rolf, "Irreversibility and Heat Generation in the Computing Process", IBM Journal of Research and Development, 5, 3, 1961, page 183. back |
Links
| Landauer, Rolf Irreversibility and Heat Generation in the Computing Process 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
Related sites:
Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty
