vol 3: Development
2 Model
page 8: Complexification
Site map
Directory
Search this site
Home
1: About
2: Synopsis
3: Development
Next: page 9: Selection
Previous: page 7: Constraint
This site is part of the natural religion project The natural religion project A new theology A commentary on the Summa The theology company
Complexification
The 'big bang' and evolution
The 'standard' scientific cosmology sees the world beginning very simple and completely symmetrical (the initial singularity) and breaking this symmetry step by step to become the complex universe we now inhabit. Teilhard de Chardin coined the term 'complexification' to describe this process. Teilhard de Chardin
Charles Darwin developed the notion of evolution by natural selection which has since become the foundation of biology. From an abstract point of view, evolution has three requirements: replication; variation; and constraint, which selects of some of the variants for further replication.
Here we take the view that various embodiments of this abstract process of evolution explain the branching and growth of the cosmic tree which is rooted in the initial singularity.
This page is concerned with replication and variation. We turn to selection in page 9: Selection
We begin with the proposition that the cosmological initial singularity corresponds to the mathematical empty set. Given this correspondence, we imagine the complexification of the universe to proceed in a manner analogous to the set theoretical construction of the natural numbers by making the empty set the member of a successor set, and so on. Jech Given the natural numbers, one can go on to construct the transfinite numbers, Set theory - Wikipedia
We now turn to the network model to get a closer view of this process, beginning with a theological hint from Thomas Aquinas. Aquinas holds that God is 'omnino simplex' altogether simple, without parts or discernible structure. Aquinas 20 We may reasonably equate god so defined with the initial singularity and the empty set, which are both without any discernible structure.
We think of the empty set as a static entity, but our world is inherently in motion. Einstein showed that we can only develop a consistent theory of the large scale structure of the universe in terms of space-time. We experience an ordered and irreversible succession of events. Our hypothesis is that such successions of events can be modelled as lines or strings of communication in a network.
From a mechanistic point of view, the working parts of a network are all computers, whose mathematical models are Turing machines. Let us assume that the computing equivalent of the empty set is the non-operation, abbreviated nop. Wikipedia - NOP Computer programmers use the nop to waste a bit of time while something else happens, like a user hits a key.
The atomic act of Turing machine is fixed by four parameters, which may be represented by a 'quadruple' or a four dimensional vector. Turing Davis The components of this vector are:
1. The internal state of the machine before the act;
2. The tape symbol read by the machine
3. The action taken by the machine - print, move left or right; and
4. The final state of the machine, after the act (the initial state for its next act)
We may consider components 1, 2 and 4 to be in the spatial domain, because they persist over time. Then component 3 naturally falls into the time domain. We will discuss this partition in more detail in the pages on physics.
Let assume that the Turing machine that performs a nop has one state, one symbol and one action, to take a step forward in time.
A clue from traditional theology
The Christian story recorded in the New Testament seems to attribute three personalities to God. Christian theologians were thus faced with the problem of explaining how God could be both one and three without inconsistency.
Aquinas records the standard answer to this problem in the Summa. Aquinas 160 sqq This answer is expressed in terms of a psychology of knowledge and love.
God the Father, contemplating Himself, produces as Image (mental Word, latin Verbum) of himself. Lonergan Unlike the abstract images in the human mind, the Image of God is a real person, the Son, distinguished from the Father by the real relationships of 'Paternity' and 'Filiation'. The love relationship between Father and Son is also a real person, the Holy Spirit.
In the model the Trinity is generated by duplication with a difference. The difference is that the copy is not the original.
So we propose that a formal model of the complexification of the world can be built on a similar idea. The 'force' promoting an increase in the formal complexity of Turing machines arises from Cantor's theorem, so we might call it the Cantor force.
Aquinas psychological model conveniently limited the personalities of the divinity to the three mentioned in the New Testament since there were only three psychological entities, mind, image and love. The Cantor force sees no such limit, driving the process from the initial singularity to the present enormous spatial size and complexity of the universe.
(revised 22 November 2007)
Further reading
Books
| Axelrod, Robert, The Evolution of Cooperation, Basic Books 1985 Amazon.com: 'This book is a must-read not only for students (broadly defined) of the social sciences, but also for politicians and bureaucrats, especially those in charge of military and foreign affairs. Axelrod's book is a tour-de-force in multi-method approaches. Although the author is a trifle repetitive and occasionally laborious, I think the profound content of the book far outweighs the minor inadequacies of its form. At the risk of sounding like a logical positivist, I would venture to say that Axelrod's approach offers hope for a bottom-up construction of cooperation in an uncertain world without a central authority.' Reeshad Dalal Amazon back |
| Cummins, Denise Dellarosa, and Colin Allen (editors), The Evolution of Mind, Oxford University Press 1998 Introduction: This book is an interdisciplinary endeavour, a collection of essays by ethologists, psychologists, anthropologists and philosophers united in the common goal of explaining cognition. ... the chief challenge is to make evolutionary psychology into an experimental science. Several of the chapters in this volume describe experimental techniues and results consistent with this aim; our hope and intention is that they lead by example in the development of evolutionary psychology from the realm of speculation to that of established research program' 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 |
| Dawkins, Richard, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design, Penguin/Pelican 1996 Preface: '[Darwinism] is, indeed a remarkably simple theory; ... In essence it amounts simply to the idea that non-random reproduction where there is hereditary variation, has consequences that are far reaching if there is time for them to be cumulative ... ' Amazon back |
| Dawkins, Richard, Climbing Mount Improbable, W. W. Norton & Company 1997 Amazon editorial review: 'How do species evolve? Richard Dawkins, one of the world's most eminent zoologists, likens the process to scaling a huge, Himalaya-size peak, the Mount Improbable of his title. An alpinist does not leap from sea level to the summit; neither does a species utterly change forms overnight, but instead follows a course of "slow, cumulative, one-step-at-a-time, non-random survival of random variants"--a course that Charles Darwin, Dawkins's great hero, called natural selection. Illustrating his arguments with case studies from the natural world, such as the evolution of the eye and the lung, and the coevolution of certain kinds of figs and wasps, Dawkins provides a vigorous, entertaining defense of key Darwinian ideas.' Amazon back |
| Lonergan, Bernard J F, and Robert M. Doran, Frederick E. Crowe (eds), Verbum : Word and Idea in Aquinas (Collected Works of Bernard Lonergan volume 2) , University of Toronto Press 1997 Jacket: 'Verbum is a product of Lonergan's eleven years of study of the thought of Thomas Aquinas. The work is considered by many to be a breakthrough in the history of Lonergan's theology ... . Here he interprets aspects in the writing of Aquinas relevant to trinitarian theory and, as in most of Lonergan's work, one of the principal aims is to assist the reader in the search to understand the workings of the human mind.' Amazon back |
| Teilhard de Chardin, Pierre, The Phenomenon of Man, Collins 1965 Sir Julian Huxley, Introduction: 'We, mankind, contain the possibilities of the earth's immense future, and can realise more and more of them on condition that we increase our knowledge and our love. That, it seems to me, is the distillation of the Phenomenon of Man.' Amazon back |
Papers
| 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
| Aquinas 20 Summa: I 3 7: Whether God is altogether simple?? 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back |
| Wikipedia - NOP NOP - Wikipedia, the free encyclopedia 'In computer science NOP or NOOP (short for No OPeration) is an assembly language instruction, sequence of programming language statements, or computer protocol command that does nothing at all (besides wasting cpu clock cycles)' 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
Related sites:
Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty
Copyright: You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.
