vol 2: Synopsis
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1: About
2: Synopsis
3: Development
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This site is part of the natural religion project The natural religion project A new theology A commentary on the Summa The theology company
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III. Modern physics | |||
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19. John von Neumann | |||
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IV. Divine dynamics | |||
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I. Motivations and possibilities
page 1: Source: I am a conscious particle contemplating my position in a vast universe. I was brought up to understand my position in life according to the beliefs of the Roman Catholic Church. Long ago, I lost faith in this Church, and have ever since been seeking a new world view. Here it is (so far!). back
page 2: Compassion: The God of the Old Testament is presented as a hard man. He demands unconditional love from his creatures, but is not above violence toward them. This violence is is quite unnecessary if his power is what it is claimed to be. The God of the New testament and the natural god can be compassionate, stepping in to help individuals experiencing hardship. back
page 3: Naming: At the root of language is naming. '... from the soil Yahweh God fashioned all the wild beasts and all the birds of heaven. ... The man gave names to all the cattle, all the birds of heaven and all the wild beasts.' Genesis 2.19-20. Naming yields immense power, since for many purposes we no longer have to move things, which may be heavy and dangerous, to express ourselves, merely their names. back
page 4: Language: Mind thrives on language, which comes in many forms. We think of language as any code that can be used to share information between independent entities. As we develop from babies, we absorb and respond to the human language around us. Textual representation of language enables us to share knowledge through space and time. The fundamental language of the universe appears to be quantum mechanics and all other languages are built up from this. back
page 5: Body: Christian religions see our bodies as a burden, damaged by original sin and prone to temptation, sickness and death. They propose an alternative world of disembodied entities, pure spirits, and claim that we will live on in this world after death. The bad news is that this picture mistakes formal distinctions for a real ones. Although we can name spiritual and material features of the world, these parts are inextricably bound together. back
page 6: Evolution: We understand things best through historical narratives. We see the present structure of the universe as a product of its historical evolution. The scientific story tells us the that universe began as an initial point with no discernible structure and slowly evolved into the huge and immensely complex system that enfolds and sustains us. back.
page 7: Mind: Each of us experiences our own divinity. Of all things, death is most certain, and its inverse, birth. No element of the universe is guaranteed survival. Our best strategy is to adapt to changing circumstances. Compared to the rate of change around us, our bodies are relatively fixed. It is through adaptability of mind that the human species has dominated Earth. Mind as we understand it is not confined to us, or even to animals. We see intelligent mental function at every level of complexity and specialization from particle to divinity. back
page 8: Revelation: In the Christian tradition God reveals himself through the words of the prophets recorded in the Bible. Here, where we identify God and the universe, every event and every human experience becomes a revelation of God. Traditional theology explains the Biblical data using hypotheses developed by ancient Greek philosophers, the 'Fathers of the Church', and their successors. Here we identify theology as the broad trunk of the scientific tree, since knowledge of the universe is knowledge of god. back
II. A brief history of dynamics
page 9: Dynamics: Dynamics tries to explain why things behave as they do. It is as old as the need for survival. Dynamics is founded on revelation. The world reveals itself every time it moves. Hunters, farmers and all living creatures study these revelations, looking for paths to a better life. Theology studies the dynamics of the whole with a view to giving overall guidance to human activity. back
page 10: Aristotle (384-322 bc): We begin the story of dynamics with Aristotle's Physics, written about 350 bc. Many of the earliest known writers, like Parmenides and Zeno and down through Plato held that 'real' reality was eternal and immutable. Motion was somehow second class. Aristotle made the first big intellectual step away from that position toward the modern view (pioneered by Heracleitus) that all is dynamics constrained only by local consistency or 'reasonableness'. back
page 11: Thomas Aquinas (1224-1274): Aquinas combined ancient Greek and Medieval science with Christian belief to produce a theological classic, the Summa Theologiae. I find the high point of the Summa is his treatment of the Trinity, the Christian belief that there are three divine Persons in the one God. Aquinas explains that although the relationships of knowledge and love are not real among us, they are in god. Reading this set me thinking about one god with an unlimited number of personalities, many of which are visible to us. back
page 12: Martin Luther (1483-1546): An axiom of political dynamics is that power corrupts. and the power of the Catholic Church is no exception. Martin Luther, building on widespread disaffection with high level corruption in the Church, was the catalyst for a democratic revolution in church and state which helped to found the modern free world. back
page 13: Galileo Galilei (1564-1642): The rise of scientific investigation based on observation of the world led to a linguistic revolution. Students of nature found it necessary to extend natural languages with technical terminology in order to name all the things they found. Galileo saw that the natural philosopher needed to add mathematics to natural language as well. He wrote 'Philosophy is written in this grand book - the universe, which stands continually open before our gaze. But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics ...'. back
page 14: Isaac Newton (1643-1727): Newton, building on the work of the Galilean era, showed that the heavens and the earth are physically one. Using a mathematical model and astronomical observations, Newton demonstrated that the same forces govern both terrestrial and extraterrestrial bodies. Not only did this unite physics and astronomy, but Newton's methods caused a revolution in mathematics. Mathematics is still expanding on the momentum it gained from his work.. back
page 15: Analysis: The mathematical study of motion has been a a problem since earliest times. Zeno of Elea (490-430 bc) developed many mathematical arguments to show that motion is impossible. The invention of the calculus by Newton (and independently by Leibniz) made the logical treatment of motion, continuity and infinity live issues in mathematics. Analysis is the department of mathematics that arose to deal with the difficult relationship between discrete and continuous quantities. back
page 16: Georg Cantor: (1845-1918) The natural numbers, 1, 2, 3 ... are infinite, since we can always make another one by adding 1 to the number we already have. It was known in antiquity that Pythagoras' theorem implies that there are quantities that cannot be measured by the natural numbers or by the rational numbers, ratios (eg 3/5) of natural numbers. To measure such quantities, we must invent the 'irrational' or real numbers. Cantor showed that the step from natural to real numbers is not unique, but the first an endless series of steps to even bigger number spaces, which he called the transfinite numbers. Following Cantor, our theology is based on the hypothesis that only the transfinite numbers are big enough to begin to model God. back
III. Modern Physics
page 17: Albert Einstein (1879-1955): At the turn of the twentieth century, even the existence of atoms was moot. Einstein not only produced a new vision of physical space through the special and general theories of relativity, but made great contributions to the new idea that the physical world was quantized as well as continuous. In particular he showed that light, even though it had wave properties, was emitted and moved as a particle, the photon. back
page 18: Quantum mechanics: Quantum mechanics began with the work of Max Planck at the turn of the twentieth century. It took nearly thirty years to reach its modern form, largely because the ideas it introduced into physics were very new and strange. The development of quantum mechanics was driven by a growing list of inconsistencies between Newtonian physics and observations of the microscopic world of atoms, electrons, photons and other particles. back
page 19: John von Neumann (1903-1957): When George Cantor first announced the transfinite numbers, some theologians objected on the ground that the only actual infinity in existence is God. David Hilbert showed that these new infinities fitted easily into mathematics and described new class of infinite spaces known as function spaces. John von Neumann used function space ideas to resolve the apparent conflict between the particle and wave (discrete and continuous) descriptions of the world, opening the way for the consistent development of quantum theory. back
page 20: The 'wave function' of the universe: Quantum mechanics is our best description of the physical universe. We begin from elementary events and show how these events are assembled into larger and larger events, culminating in the total event which we call the universe. The quantum mechanical description of the whole system is sometimes (for historical reasons) called the wave function(s) of the universe. This class of functions exists in transfinite function space. back
page 21: Quantum field theory: Quantum mechanics, like Newtonian mechanics, provides a general paradigm for the study of motion. Newtonian mechanics struck trouble when it came to deal with electromagnetism. This problem ultimately led to the development of quantum theory. Quantum theory, in its turn, revealed itself to be very difficult to harmonize with Einstein's special theory of relativity. Quantum field theory has evolved to deal with this difficulty and provides us with a wide ranging picture of the universe called the standard model. back
page 22: Probability: One of the most startling features of quantum mechanics from the point of view of a classical physicist is that it does not always make definite predictions. Often it merely assigns probabilities to the different possible outcomes of an initial situation. This has led physicists to believe that the quantum world is not completely deterministic, as the Newtonian world it replaced was believed to be. Instead, as Max Born described wave mechanics: 'The motion of particles follows probability laws but the probability itself propagates according to the law of causality.' The theory of probability is fundamental, and shows us how to understand systems that are partially controlled by the nature of their constituents and partially free. It enables us to measure constraint and freedom, a first step toward modelling an optimally constrained (and free) system. back
page 23: Life: From the scientific point of view, the universe is a vast network of interacting particles which is responsible for its own movement and structure. From earliest times, life has been described as self motion, so it is natural to see the universe as a living organism, This organism is partitioned into smaller organisms, such as you and I and all the other entities we can distinguish in the whole. Acting together, these partial events form the life of the universe, tantamount to the life of God. back
page 24: Cosmology: The general theory of relativity embraces the whole of the physical universe. The union of the relativistic picture of the whole with the field theory picture of the microscopic details gives us cosmology, our picture of the universe as a whole. In the context of this site, modern cosmology may be considered the study of God's body. A cosmological model of the universe is a model of god. back
IV. Divine dynamics
page 25: God: Can God make a stone too big for himself to lift? This ancient conundrum points to the only possible restriction on the nature of God: consistency. Here, by God, we mean the whole of reality. Is reality divided into two, God and the universe? or is it one, simply God. We take the latter view, and ask all the classical questions about God, its size, power, knowledge, durability, and so on. back
page 26: Kurt Goedel (1906-1978): For thousands of years people equated consistency with determinism, holding that a logically consistent sequence of propositions could have only one outcome. This feeling lies behind the notion that God knows and controls everything. Kurt Goedel, working on a question asked by David Hilbert, showed that consistency does not always mean determinism. Goedel's discovery is consistent with the probabilistic nature of quantum mechanics, and indeed of all processes in the universe. back
page 27: Alan Turing (1912-1954): What Goedel did for the 'static' structure of the Cantor universe, Turing did for its dynamics. He showed that, given a reasonable definition of a computer, there are some computable problems which can be solved, but there are many other incomputable problems which cannot. Goedel's result that shows that there will always be incompleteness, no matter how big the system. We can interpret Turing's result to mean that there will always be incomputable problems, no matter how big the computer. From this we conclude that if the whole universe may be modelled as a computer, there are some computations it will never complete. The universe is in this sense eternal. back
page 28: Claude Shannon (1916-2001): Shannon founded the mathematical theory of communication which underlies the current revolution in communication. He first defined information, and then showed how to transmit information faultlessly over a faulty channel by suitable encoding. The requirements for a good code have guided the search for codes ever since, and we can see that communication in the natural world is governed by the same model. From Shannon's time on, people have begun to look at the universe more as an information processor than an energy processor. back
page 29: Quantum information theory: Much of the physical theory that we have inherited from the past accepts implicitly that the world is dead and inert, needing to moved from outside by gods or angels. Modern quantum information theory suggests that the world itself is an intelligent mind, alive and self motivated at every point. Each organism within the universe contributes to its overall glory and complexity. back
page 30: The transfinite network: We can imagine any organization 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. back
page 31: Physics: We have now seen physics in two guises: the classical dress first designed by Galileo and Newton, and modern quantum field theory, which models the universe with outstanding precision although we do not fully understand it. Let us turn to our new picture, the transfinite network, and bring it down to earth. We do this by postulating that the symmetries or conservation laws of physics are images of the boundaries imposed on the transfinite network by consistency, that is by communication. We begin with spacetime and the quantum theory. back
page 32: Metaphysics: Physics centres around the study of observables. Metaphysics centres on the study of what it going on behind the scenes to make the observables look the way they do. Metaphysics studies the logical consequences (and non-consequences!) of physics. In the old days, metaphysicians could not see their own conscious existence arising out of the matter described by contemporary physics. The physics outlined above, however, extends as naturally to metaphysics as any ordinal number (by the work of Cantor's theorem), is transformed into a greater ordinal number. Here lies the power of our theory: it is invariant with respect to complexity, so that we can confidently expect the properties of complex hidden systems to be reflected in simple visible systems. back
page 33: Relationship: How does a network of Turing machines come to be? Modern physics suggests that there are particles with no size, to wit electrons, neutrinos and quarks. Particles with size are created by the bonding of particles without size. In other words relationship creates space. This insight was first developed by Thomas Aquinas in his theory of the Trinity, the Christian notion than the one God has three personalities. back
V. Applied divinity
page 34: The peace theorem: This theorem is based on the notion (well illustrated in quantum mechanics) that boundaries create structure. Further, we assume that stable boundaries create stable structure, The prerequisite for this stable structure is consistent communication between the boundaries. This notion of peace is very old, since it encapsulates the idea of peace being the result of knowledge of and obedience to god, the boundary of human existence. back
page 35: Religion: Religion is the art of peace, corresponding to the science of theology. We take religion to be all the knowledge that we acquire after birth, which together with our genetic knowledge, adapts us to live with one another on earth. Here we begin to outline the new approach to survival that arises from the theorem on peace stated above. It is the task of religion to realize the promise of the peace theorem, Vice in all its forms, from overindulgence through violence to war, has its origins in the frustration arising from nonfulfillment of need, that is starvation. The foundation of good religion, and the promotion of virtue, must then be based on the notion of fulfilling all human needs. These are not infinite. back
page 36: Politics: The world has infinite variety, but we can only do do one thing at a time, so we must choose between the possibilities. This process of choice we call politics. It is constrained by the fundamental principles of truth, justice, and equality, confronting the finite nature of the physical world. Good political decisions must meet these constraints while increasing the wealth and freedom of the community. back
page 37: Economics: The root of effective religion is effective economics, since the dissipative nature of life requires that we must all consume to live. Although capital based means of production are excellent for generating wealth, they tend to fail in distribution. Good religion not only establishes the environment necessary for the creation of wealth, but makes certain that everyone has access to adequate resources for living, and seeks to minimize waste. It can achieve this by tuning the political and economic systems according to principles derived from modelling and experience. back
page 38: Design: The effectiveness of our work depends heavily upon design and and technique. In a dynamic system like our world, the whole and the parts are continually influencing one another to iterate toward an optimal system. Our question is how do we optimize design? In traditional theology, design is already optimized by an omniscient and omnipotent God. If the universe is divine, it designs and builds itself. The theory of evolution describes an algorithm for self-design. Being intelligent, we can do better by modelling designs before we construct them, thus saving resources. Effective religion oversees design, seeking a decision process to rank designs by their conformity with the conditions for peace. back
page 39: Work: Why do we have to work? The Christian interpretation of Genesis sees work as a result of original sin. Here we disagree, and see work as a natural result of the interaction the relatively finite material aspect of the universe with its infinite spiritual aspect. We must work to maintain our spirit. It is part of our life, not necessarily irksome, since the ability to work gives us to power to ensure our survival. Work moves the world, transforming it into products for human use. As the old Latin tag has it bonum ex integro, malum ex quacumque causa : good comes from the whole, evil from any defect. Good work must be defect free, that is complete. back
page 40: Grace: The universe is creative, as is clear from the fact that it has built itself from the initial singularity. This creativity underlies the possibility of grace, that is a gift from god. We see grace in the harvest yielded by effective work. Grace arises from the power of cooperation, and the fortuitous finds of search. It is unearned wealth, physical or spiritual. back
page 41: Metanoia: Metanoia is Greek for changing ones mind, learning new things, learning a new outlook. The practical conclusion of this work is that we maximize human entropy, headroom, grace, freedom and survivability by learning to communicate, cooperate and share more effectively. The religious attitudes of small communities contain an element of 'us' and 'them' which lies at the root of religious war. In the new global religious picture, there is no us and them, we are all in this together. back
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