The Plan

The working hypothesis here is that religion is the force that binds unrelated people into a functioning community. The theoretical foundation of religion it theology. The plan here is to apply the methods of science to the study of theology, working with the assumption that the Universe is divine.

Science proceeds by the collection of data, the creation of models to explain the relationships between the data, and the testing of these models by applying them to new data. As Galileo noted, this process is equivalent to a critical reading of the 'book of nature' and is analogous to the exegetical techniques that classical theologians apply to their sacred texts. Exegesis - Wikipedia, The Assayer - Wikipedia

Galileo saw that the language of the book of nature was mathematics, which for him meant simple geometry and arithmetic. Since Galileo's time, mathematics has expanded enormously, but Galileo's intuition has remained strong, and centuries of experience have shown that mathematical language is a very effective way to express scientific models. The Universe appears to obey the rules of arithmetic, so that arithmetic is a powerful tool for dealing with all sorts of situations from shopping to the design of spacecraft. This observation motivates us to work toward a mathematical theology. Eugene Wigner: The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Mathematical modelling has a number of advantages in addition to the usefulness of mathematical structures like arithmetic, geometry, algebra, calculus, the theory of computation and so on. Arithmetic - Wikipedia, Geometry - Wikipedia, Algebra - Wikipedia, Calculus - Wikipedia, Theory of computation - Wikipedia

First, mathematics is a universal discipline, cutting across the boundaries of time, language and culture. Mathematical constructs do not embody the historical and linguistic nuances of natural language, so minimizing the possibilities of misunderstanding in translation.

Second, while natural languages are limited to one hundred thousand or so words, there are no limits on the number mathematical symbols, so that we can establish precise correspondences between mathematical symbols and the enormous number of elements of the Universe, like species, chemical compounds, stars and so on.

Mathematical theorems establish logical relationships between an hypothesis and a conclusion. A well known and very important theorem is that attributed to Pythagoras, which tells us that if we assume the axioms of Euclidean geometry, the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides. Theorem - Wikipedia, Pythagorean theorem - Wikipedia

The mathematical theology developed here depends on five key theorems.

1. Brouwer's fixed point theorem.
Ancient writers like Parmenides, Heracleitus and Plato identified a fundamental scientific problem: how can we say things that are always true about a Universe in continual motion? Over time it became accepted that the solution to this problem required reality to be divided into two: an unchanging foundation outside the Universe and the changing Universe itself. The unchanging foundation ultimately came to be identified with the Christian God, the outside creator and sustainer of the world.

Modern fixed point theorems, on the other hand, show that dynamic systems naturally include fixed points which, although they do not move, are nevertheless part of the dynamics. Given this insight, the division of reality into fixed and variable parts is no longer necessary. In particular, mathematical theorems (eg fixed point theorems) are fixed points in the dynamics of the human mathematical community. Casti: Five Golden Rules,

2. Cantor's proof for the existence of transfinite numbers.
Cantor's theorem in set theory establishes the mathematical existence of the transfinite numbers which provide us with an unbounded formal space large enough to formulate a concept of God. Cantor's infinite numbers are generated in the same way as language strings together finite numbers of words to produce an infinite variety of texts. Cantor's theorem - Wikipedia, Set theory - Wikipedia, Transfinite numbers - Wikipedia, Nowak et al: The evolution of syntactic communication

3. Gödel's incompleteness theorems.
Gödel's theorems establish the limits of formal symbolic systems. David Hilbert proposed that all mathematical problems should have definite solution. Gödel showed that this was not necessarily the case. As a consequence, deterministic formal systems are surrounded by a halo of indeterminism. On the whole, the future is unpredictable, something we not only observe in everyday life, but a feature enshrined in the uncertainty principle of quantum mechanics. Kurt Goedel I: On formally undecidable propositions . . . Goedel, Gödel's incompleteness theorems - Wikipedia, Uncertainty principle - Wikipedia, Hilbert's problems - Wikipedia

4. Turing's theorem on incomputability.
David Hilbert thought that not only should all mathematical problems have a definite solute, but that there should also exist a definite formal process for arriving at each solution. Turing showed that this is not the case: there are problems that cannot be solved by any computer, no matter how powerful. On the other hand there is a countable infinity of soluble problems which form the fixed intelligible foundation of the world. Alan Turing: On computable numbers . . . , Davis: Computability and Unsolvability

5. The mathematical theory of communication.
Shannons theorems on communication explain why the Universe is a quantized and lay the foundation for the hypothesis that the Universe is a layered communication network. Claude E Shannon, Claude Shannon - Wikipedia

Given this mathematical background, the heart of the plan is to expand physical ideas from the world of particles and forces to the human domain. This expansion relies on the fact that some properties of the world are invariant with respect to complexity. Subatomic particles are simple compared to vast ordered sets of particles like a person, a planet or a galaxy. Yet everything in the Universe has something in common: everything is a part of the whole, interacting with other parts. The uniting element is communication. In order to reunite God and the World, we model both as a transfinite computer network.

All this may seem a roundabout way to approach an ancient discipline like theology. The difficulty is that in the West, theology has been dominated by Christian thought for nearly two thousand years. There is very little non-Christian theological infrastructure to build on. To build a new theology and a new religion, it is necessary to build a new symbolic ecosystem for it to live in.

The output of religion is algorithms for living. Most of the algorithms we study are already deeply entrenched in human societies, but expressed in a multitude of different languages, customs and views of the world. The hope here is to build a consistent and transparent environment in which such algorithms can be expressed in a common language that embraces all the activities of life.

The root of the peaceful life seems to reside in tolerance. How far can tolerance go before the system breaks down? The fundamentalist temperament tends to hold us intolerantly to the letter of some law. But when we look at the Universe as a whole, we see that the fixed points needed to define consistent behaviour are very few and far between. Nowhere is this more obvious than in the realm of quantum mechanics, where a given formal arrangement can lead to an infinity of different outcomes.

The same lightness, we believe, can operate in human affairs. We live in a Universe of divine possibilities. The only constraint on our activities is that we minimize harm. We are foolish destroy the capital (physical, biological and spiritual) upon which the productivity of our lives depend. With this proviso, the possibilities for human development are literally transfinite. Productivity - Wikipedia, Capital (economics) - Wikipedia

Investment in natural theology may be the most productive use of capital we can imagine. Unlike most capital goods, true knowledge never wears out, iy is heavenly treasure that neither moth nor rust consume. Matthew 6:20

(revised 3 January 2011)

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Casti, John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory).  Amazon   back

Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.'  Amazon   back

Galilei, Galileo, and Stillman Drake (translator), Discoveries and Opinions of Galileo: Including the Starry Messenger (1610 Letter to the Grand Duchess Christina), Doubleday Anchor 1957 Amazon: 'Although the introductory sections are a bit dated, this book contains some of the best translations available of Galileo's works in English. It includes a broad range of his theories (both those we recognize as "correct" and those in which he was "in error"). Both types indicate his creativity. The reproductions of his sketches of the moons of Jupiter (in "The Starry Messenger") are accurate enough to match to modern computer programs which show the positions of the moons for any date in history. The appendix with a chronological summary of Galileo's life is very useful in placing the readings in context.' A Reader.  Amazon   back

Goedel, Kurt, "On formally undecidable propositions of Principia Mathematica and related systems, I" in Solomon Fefferman et al (eds) Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...'  Amazon   back

Papers

Nowak, Martin A, Joshua B Plotkin and Vincent A A Jansen, "The evolution of syntactic communication", Nature, 404, 6777, 30 March 2000, page 495-498. Letters to Nature: 'Animal communication is typically non-syntactic, which means that signals refer to whole situations. Human language is syntactic, and signals consist of discrete components that have their own meaning. Syntax is requisite for taking advantage of combinatorics, that is 'making infinite use of finite means'. ... Here we present a model for the population dynamics of language evolution, define the basic reproductive ratio of words and calculate the maximum size of a lexicon.'. back

Turing, Alan, "On Computable Numbers, with an application to the Entscheidungsproblem", Proceedings of the London Mathematical Society, 2, 42, 12 November 1937, page 230-265. 'The "computable" numbers maybe described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost as easy to define and investigate computable functions of an integrable variable or a real or computable variable, computable predicates and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an account of the rewlations of the computable numbers, functions and so forth to one another. This will include a development of the theory of functions of a real variable expressed in terms of computable numbers. According to my definition, a number is computable if its decimal can be written down by a machine'. back

Links

Alan Turing On Computable Numbers, with an application to the Entscheidungsproblem 'The “computable” numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique.' back

Algebra - Wikipedia Algebra - Wikipedia, the free encyclopedia 'Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.' back

Arithmetic - Wikipedia Arithmetic - Wikipedia, the free encyclopedia 'Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos “number”) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.' back

Brouwer fixed point theorem - Wikipedia Brouwer fixed point theorem - Wikipedia, the free encyclopedia 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. back

Calculus - Wikipedia Calculus - Wikipedia, the free encyclopedia '. . . Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. . . .' back

Cantor's theorem - Wikipedia Cantor's theorem - Wikipedia, the free encyclopedia 'In elementary set theory, Cantor's theorem states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by a much simpler proof than that given below, since in addition to subsets of A with just one member, there are others as well, and since n < 2n for all natural numbers n. But the theorem is true of infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite. The theorem is named for German mathematician Georg Cantor, who first stated and proved it.' back

Capital (economics) - Wikipedia Capital (economics) - Wikipedia, the free encyclopedia 'In economics, capital, capital goods, or real capital refers to already-produced durable goods used in production of goods or services. The capital goods are not significantly consumed, though they may depreciate in the production process. Capital is distinct from land in that capital must itself be produced by human labor before it can be a factor of production.' back

Claude E Shannon A Mathematical Theory of Communication 'The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.' back

Claude Shannon - Wikipedia Claude Shannon - Wikipedia, the free encyclopedia 'Claude Elwood Shannon (April 30, 1916 – February 24, 2001), an American electrical engineer and mathematician, has been called "the father of information theory". Shannon is famous for having founded information theory and both digital computer and digital circuit design theory when he was 21 years-old by way of a master's thesis published in 1937, wherein he articulated that electrical application of Boolean algebra could construct and resolve any logical, numerical relationship. It has been claimed that this was the most important master's thesis of all time.' back

Eugene Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

Exegesis - Wikipedia Exegesis - Wikipedia - the free encyclopedia 'Exegesis (from the Greek ἐξήγησις from ἐξηγεῖσθαι 'to lead out') is a critical explanation or interpretation of a text, especially a religious text. Traditionally the term was used primarily for exegesis of the Bible; however, in contemporary usage it has broadened to mean a critical explanation of any text, and the term "Biblical exegesis" is used for greater specificity. . . . ' back

Geometry - Wikipedia Geometry - Wikipedia, the free encyclopedia 'Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.' back

Gödel's incompleteness theorems - Wikipedia Gödel's incompleteness theorems - Wikipedia 'Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, a corollary of the first, shows that such a system cannot demonstrate its own consistency.' back

Hilbert's problems - Wikipedia Hilbert's problems - Wikipedia, the free encyclopedia 'ilbert's problems are a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21 and 22) at the Paris conference of the International Congress of Mathematicians, speaking on 8 August in the Sorbonne. The complete list of 23 problems was later published, most notably in English translation in 1902 by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society.' back

Kurt Goedel I On formally undecidable propositions of Principia Mathematica and related systems I '1 Introduction The development of mathematics towards greater exactness has, as is well-known, lead to formalization of large areas of it such that you can carry out proofs by following a few mechanical rules. The most comprehensive current formal systems are the system of Principia Mathematica (PM) on the one hand, the Zermelo-Fraenkelian axiom-system of set theory on the other hand. These two systems are so far developed that you can formalize in them all proof methods that are currently in use in mathematics, i.e. you can reduce these proof methods to a few axioms and deduction rules. Therefore, the conclusion seems plausible that these deduction rules are sufficient to decide all mathematical questions expressible in those systems. We will show that this is not true, but that there are even relatively easy problem in the theory of ordinary whole numbers that can not be decided from the axioms. This is not due to the nature of these systems, but it is true for a very wide class of formal systems, which in particular includes all those that you get by adding a finite number of axioms to the above mentioned systems, provided the additional axioms don’t make false theorems provable.' back

Matthew 6:20 New International Version 6:20 ". . . store up for yourselves treasures in heaven, where moth and rust do not destroy, and where thieves do not break in and steal.' back

Productivity - Wikipedia Productivity - Wikipedia, the free encyclopedia 'Productivity is a measure of the efficiency of production. Productivity is a ratio of what is produced to what is required to produce it. Usually this ratio is in the form of an average, expressing the total output divided by the total input. Productivity is a measure of output from a production process, per unit of input. At the national level, productivity growth raises living standards because more real income improves people's ability to purchase goods and services, enjoy leisure, improve housing and education and contribute to social and environmental programs. Productivity growth is important to the firm because it means that the firm can meet its (perhaps growing) obligations to customers, suppliers, workers, shareholders, and governments (taxes and regulation), and still remain competitive or even improve its competitiveness in the market place.' back

Pythagorean theorem - Wikipedia Pythagorean theorem - Wikipedia, the free encyclopedia 'In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). This is usually summarized as: The square on the hypotenuse is equal to the sum of the squares on the other two sides.' back

Set theory - Wikipedia Set theory - Wikipedia, the free encyclopedia 'Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.' back

The Assayer - Wikipedia The Assayer - Wikipedia, the free encyclopedia 'The Assayer (Il Saggiatore in Italian) was a book published in Rome by Galileo Galilei in October 1623. . . . This is the book containing Galileo’s famous statement that mathematics is the language of God. . . . "Philosophy [i.e. physics] is written in this grand book — I mean the Universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth."' back

Theorem - Wikipedia Theorem - Wikipedia, the free encyclopedia 'In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms.' back

Theory of computation - Wikipedia Theory of computation - Wikipedia, the free encyclopedia 'In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory, computability theory and computational complexity theory.' back

Transfinite numbers - Wikipedia Transfinite numbers - Wikipedia, the free encyclopedia 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back

Uncertainty principle - Wikipedia Uncertainty principle - Wikipedia, the free encyclopedia 'In quantum physics, the Heisenberg uncertainty principle states that the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both be known with arbitrary precision. That is, the more precisely one variable is known, the less precisely the other is known. This is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but rather about the nature of the system itself.' back