natural theology

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I. Motivations and possibilities

1. Source
2. Compassion

3. Naming
4. Language

5. Body
6. Creation

7. Mind
8. Revelation

II. A brief history of dynamics

9. Dynamics
10. Aristotle

11. Aquinas
12. Luther

13. Galilei
14. Newton

15. Darwin
16. Cantor

III. Modern physics

17. Einstein
18. Quantum mechanics

19. von Neumann
20. Ψ Universe

21. Symmetry
22. QFT

23. Recursion
24. Meaning

IV. Divine dynamics

25. God
26. Gödel
27. Turing

28. Shannon
29. Quantum IT

30. Network
31. Physics

32. Metaphysics
33. Trinity

V. Applied divinity

34. Evolution
35. Religion

36. Politics
37. Economics

38. Design
39. Work

40. Heaven
41. Metanoia

I. Motivations and possibilities

page 1: Source: I am a conscious personality contemplating my position in the Universe. I was brought up to my life according to the beliefs of the Roman Catholic Church. Long ago, I lost confidence in this Church, and have ever since been seeking a new world view. Here it is (so far!). back

page 2: Compassion: From the evolutionary point of view, a good religion makes its adherents fitter. It is not surprising that the traditional religions place strong emphasis on compassion, the feeling that a caring parent has for a suffering child. Compassion is the human answer to the hardships imposed upon us by the evolutionary process. 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. Genesis. back

page 4: Language: One of the most amazing things about our world is that we can share very complicated ideas with strings of symbols like these. How is this possible? The answer lies in the fact that the dynamic processes in our minds have fixed points which can be placed into correspondence with words and sentences. 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 may not be true and there appears to be no way to tell, since it is assumed that we cannot see these purely spiritual creatures. Aquinas 261, Paul, back

page 6: Creation: Where did we come from? The traditional Christian answer is to be found in Genesis: 'In the beginning God created the heavens and the earth. . . .' Genesis 1:1-2. Why did God create the world? A Catholic answer is to be found in the dogmatic constitution Dei Filius of the first Vatican Council: "The world was made for the glory of God". This means in effect that God made the world to show off to us, a rather anthropocentric view. Here we propose that creation is the emergence of fixed points in the divine dynamics, so that all creation is divine. Dei Filius - Wikipedia, back

page 7: Mind: We are aware of our own existence in the moving world. We survive by adapting to changing circumstances. Compared to the rate of change around us, our bodies are relatively fixed. It is through adaptability of mind that we have learned to dominate the Earth. Mind as we understand here is not confined to us, or even to animals. We see intelligent creative activity every level of complexity and specialization from the simplest particles to the whole. back

page 8: Revelation: The Christian Churches base their claims to be exclusive communication channels to God on the Bible. This notion is expressed most formally by the Roman Catholic Church, and has been recently reaffirmed by the Second Vatican Council in its Dogmatic Constitution on Divine Revelation. Here we see the whole Universe as divine so that all our experience is revelation of God and all our action influences God. Second Vatican Council - Dei Verbum, back

II. A brief history of dynamics

page 9: Dynamics: Dynamics is our explanation of why things behave as they do. It is as old as the need for survival and is founded on revelation. The World reveals something about itself every time it moves. All living creatures, hunters, farmers, and scientists study these revelations, looking for ways to predict and exploit future behaviour. 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 which contains certain fixed points connected by consistency and '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. For me the high point of the Summa is his treatment of the Trinity, the Christian belief that there are three divine Persons in one God. Aquinas explains that although the relationships of knowledge and love are not substantial among us, they are in God. Reading this set me thinking about the divine World, one God with an unlimited number of personalities, each, like me, a particle in the Universe. back

page 12: Martin Luther, (1483-1546): An axiom of political dynamics is that power corrupts (because it evades error correction), and the power of the Catholic Church is no exception. Luther, building on widespread disaffection with high level corruption in the Church, was the catalyst for a revolution in church and state which was a step toward the modern concept of a 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. Here we follow this trend by working toward mathematical theology. Mathematical theology, back

page 14: Isaac Newton (1643-1727): Newton applied Galileo's idea. He invented calculus as a means to represent movement in terms of static mathematical formalism. 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 started a revolution in the mathematics ideas driven by problems raised by calculus. back

page 15: Continuity: 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. Zeno's paradoxes - Wikipedia, back

page 16: Georg Cantor: (1845-1918) The natural numbers, 1, 2, 3 . . . are infinite, since we can always add another one. . It was known in antiquity that Pythagoras' theorem implies that there are quantities that cannot be measured by the 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 mathematical theology is based on the hypothesis that the transfinite mathematical space is are big enough to model parts of the divine whole. back

III. Modern Physics

page 17: Albert Einstein (1879-1955): 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 the properties of a continuous wave, was emitted and moved as particles, photons. 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. The development of quantum mechanics was driven by a growing list of inconsistencies between classical Newtonian physics and observations of the microscopic world of atoms, electrons, photons and other elementary 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 help resolve the apparent conflict between the particle and wave (discrete and continuous) descriptions of the world. 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. An attempt to descibe the whole system quantum mechanically is sometimes (for historical reasons) called 'the wave function of the Universe'. This class of functions exists in transfinite function space. back

page 21: Symmetry: One of the most startling features of quantum theory although we can use it to define the nature of various events very precisely, we cannot use it to predict when such events will happen. This has led physicists to believe that the quantum world is not ascompletely deterministic, as the classical Newtonian world it replaced. 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. Born rule - Wikipedia, back

page 22: 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. To describe events in spacetime, must be harmonized with Einstein's theory of special relativity. The resulting 'quantum field theory' has led to a picture of the Universe called the standard model, which works very well but still has some difficulties. back

page 23: Recursion: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. By communicating with one another, these partial events form the life of the Universe, tantamount to the life of God. back

page 24: Meaning: The general theory of relativity embraces the whole of the Universe. The union of the relativistic picture of the whole with the field theory picture of the microscopic details gives us cosmology. In the context of this site, modern cosmology is 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 Gödel (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 Gödel, working on a question asked by David Hilbert, showed that consistency does not always mean determinism. Gödel'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 Gödel 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 problems which can be solved, called 'computable', and there are many others which cannot 'incomputable' problems. Gödel's result that shows that there will always be incompleteness, no matter how big the system. Turing's result shows that there will always be incomputable problems, no matter how big the computer. From this we see that if the whole Universe be modelled as a computer network, some processes will lead to a definite result, others will not. 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 that it is possible to transmit information without error over an error prone 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 as an information processor as well as 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. The filing system is the space of Cantor's theory of transfinite cardinal and ordinal numbers, and the processes are members of the set of computing machines. The result is a transfinite computer network. This network provides a mathematical model large enough to point toward God, but with sufficient finesse to deal with every detail of the world, no matter how small. back

page 31: Physics: Our first application of the transfinite computer network is to physics. We now understand that quantum mechanics is a method for modelling the content and frequency of messages on this network, which we identify with physical particles. An essential feature of a communication network is that it treats all messages equally. In physics this indifference is called symmetry, and we find that the laws of physics correspond to symmetries in nature. Gravitation, for instance, is completely indifferent to the nature of the particles with which it interacts, and the other fields of force have more detailed communication protocols. back

page 32: Metaphysics: Mathematical fixed point theorems tell us that under certain conditions, dynamic systems have fixed points, that is points that are part of the motion but do not move. Physics centres around the study of these observable fixed points. Metaphysics centres on the study of what it going on behind the scenes to make the observables look the way they do. The network model interprets this hidden process as computation and we explain the halted states of computers that have completed their computation. We understand the fundamental computers in the Universe to be the eigenfunctions of quantum operators. We guess that these eigenfunctions form a countable set that corresponds to the set of halting computers. back

page 33: Trinity: In a network, a relationship is a message or a set of messages. The general theory of relativity suggests that the Universe started as a structureless initial singularity whose only property was to exist, like the Classical God. We understand that the structured Universe we inhabit has come to be within the initial singularity through the formation of new fixed points in the moving world. 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: Evolution: Christian cosmology holds that God created the Universe from nothing as an entity other than itself. This is a bit hard to understand, given that God is the fullness of being, ie that there is no room for anything to exist other than God. Here we see creation as the emergence of fixed points in the divine dynamics, starting from the initial singularity, which seems identical to the absolutely simple divinity proposed by Aquinas and others. Consequently, we are inside, rather than outside God, and all our experience is experience of God. back

page 35: Religion: Religion is the art or technology of peace, corresponding to the science of theology. 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 by setting up boundaries of behaviour consistent with diviner law. Violence has its origins in frustration arising from starvation of one sort or another. The foundation of good religion, and the promotion of virtue, must then be based on the notion identifying of fulfilling all real human needs. These are not infinite. back

page 36: Politics: The world has infinite variety, but we can only do one thing at a time. 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 regulation and distribution. Good religion not only establishes the environment necessary for the creation of wealth, but controls the tendency of power to corrupt, adequate resources for living, and controls waste and environmental impact. It can achieve this by tuning the political and economic systems according to principles derived from scientific theology. 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. 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. 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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Further reading

Books

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Dei Verbum, Second Vatican Council, and Walter M Abbott and Joseph Gallagher (translation editors), Dogmatic Constitution on Divine Revelation The Documents of Vatican II, Geoffrey Chapman 1972 'God, who through the Word creates all things (cf. Jn. 1:3) and keeps them in existence, gives men an enduring witness to Himself in created realities (cf. Rom. 1:19-20). Planning to make known the way of heavenly salvation, He went further and from the start manifested Himself to our first parents. Then after their fall His promise of redemption aroused in them the hope of being saved (cf. Gen. 3:15), and from that time on he ceaselessly kept the human race in His care, in order to give eternal life to those who perseveringly do good in search of salvation (cf. Rom. 2:6-7).' para 3, page 112. 
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Aquinas 261 Whether an angel is altogether incorporeal 'I answer that, There must be some incorporeal creatures. For what is principally intended by God in creatures is good, and this consists in assimilation to God Himself. And the perfect assimilation of an effect to a cause is accomplished when the effect imitates the cause according to that whereby the cause produces the effect; as heat makes heat. Now, God produces the creature by His intellect and will (14, 8; 19, 4 ). Hence the perfection of the universe requires that there should be intellectual creatures. Now intelligence cannot be the action of a body, nor of any corporeal faculty; for every body is limited to "here" and "now." Hence the perfection of the universe requires the existence of an incorporeal creature.' back
Born rule - Wikipedia Born rule - Wikipedia, the free encyclopedia 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see Bra-ket notation), then the measured result will be one of the eigenvalues λ of A, and the probability of measuring a given eigenvalue λi will equal <psi,|Pi|psi> where Pi is the projection onto the eigenspace of A corresponding to λi'. back
Dei Filius - Wikipedia Dei Filius - Wikipedia, the fre encyclopedia 'Dei Filius is the incipit of the dogmatic constitution of the First Vatican Council on the Catholic faith, which was adopted unanimously on 24 April 1870. The constitution set forth the teaching of "the holy Catholic Apostolic Roman Church" on God, revelation and faith' back
Genesis Genesis 2 '19 So the LORD God formed out of the ground all the wild animals and all the birds of the air, and he brought them to the man to see what he would call them; whatever the man called each living creature was then its name.

20 The man gave names to all the tame animals, all the birds of the air, and all the wild animals; but none proved to be a helper suited to the man.' back

Paul Galatians, 5:16-24, English Standard Version '16 But I say, walk by the Spirit, and you will not gratify the desires of the flesh. 17 For the desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh, for these are opposed to each other, to keep you from doing the things you want to do. 18 But if you are led by the Spirit, you are not under the law. 19 Now the works of the flesh are evident: sexual immorality, impurity, sensuality, 20 idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions, 21 envy, drunkenness, orgies, and things like these. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God. 22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such things there is no law. 24 And those who belong to Christ Jesus have crucified the flesh with its passions and desires.' back
Second Vatican Council - Dei Verbum Dogmatic Constitution on Divine Revelation 'Dei Verbum' SOLEMNLY PROMULGATED BY HIS HOLINESS POPE PAUL VI ON NOVEMBER 18, 1965, 'PREFACE 1. Hearing the word of God with reverence and proclaiming it with faith, the sacred synod takes its direction from these words of St. John: "We announce to you the eternal life which dwelt with the Father and was made visible to us. What we have seen and heard we announce to you, so that you may have fellowship with us and our common fellowship be with the Father and His Son Jesus Christ" (1 John 1:2-3). Therefore, following in the footsteps of the Council of Trent and of the First Vatican Council, this present council wishes to set forth authentic doctrine on divine revelation and how it is handed on, so that by hearing the message of salvation the whole world may believe, by believing it may hope, and by hoping it may love.' back
Zeno's paradoxes - Wikipedia Zeno's paradoxes - Wikipedia, the free encyclopedia 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' back

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