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10 February 2008

Notes 2008: 3 February Notes 2008: 27 January

1 February 2008

Development Chapter 3 Physics page 7: Entanglement When quantum systems communicate they become entangled. so that they share a state which cannot be represented as a product of the component states. This loss of independence is manifested in quantum correlations which are observed even when entangled particles are moved a long way apart. Classical probability theory cannot explain this correlation, which is an intrinsic feature of the quantum mechanical method of computing probabilities.

28 January 2008

Notes 2008: 20 January Notes 2008: 13 January Notes 2008: 6 January

22 January 2008	Notes 1999: 3 January Notes 1999: 4 April Notes 1999: 17 January Notes 1999: 11 April Notes 1999: 24 January Notes 1999: 18 April Notes 1999: 31 January Notes 1999: 25 April Notes 1999: 7 February Notes 1999: 2 May Notes 1999: 14 February Notes 1999: 9 May Notes 1999: 21 February Notes 1999: 16 May Notes 1999: 28 February Notes 1999: 23 May Notes 1999: 7 March Notes 1999: 30 May Notes 1999: 14 March Notes 1999: 13 June Notes 1999: 21 March Notes 1999: 20 June Notes 1999: 28 March Notes 1999: 27 June
20 January 2008	Development Chapter 3 Physics page 6: Invariance with respect to complexity Cantor generated the transfinite cardinal numbers (and their associated ordinals) through an invariance law which operates identically no matter what the cardinal number of the set upon which it operates. We call this feature invariance with respect to complexity and see that it is a feature of quantum mechanics also. Since quantum theory operates indifferently at al levels of complexity it provides a bridge between the unity and multiplicity of the universe.
18 January 2008	Development Chapter 3 Physics page 5: Hilbert spaces and the symmetric network We have proposed a transfinite symmetric network as a phase space for the universe. Transfinite network Here we place this network into correspondence with the transfinite dimensional Hilbert space which houses the 'wave function of the universe' and show how quantum mechanics serves as a method to compute the traffic between nodes of the transfinite network.
16 January 2008	Development Chapter 3 Physics page 4: Quantum mechanics Quantum mechanics is the modern working model of the physical universe. It sees the world as comprising observable physical events and an unobservable logical structures, state functions, which control (to some degree) the nature and frequency of events. The quantum mechanical formalism is invariant with respect to complexity and can apply to any layer in the transfinite network. From an information theoretic point of view, quantum mechanical systems can be viewed as message sources.
9 December 2007	Development Chapter 3 Physics page 3: The initial singularity The large scale structure of the universe is described by the general theory of relativity which predicts that the present universe expanded from an initial dimensionless point. In the network model, we interpret gravitation as a manifestation of the hardware layer of the universal network. Following an analogy with the theology of the Trinity, we propose a model for the growth of the universal network.
9 December 2007	Development Chapter 3 Physics page 2 Why is the universe quantized? Quantum mechanics sees the world as comprising discrete observable physical events controlled by invisible and continuous state functions which explain the nature and frequency of observed events. In the network model, the mathematical theory of communication explains quantization by showing that we can minimize error by maximizing the distance between different messages. Quantization is thus a feature of error resistant communication.
9 December 2007	Development Chapter 3 Physics page 1: Action and Time Following our method, we begin to construct a map between our model and the real world. We begin with physics because it studies the simplest elements of the world. The first point of contact between our model and physics is the identification of action with computation, Drawing on quantum theory, we identify the time rate of action with energy. back
9 December 2007	Development Chapter 3 Physics: Introduction If we assume that the universe is divine, physics is the study of God's body. The body is the most abstract, that is the least complex, of the layers of complexity in the structure of the universe. Physics sets the stage by providing the alphabet for all other levels of complexity.
9 December 2007	Development Chapter 2 Model 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,
12 December 2007	Development Chapter 2 Model 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.
9 December 2007	Development Chapter 2 Model 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. 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.
26 November 2007	Development Chapter 2 Model 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.
22 November 2007	Development Chapter 2 Model 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.
21 November 2007	Development Chapter 2 Model 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
21 November 2007	Development Chapter 2 Model 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.
20 November 2007	Development Chapter 2 Model 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.
20 November 2007	Development Chapter 2 Model 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.
19 November 2007	Development Chapter 2 Model 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.
18 November 2007	Development Chapter 2 Model 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.
18 November 2007	Development Chapter 2 Model 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.
17 November 2007	Development Chapter 2 Model Introduction 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.
	Development Chapter 1 Epistemology page 8: Security: Our security depends upon understanding our environment. The ancient theory that the world is the creation of an mysterious God who has left vague instructions for our wellbeing is no longer tenable. The environment we must know to survive is always before our eyes, and we need a scientific theology to understand it comprehensively.
	Development Chapter 1 Epistemology page 7: Limits to knowledge: What are the limits to human knowledge? Can we know everything? The theory of relativity tells us that certain parts of the universe are hidden from us by event horizons. Many other things are similarly hidden from us by our inability to communicate with them. In addition, we may identify a need for secrecy, where communication would decrease the fitness of an individual. We may contrast the need for secrecy and the need to know, both based on the value of knowledge to life.
	Development Chapter 1 Epistemology page 6: Evidence: Although things may look good and seem reasonable, we need to test them to be sure of them. The foundation of trust is evidence that the person or thing trusted has passed a complete set of relevant tests. The future remains to some degree uncertain, however. A dog which has never bitten may yet bite, so our search for complete security is never fully complete.
	Development Chapter 1 Epistemology page 5: Honesty and deception: Am I telling the truth? Is nn telling the truth? These can often be important questions, especially in matters of love and war. We assume that physical things always tell the truth, and that people who are deceived about them are not looking at them in the right way. On the other hand, evolutionary theory suggests that deceptions is a common feature of survival strategies.
17 November 2007	Development Chapter 1 Epistemology page 4: Truth: What is true? Something that says it as it is. So if there are 100 litres of fuel in the tank, a true fuel gauge reads '100 litres'. We trust what we know to be true. If the gauge is dodgy, it may read one hundred litres when in fact the tank holds but fifty, and the pilot may be doomed to run out of power before she comes to a landing place. The only way we can decide if something is true is to devise a method of testing it.
19 June 2007	Development Chapter 1 Epistemology page 3: Scientific method: Scientific method is the modern standard approach to quality knowledge. Science gives primacy to evidence, and encourages the free use of imagination to develop hypotheses (stories) to fit the evidence. We learn to act without explicit understanding of what we are doing. One can speak without knowing linguistics, and walk while ignorant of dynamics and physiology. Science makes the information content of our arts explicit, so that our skills can be honed.
	Development Chapter 1 Epistemology page 2: Abstraction: Mathematics lies in the imaginative (theoretical) realm of science. The beauty of mathematics is that is is an armchair science. We can do it with pencil and paper without going out into the world and getting wet and dirty. In mathematics, we simply write symbols on paper, and the move them round, either physically or mentally in order to understand their behaviour. This provides both the strength and weakness of mathematics: its strength is that it is very clear and controlled; its weakness that it does not necessarily have anything to do with the observable world.
	Development Chapter 1 Epistemology page 1: Trust: Is there life after death? Is this dog going to bite me? Is this structure strong enough to hold me? Will this person repay me if I lend him money? Should I go to war to save my country from what our government claims is a clear and present danger? All these are questions of faith and trust, and bear more or less on the fitness and survival of individuals and communities. Is it reasonable to believe this communication?
	Development Chapter 1 Epistemology Introduction Our survival, health and happiness depend very much on the way we act. In general we call the control of action art, or 'knowhow', something we learnt by study and practice. Art is informed by knowledge, and the quality of our art relates to the quality of our knowledge. Epistemology is the science responsible for quality control in the knowledge industry.

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