vol 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
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 the physical and spiritual features of the the world.
Life is dynamic. My life changes from moment to moment. I am in continual dialogue with my environment, be it a mountain, a power saw or a loud and crowded party. My experience of life is embodied in a fantastically complex physical system. I am a coalition of trillions of cells; each cell is a coalition of countless molecules. Physics tells us that even when we magnify an atom trillions of times we continue to uncover processes that are part of life.
Dynamics is central to all modern science, and its history stretches back into the mists of time. The essence of survival is to act appropriately at every moment of life: to particularly avoid acts leading to injury or death. To do this, we must be able to predict the behaviour of the world and the effects of our actions. This is the role of knowledge. To know someone or something is to be able to predict what they will do in certain circumstances. We do this by creating within ourselves a model of the thing known, and using the model to simulate its behaviour under different conditions.
Mathematical modelling
Mathematics is the most general and abstract form of language. Mathematical modelling of the world begins with arithmetic. The history of arithmetic is probably as long as the history of written language. While we normally distinguish stars from sheep and atoms, arithmetic pays attention only to the property of identifiable unity. Counting applies equally to stars, sheep and atoms.
Arithmetic begins with numbers. The properties of numbers can be written down succinctly in the form of Peano's axioms. The natural numbers flower into the infinite hierarchy of transfinite cardinal and ordinal numbers which define the space in which this site operates.
The specific strength of this model is that it may be used to express the relationship between the matter and spirit. In this application it would suggest that there is not an absolute divide between the material and spiritual elements of the universe. Rather, there is an infinite layered spectrum of complexity running from pure matter to pure spirit
The existence of this spectrum suggests a new way to look at the nature and existence of God. Beginning with the mathematical model constructed in this part of the site, we go on to develop a theological model of the whole of existence. This model will serve as a foundation for the interpretation and construction of religion.
Further reading
Books
| 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 |
| 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 |
| Hazewinkel, Michiel, and (managing editor), Encyclopaedia of Mathematics (6 volumes), Kluwer Academic and Toppan 1995 'The Encyclopaedia of mathematics aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-85.' Amazon back |
| Hodges, Andrew, Alan Turing: The Enigma, Burnett 1983 Author's note: '... modern papers often employ the usage turing machine. Sinking without a capital letter into the collective mathematical consciousness (as with the abelian group, or the riemannian manifold) is probably the best that science can offer in the way of canonisation.' (530) Amazon back |
| Kauffman, Stuart, At Home in the Universe: The Search for Laws of Complexity, Oxford University Press 1995 Preface: 'As I will argue in this book, natural selection is important, but it has not laboured alone to craft the fine architectures of the biosphere ... The order of the biological world, I have come to believe ... arises naturally and spontaneously because of the principles of self organisation - laws of complexity that we are just beginning to uncover and understand.' Amazon back |
| Khinchin, A I, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.' Amazon back |
| Smolin, Lee, The Life of the Cosmos, Oxford University Pres 1997 Jacket: 'Smolin posits that a process of self-organisation like that of biological evolution shapes the universe, as it developes and eventually reproduces through black holes, each of which may result in a big bang and a new universe. Natural selection may guide the appearance of the laws of physics, favouring those universes which best reproduce. ... Smolin is one of the leading cosmologists at work today, and he writes with an expertise and a force of argument that will command attention throughout the world of physics.' Amazon back |
Papers
| Imamizu, Hiroshi, "Human cerebellar activity reflecting an acquired internal model of a new tool", Nature, 403, 6766, 13 January 2000, page 192-195. Letters to Nature: 'Theories of motor control postulate that the brain uses internal models of the body to control movements accurately. ... Previous studies have shown that the cerebellar cortex can acquire internal models through motor learning. Because the human cerebellum is involved in higher cognitive function as well as motor control, we propose a coherent computational theory in which the phylogenetically newer part of the cerebellum similarly acquires internal models of objects in the external world.'. back |
| West, Geoffrey B, "A general model for the structure and allometry of plant vascular systems", Nature, 400, 6745, 12 August 1999, page 664-667. Letters to Nature: 'Vascular plants vary in size by about twelve orders of magnitude, and a single individual sequoia spans nearly this entire range as it grows from a seedling to a mature tree. .. Here we present an integrated model for the hydrodynamics, biomechanics and brnching geometry of plants, based on the application of a general theory of resource distribution through hierarchical branching networks to the case of vascular plants.'. back |
| Schnellnhuber, H J, "'Earth system' analysis and the second Copernican revolution", Nature, 402 supplement, 6761, 2 December 1999, page C19-C23. Impacts of forseeable science: 'Optical magnification instruments once brought about the Copernical revolution that put the Earth in its correct astrophyscial context. Sophisticated information compression techniques including simulation modelling are now ushering in a second 'Copernican' revolution. The latter strives to understand the 'Earth system' as a whole, and to develop, on this cognitive basis, concepts for global environmental management.'. back |
Links
| Argonne National Laboratory The QED Project - Home Page The aim of the QED project is to build a single, distributed, computerized repository that rigorously represents all important, established mathematical knowledge back |
| LMS Bulletin of the London Mathematical Society You must register to enter the Cambridge Journals Online site. One may then browse abstracts of articles in journals published by CUP, and purchase copies of the articles themselves. back |
| St Andrews University History of Mathematics The MacTutor History of Mathematics archive was created and is maintained by John O'Connor and Edmund F Robertson . It was developed initially as part of the Mathematical MacTutor system for learning and experimenting with mathematics. back |
| University of Tennessee, Knoxville Mathematics Archives WWW Server The goal of the Mathematics Archives is to provide organized Internet access to a wide variety of mathematical resources. The primary emphasis is on materials which are used in the teaching of mathematics. Currently the Archives is particularly strong in its collection of educational software. ... A second strength of the Archives is its extensive collection of links to other sites that are of interest to mathematicians. back |
| W3C W3C Document Object Model 'The Document Object Model is a platform- and language-neutral interface that will allow programs and scripts to dynamically access and update the content, structure and style of documents. The document can be further processed and the results of that processing can be incorporated back into the presented page. This is an overview of DOM-related materials here at W3C and around the web.' 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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