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volume II: Synopsis

section 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.Genesis creation narrative - Wikipedia

Although we call this creation, the Christian belief in the omniscience of God, which holds that God knows all things, past, present and future, suggests that the Universe pre-existed in the mind of God, so that we might be more accurate to say that the Universe was created out of God, rather than out of nothing. Aquinas 96: Are there ideas?

The traditional creation story also suggests that God could have made the Universe differently. In fact, some believed that the first version of the Universe was error free, evil only becoming manifest when the first people disobeyed God. Modern physics gives the impression that the Universe was created with very precise initial conditions which have constrained its evolution to give the Universe we now experience. Fall of Man - Wikipedia

Our hypothesis, that the Universe is divine leads us to modify some of these ideas. First, there can be little doubt, given the observational and theoretical evidence, that the Universe started as a very simple system and 'complexified' to its present state. This complexification serves as our definitions of creation. Teilhard de Chardin

If it is true that the Universe started as an undifferentiated point, and there is no controlling power outside it, there can be no initial conditions. For initial conditions are information, information is represented physically, and there are no distinct points in the initial singularity to represent this information. Since it is unconstrained, this Universe could not be 'made' differently. Like the traditional Western God, the Universe simply exists and that is that. We cannot say why.

Three of the most secure 'laws' of modern physics are the conservation of action and the first and second laws of thermodynamics. The first law tells us that energy, that is the time rate of action, is conserved. The second tells us that on a sufficiently large scale, entropy never decreases. Entropy is a count of possibilities, and so a measure of uncertainty. Information is that which carries certainty. Shannon supposed (and we shall follow) that the information carried by a definite point in a space of possibilities is equal to the entropy of the space. Khinchin

The question: How does the Universe create itself? thus becomes the question how does entropy increase? This in tern becomes how does the number of fixed points in the divine dynamics increase. The answer seems to lie in the making and breaking of symmetries.

To understand creation from nothing we must start from nothing. Our model of nothing is what physicists and mathematicians call symmetry. A perfect sphere is symmetrical because it does not matter which way we turn it it always looks exactly the same. Insofar as it is symmetrical, the sphere carries no information, It is meaningless. Nevertheless the symmetry of the sphere lies 'within' the sphere which is itself a definite fixed point in the world.

The geometric manifestation of symmetry is continuity: nothing changes as we move along a continuous line. The motion generates zero information because the space in which we are moving has zero entropy. A continuum without marks is a single entity. Its arithmetic entropy is one. In the logarithmic measure of entropy, its entropy is zero.

The dynamic manifestation of continuity is motion. A spinning coin has entropy of 1 bit, but it does not have a definite state because it is in motion. When it lands it assumes a definite state, and we receive 1 bit of information. Similarly an isolated quantum system evolves as a superposition of an set of definite dynamic states. We can compute the entropy of a superposition by applying Shannon's formula to the probability of observing each each element of the superposition. The information we receive from a quantum observation is equal to the entropy of the system observed. Decoherence-free subspaces - Wikipedia

Information that comes from entropy by breaking a symmetry in favour of a certain fixed point, is the heart of creation. For by establishing a new fixed point, we also establish a new symmetry which can be broken in its turn to create a new fixed point and so on. In colloquial language, every answer asks new questions. Because of this science will never die, and we see no upper limit to the complexity of the Universe.

This situation may become clearer by applying mathematical theorems due to Brouwer, Cantor, Gödel, Turing and Shannon.

Fixed point theorems tell us that when a closed convex system is mapped to itself, there is at least one fixed point. Since there is nothing outside the Universe, if we understand the dynamics of the Universe as the Universe mapping onto itself, there must be fixed points. One part of the Universe that maps onto itself is the mathematical community, whose fixed points are the theorems (like the list above) documented in the mathematical literature. Brouwer fixed point theorem - Wikipedia

Cantor showed that the existence of any set (or point) implies the existence of a larger set of permutations and combinations of the original set. Cantor's theorem - Wikipedia

Gödel demonstrated that there are unanswerable questions in any system as complex as arithmetic, ie any system that can add up. Unanswerable questions are closely related so symmetries, regions of indeterminacy. Gödel's incompleteness theorems - Wikipedia

Turing showed that there are only a limited number of deterministic mappings of the Universe onto itself. These mappings are the computable functions. If we model the dynamics of the Universe as the natural numbers mapping onto themselves, we find that the ℵ0 computable mappings are a negligible fraction of the ℵ1 possible mappings. Universal Turing Machine - Wikipedia

Shannon showed that we can use computation to establish error free channels of communication but that there is a limit on the rate of communication defined by the nature of the channel. We guess that stable structures in the Universe represent error free networks of communication. Shannon's theory also shows that there is a selective advantage in long complex messages. Each message is a point in a message space. As the messages are made longer the size of the space grows faster than the size of the messages so that longer messages can be placed further apart and have a lower probability of confusion and error. On the other hand, we see that time is of the essence in most operations, so we are faced with an uncertainty principle where speed is traded for accuracy.

We thus have a bootstrapping situation. Pure dynamics, that is pure action, is subject to no constraint but self consistency. This idea was worked out in detail in the classical model of God presented by Aquinas. Thomas Aquinas

Pure dynamics, mapping onto itself because it has nowhere else to go, creates fixed points. These fixed points, however, cannot determine the future, so each becomes in its turn a dynamic symmetry itself subject to the fixed point theorem. An example of this process is the mathematics community itself, a seething maelstrom of ideas that regularly produce a theory or a theorem recorded in the literature, which may itself become a centre of development.

The symmetry with respect to complexity which is built in to the transfinite network suggests that we can apply the analogy of the mathematics community at all scales. The first question to ask this system is Should we promote creation? Many, the 'conservatives' would say that the old ways are the best and we should change nothing.

Here we take the view that creation should be promoted. In essence, given the infinite spiritual layers available to us, any problem facing us has a very high probability of solution if we are prepared to search widely and revisit old decisions. We cannot maintain peace and stability in a changing world by sitting still

The next question is How do we promote creation? Peace is the opposite of violence, and violence is a low entropy state in which poorly defined actions are endowed with large amounts of energy. This suggests that the search for peace involves dealing with dangerously large accumulations and releases of energy. In the case of natural disasters like earthquakes and cyclones, there is little we cannot stop the release of energy, we can only take shelter.

In human space, however, we can do a lot to prevent huge concentrations of murderous power in the likes of Hitler, Stalin, Mao and the President of the United States. Theory and experience suggest that power to govern must arise from the people themselves unconstrained by monarchical violence: it seems that true democracy is the road to peace.

As we improve our communication with one another (unconstrained by secret police and forced education) we may increase cooperation at the expense of antagonism in the processing of human life. This in turn increases productivity, allowing more time to be devoted to less survival oriented activity, increasing our spiritual depth. A virtuous circle.

We see the vicious opposite to this virtuous circle operating wherever attempts to suppress and control communication leads to violence. Here we see the evil associated with the dictatorships of the world which seek to reduce the entropy and information of a whole population to that of a 'dear leader' or military oligarchy.

(revised 27 May 2013)

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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!)

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.' 
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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.'  
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Links
Aquinas 96 Summa I, 15, 1: Whether there are ideas 'I answer that, It is necessary to suppose ideas in the divine mind. For the Greek word Idea is in Latin "forma." ' 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
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
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
Decoherence-free subspaces - Wikipedia Decoherence-free subspaces - Wikipedia, the free encyclopedia 'A decoherence-free subspace (DFS) is a subspace of a system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. . . . Since quantum computers cannot be isolated from their environment (i.e. we cannot have a truly isolated quantum system in the real world) and information can be lost, the study of DFSs is important for the implementation of quantum computers into the real world.' back
Fall of Man - Wikipedia Fall of Man - Wikipedia, the free encyclopedia 'In Christian doctrine, the fall of man, or simply the fall, was the transition of the first humans from a state of innocent obedience to God to a state of guilty disobedience to God. Though not named in the Bible, the concept for the Fall comes from Genesis chapter 3. Adam and Eve live at first with God in a paradise, but the serpent tempts them into eating the fruit from the tree of knowledge of good and evil, which God forbade. After doing so they become ashamed of their nakedness and God consequently expelled them from paradise. Many Christian denominations believe that the fall corrupted the entire natural world, including human nature, causing people to be born into original sin, a state from which they cannot attain eternal life without the gracious intervention of God.' back
Genesis creation narrative - Wikipedia Genesis creation narrative - Wikipedia, the free encyclopedia 'The Genesis creation narrative (or creation myth) in the first two chapters of the Book of Genesis describes the divine creation of the world including the first man and woman. It was a product of the cultural world of the ancient Near East and yet distinctively different, incorporating older Mesopotamian myths, but adapting them to the unique conception of the Hebrews' one God.' 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
Heraclitus - Wikipedia Heraclitus - Wikipedia, the free encyclopedia 'Heraclitus of Ephesus (Greek: Ἡράκλειτος ὁ Ἐφέσιος—Hērákleitos ho Ephésios; c. 535 – c. 475 BCE) was a pre-Socratic Greek philosopher, a native of the Greek city Ephesus, Ionia, on the coast of Asia Minor. . . . Heraclitus is famous for his insistence on ever-present change in the universe, as stated in his famous saying, "No man ever steps in the same river twice" (see panta rhei, below). He believed in the unity of opposites, stating that "the path up and down are one and the same", all existing entities being characterized by pairs of contrary properties. His cryptic utterance that "all entities come to be in accordance with this Logos" (literally, "word", "reason", or "account") has been the subject of numerous interpretations.' ' back
Thomas Aquinas Summa Theologica I, 2, 3: Whether God exists? 'I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . ' back
Universal Turing Machine - Wikipedia Universal Turing Machine - Wikipedia, the free encyclopedia 'Alan Turing's universal computing machine (alternately universal machine, machine U, U) is the name given by him (1936-1937) to his model of an all-purpose "a-machine" (computing machine) that could process any arbitrary (but well-formed) sequence of instructions called quintuples. This model is considered by some (for example, Davis (2000)) to be the origin of the stored program computer -- used by John von Neumann (1946) for his "Electronic Computing Instrument" that now bears von Neumann's name: the von Neumann architecture. This machine as a model of computation is now called the Universal Turing machine.' back

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