vol VII: Notes
2016
Notes
Sunday 24 January 2016 - Saturday 30 January 2016
[Notebook: DB 80: Cosmic plumbing]
[page 3]
Sunday 24 January 2016
Do I understand myself? Not really, mainly because my insights into the information I receive are sometimes apparently random events. I see an insight as becoming conscious of an act of decoding. In normal conversation in my native language insight is effectively instantaneous, as it is in the normal operations of my building trade, measuring, cutting and fixing, At a higher level, however, insights come less frequently, as in breakthroughs in design. In this theological realm, they are rarer still and I am finding myself held up for long periods trying to find a way through the thicket of misunderstanding. The same structure is to be found in our collective understanding of the world, exemplified by the work of pioneers in various fields who see meaning where others do not, like Galileo, Newton, Einstein and co. We sometimes call the inability to go ahead a mental block. I presume that my subconscious mind is working on the problem, but has not found an answer yet. From a formal point of view, we can imagine each new answer as the discovery of a proof or process that takes us through the thicket, rather like finding or building a new track through a state previously seen as wilderness. I write things like this to reassure myself that if I keep at it I will eventually find a way through my present impasse, as the mathematical
[page 4]
community, for instance, found a proof of 'Fermat's last theorem'. Indecision is a different thing, since one has a series of options for action and cannot yet decide which to take. It too can be overcome by insights that reveal that course of action superior to all the others. For me the current issue is how to make the Catholic Church aware of the ideas contained in the following little essay: paradigm change in theology. Wiles' proof of Fermat's Last Theorem - Wikipedia
Paradigm change in theology: bringing God back home
The Christian history of salvation is a fictional story that lightly touches history and the nature of the world we inhabit. Nevertheless it has served the political purpose of providing a framework of belief upon which people have built many stable societies.
Although it hopes to evangelize the world, Catholicism remains just one of the theologies that have evolved over the last 5000 years.
Most of these theologies proceed on the assumption that God is an invisible mystery about which we can know and say nothing. Thomas Aquinas is following well established tradition when he says we cannot say what God is, only what it is not.
The story of science suggests that new scientific developments often take a broader view of the world within which the old view turns out to be a special case. Christians understand the world to be a flawed creation of the invisible God about which we know nothing. They say God is not the universe.
Let us make a new hypothesis God is the universe. That is the universe is not a perfect creation crippled by God in response to human disobedience, but itself fulfills all the traditional roles of God, creator, sustainer, judge. Included in it are Christianity, all Christians and the theological and religious beliefs of everybody.
Many of the ancient religions cast their adherents as chosen people, with the implication that non-adherents are not-chosen. The not-chosen may nevertheless think themselves chosen by their own God, so we come to the modern problem: we are trying to create peace among disparate people who are listening to different Gods. The only solution is to agree that there is just one God.
There are many Gods precisely because God is considered to be mysterious and invisible. Anybody can put words into God's mouth and give it a certain personality. By agreeing on a visible God, we lay the foundations for a politically united planet. By multiplying Gods, we lay the foundations for war.
If the universe is divine we all walk in God and all experience must be experience of God. This means that theology, the traditional theory of everything, can become a real science. Since God is one, and science connects us to reality, we can expect scientific theology to become unified.
We have a tendency to think that we are smarter and better than the universe that created us. This error is coupled to the idea that we are special creations of God, pilgrims passing through this world on our way to a better place. In the light of what we know about the universe, this claim is coupled to denial of evolution, that is the creative power of the universe.
We observe that death is a reality in the world, but it is countered by reproduction. Reproduction is seldom perfect. There are variations. Each of these variations is selected by its environment to reproduce or not. What we see now is the outcome of three or four billion years of successful reproduction embracing billions of generations of a huge number of individuals.
We may look at this world as a communication network. Everything communicates with everything via gravitation. Then there are smaller local networks. I am a networked community of some hundred trillion personal cells and attendant hordes of bacteria and viruses which more or less work together to make me.
Every organism has its communication protocols. We have speech, which lays the foundation for politics and large scale cooperation. There can be no doubt that our cooperative abilities account for our huge success as a species.
The cells in my body cooperate because they share a common doctrine encoded in my DNA. Religion serves the same role in human communities. Not all communities are built around a document, but no community can exist without communication protocols shared by all its members. In some communities, the land itself provides the common protocol. This seems to be the way the original Australians derived guidance from their environment.
Science follows this approach. It is based on fictions, we call them hypotheses. The game is to dream up testable fictions and test them. Is the universe divine? An immediate problem: traditionally, God is completely simple, a consequence, Aquinas says, of the fact that it is pure act. The world, on the other hand, is very complex.
An answer may lie in the mathematical fixed point theory. Since God is everything, we may model the life of God as God mapping itself onto itself. Fixed point theory tells us that such mappings often have fixed points, x, such that f(x) = x. These points are not outside the dynamics, they are simply points that do not move.
These fixed points of the divine dynamics may explain the complexity of the world. The structure of the world is not outside the seamless simplicity of God, it is part of it. With this problem out of the way we can proceed to develop scientific theology.
Random events exist in a world where no algorithm is known, even though such algorithms may exist. Maybe this is why we see random choices in quantum mechanics, where we see that different algorithms are chosen with different probabilities given different initial conditions. The probability is measured by the Born rule which measures the overlap between states. The overlap is time and space dependent, so that we can imagine that in a local moment of space-time the next step is inevitable, but as we move in space-time, probabilities emerge for other events which are fixed points in the ruling differential equation. Born rule - Wikipedia
Harris: Jail time for the psychological abuse of children. What abut the weird ideas that cultures instill in their offspring? I claim to have been psychologically abused by being led to believe the fictional Catholic history of salvation. It is hard to hold my teachers morally responsible for this abuse, however, because they had also been indoctrinated and firmly believed what they had been told. My task has been to break this chain of indoctrination in myself and replace it with a plausible alternative, first for myself, and then begin to propagate it to others. I am pleased to see that my own children have abandoned ancient religion and live by modern secular standards of human rights and evidence based decision making. Lia Harris
Clear insight motivates me to act, uncertainty to withhold judgement.
[page 5]
In general, however, we are acting under pressure of time and have to act without certainty. One strength of the system of judicial inquiry is to budget sufficient time and money to go into a situation in detail. Owen. Sir Robert Owen
While I think I can learn a lot from reading Chaitin, something inhibits me from doing this now. As ever the question is should I force myself to do it, or just wait until I clearly want to. Do I make more progress by trying to push myself or just going along with myself? Time pressure or no time pressure? The state of the world inclines me to work as fast as I can because I think I can contribuite to theological peace, but how is this speed to be achieved when one is looking for a series of insights to build a watertight theological narrative? It may be that the desire for instant gratification is a source of violence. Chaitin
On the verge of Chaitin. Am I ready for it? What does this mean? That my mind judges that I am in a context where I can profit from this reading? Now the sun is out and I will go and do a bit of construction on my verandah.
Chaitin page 2: Jones and Matijasavic (1984): 'Their work gives a simple straightforward proof, using almost no number theory, that there is an exponential diophantine equation with one parameter p which has a solution if and only if the pth computer program (ie the program with Gödel number p) ever halts.' J .P. Jones and Y. V. Matijasevic
Digitization opens the deterministic (rule bound) element of the universe to occupy the whole space inside the bounds determined by the theories of [Cantor], Gödel, Turing and Shannon.
Monday 25 January 2016
[page 6]
Halted algorithm produces output, ie (in the physical world) an observable.
Chaitin page 7: '. . . any computation can be coded in an exponential diophantine equation . . . .'
'. . . all mathematics, once formalized, is mirrored in the properties of whole numbers.'
Chaitin: He is basically using a form of Gödel numbering to convert the string of symbols in an algorithm into a numerical string. The common feature is that both notations are position significant, ie ordering is of the essence. In Hilbert space no mention is made of the ordering of the basis vectors, but all the other state vectors are ordered with respect to the basis, the same element in each state vector corresponding [to a particular] element in the basis vector. The effect of this is to make the ordering relevant when we are computing dot products and overlap integrals.
[page 7]
Feynman: What do you care Feynman
Stopping a little bit now and then to smell the flowers and develop a sensory picture of the divinity of the Universe. Up until now the project has gone forward with the intensity that developed in my last three years in the Order. I read Lonergan's Insight while I was in the convent in Wahroonga. It gripped me so much that I began getting up at 3am to get in a couple of hours of work before the waker up came around knocking on our doors yelling benedicamus domino, to which we replied deo gratias to show that we were awake.
Lonergan invented something he called empirical residue, meaningless data. He established as a principle that God should be completely meaningful, that is intelligible Since he had imported empirical residue into the observable universe it obviously could not be divine because it was not completely intelligible. q.e.d. Wrong. Every observable event on the universe is a consequence of previous observable events which give it meaning. There are no meaningless data, so by Lonergan's standard the Universe could be divine. I believe I began to explain this to my teachers by the time we moved to the convent in Canberra, asking why we needed to believe in the hypothesis that God is other than
[page 8]
the universe. Eventually this became known to the Master of Studies and I was called in for long talks. As I remember it I was trying to take the Galilean line that we have to observe and measure the world if we want to know it. The Master, Father Fitzgerald was defending the philosophical position that we deduce our knowledge of the world from first principles 'per se nota', ie alleged to be obvious like empirical residue. After two years of this I was asked to leave, having written my first attempt at mathematical theology 'How Universal'. Meanwhile I boiled off some of the tension by building loads of furniture for the Canberra convent and continuing my clandestine love affairs with various brethren. Since then I have rarely relaxed from continuing to follow this path because I think it is of critical importance for the theological community to move from fairy tales to reality. How Universal is the Universe (1967)
Chubb Chief Scientist: economic value of science. Australian Office of the Chief Scientist
Eureka Street: An article in two parts, one scientific and the other political. Politics occurs at any point where to entities communicate with a view to arriving at a common course of action. This is a very general definition since it could apply to a parliament, a national vote or the decision made by some atoms to bond together to form a molecules, eg 2 hydrogens and an oxygen get together
[page 9]
to form water. Such bonding generally releases energy. In the case of a parliament an agreement is reached and passed as an act of parliament and energy is released (in the form of money) to put the act into action in the real world.
Chaitin describes the selective process that separates computable from incomputable, expanding Gödel's proof to show that there can be a countable infinity of solutions to some diophantine equations, but there is an uncountable infinity of insoluble equations, that is starting position from which a computer does not halt [dark energy?].
A computer network is naturally described by diophantine rather than continuous equations.
The politics of paradigm change, the Galileo story. Galileo affair - Wikipedia
Feynman on political force: NASA and managerial denialism: page 157: 'The press was reporting rumours that NASA was under great political pressure to launch the shuttle . . . '
Pressure and error, an essential feature of sport: put the opponents under pressure so they make errors. Australian Open tennis.
Basically, the Holy Inquisition judged that Galileo was expressing ideas
[page 10]
they could not agree with and so they punished him. He was lucky to escape torture and death. I got off far more lightly, and at the beginning of my life, in a free country, so I have been able to develop my position for about 40 years in an academic desert.
Feynman page 215: 'So that's my theory: because of the exaggeration at the top being inconsistent with the reality at the bottom, communication got slowed up and eventually jammed. That's how it is possible that the higher ups did not know.'
'For a successful technology, reality must take precedence over public relations, for nature [god] cannot be fooled'. page 237.
Tuesday 26 January 2016
Invasion day, remembering the day when Australia was for better or worse taken into the British Empire as an offshore prison camp. It was not a good day for the locals since the prison camp infected them with all sorts of evils ranging from viruses and bacteria to firearms and government by a sexist, racist power hungry nation whose elite can see people solely as either economic units or impediments to development that need liquidation. Australia Day - Wikipedia
[page 11]
I would like to think of myself as an arms developer producing the necessary social software to defeat the forces of theological and religious monarchical dictatorship. We think we are doing the work of God, but the god we have created is a false god, and is leading us astray.
The attempt to find a foundation for true theology in the physical world is slow and rather stressful, but it seems to me to [be] a foolproof answer for anybody who wants to claim that the world is not divine.
So far we have found it [very difficult] to manage large scale paradigm changes (revolutions) without bloodshed. I fear the theological revolution I am trying to motivate. It cannot be introduced by fiat. for that would be the monarchical approach, waging war to bring 'peace'. Instead it must grow from a seed, and I am trying to construct one species of seed, a formalism which when introduced into a suitable environment comes to life and grows [something like DNA or a computer program]. Looking at history, I think my little idea may take many more years to reach puberty, but programming this dream, an exercise in political software, is very exciting even at the one person scale. At present I see that the world spends about ten hours a month reading this site and it has not grown for years, so it is not alive yet. Basically we want to see evidence based education replace authoritarian education. This is well under way in all fields but theology.
[page 12]
We might trace every new paradigm to a key idea. Einstein based the special theory on the idea that it takes time to travel though space, but we can move one way through time without moving through space [which suggests that time is prior to space]. The general theory is based on the idea that coordinates do not have immediate metrical meaning, the application in a differential manifold of Cantor's idea of one-to-one correspondence and its corollary, that anything can correspond to anything so we can make relatively infinite structures from finite structures by permutation. Galileo saw that we must measure the world to know it and my hobby horse is that if theology is to be a science god, or at least the fixed points of god, must be observable.
The Church is based on a completely false view of humanity. It is the view of an absolute monarchy which sees its subjects as its property, to be disposed of at will under pain of death. The Galileo affair exhibits the Papacy acting in exactly the manner of the Code of Canon Law where it defines papal power. The alternative to monarchy is equality, we are all equal before the law, from pope to newborn child. Code of Canon Law 333: The Roman Pontiff
I want to work within the Church but can only do so if the Church is broad enough to hold me. At present I think an interpretation of its formal constitution says that
[page 13]
it is not, but that constitution can be changed to accept the full domain of human evidence based thought.
Fixed points carry energy in the same way as particles in motion, since at this level energy is not yet differentiated into potential and kinetic, ie this is the layer with no fixed points, the initial point or singularity [?].
Politics: monarchy vs freedom. The bound on freedom is when it causes unjustified harm to others [the aim of justice should not be to harm the person in error, but to correct the error, not the sinner but the sin].
A computer is a multidimensional point that comes to life when the power is turned on.
Superposition = sequence: parallel exclusion principle.
Digital music.
I make things to help make myself. Life as a work of art / technology, personal religion defined by personal theology.
Meaning of x = all the links between x and the not-x's in this world.
[page 13]
Wednesday 27 January 2016
Thursday 81 January 2016
We assume that an invariant Lagrangian corresponds to a program of minimal complexity.
Chaitin page 91: '. . . we can start with a very concrete straightforward approach, namely to consider the size of a LISP expression measured by the number of characters it has.'
The Church still suffers from the belief that it has a divine right to lay down the law for everybody.
Chaitin: 'So we shall now study, for any given LISP object, its program size complexity, which is the size of the smallest program . . . for calculating it.'
Chaitin page 92: 'The complexity of an S-expression is the size of the smallest S-expression that evaluates it,. . . ' by a deterministic computation.
'. . . the probability of a k-character program is 128-k
Chaitin page 8: 'Any proof can be encoded in an exponential diophantine equation,' Jones and Matijasevic.
In a regular computer the formal structure must be physically realized.
Travel in space = shift register.
[page 15]
Friday 29 January 2016
Chaitin is principally concerned with quantities of information measured in bits. From this point of view his ideas seem to be an exploration of the cybernetic principle of requisite variety: a system can be controlled (proven, made deterministic) only by a system of greater or equal complexity (entropy). So letters cannot control words, words sentences, and so on. We generate complexity formally by making strings, and given equivalent information density per unit length, a short string (list) cannot determine a long list, ie the long list is incomputable, uncertain or incomplete with respect to the short list. On the other hand long lists can control short lists, the essence of Shannon's theory. Claude E Shannon
Barrow and Tipler page 83: 'Goethe detects and rejects the systemic bias in Man's (sic) self-image which tempts him to elevate himself relative to the world at large.: "Man is naturally disposed to consider himself as the centre and end of creation and regard all the beings that surround him as bound to subserve his personal profit. . . . He cannot imagine that the least blade of grass is not there for him (J W Eckermann: Conversations of E with Goethe and Soret). Von Goethe, Barrow & Tipler: The Anthropic Cosmological Principle
What we are interested in here is the evolution of software toward programs which execute with the maximum minimization of the use of resources to achieve a given end, eg ordering a random input like a cloud of names and numbers into an alphabetic or numeric list that is easy to access, exponentially faster than reading a random list to find a number. Sorting algorithm - Wikipedia
[page 16]
Barrow and Tipler page 84: Darwin: 'The old argument from design in nature as given by Paley, which formerly seemed to me so conclusive, fails now that the law of natural selection has been discovered.' (D, Autobiography, Dover) Darwin
Evolution, like gravitation, is a second order process, ie myself and my environment interact with one another, from generation to generation, but also moment to moment. Over the years I have radically modified my environment by building a house to protect my family and all my stuff from the elements and to serve as a 'machine for living', with facilities for eating, grooming, sleeping etc. This house (and the material culture of which it is part) isolates me from many of the forces of nature that select organisms not so well interfaced with and protected from the dangers of their environment.
The weakness and hypocrisy of the Church are well demonstrated by its practice of handing things over to the secular arm when they become too realistic for it. Once it was execution, now it is the attempt to purge itself of child abuse, sexism and its general mismanagement of everything to do with human reproduction on the premise that it is for the monarch to control reproduction, not those actually involved in doing it. Einstein taught us that we must work from particular (local) to general (global), not the other way around, starting from some premisses laid down by the ruling class.
Physics is not primarily concerned with meaning but
[page 17]
with measurable quantity. The basic unit of measurement is the quantum of action, and the skill of the physicist is to devise a scenario that gives the observed rates of action per category of action, that is per particle parametrized by energy, momentum and direction of travel, eg an electron with energy 1 GeV travelling north.
Saturday 30 January 2016
The world starts off very simple so that it can be modelled by quantum mechanics which is linear, meaning that it is represented by first order differential equations. Creation really starts when we introduce communication between independent entities, that is we introduce orthogonality = space. This happens at a universal scale with the general theory of relativity, which gives us a kinematic view of the large scale creation of space and the overall structure of the resulting universe, which is 'context free' ie unconstrained [generally covariant]. Creation proceeds by the mutual emergence of context, ie the creation of a network whose element is a communication link between two points in space. The first formal implementation of this idea is the ancient notion of the procession of the Word. Trinity - Wikipedia
Am I obsessed with theology? Yes, but in a nice way, because it is an exciting and interesting quest with significant implications
[page 18]
for our self image and our management of our impact on the world. To date we have run our economy on the basis that the world exists just for us. We have known theoretically for a long time that we depend on the environment for our existence but saw this as the work of a benevolent and omnipotent god that could make sure all turned out for the best. Now we know that at all scales how we act on the environment elicits an reaction of the environment on us which is slowly bringing the needs of the real environment into the political and economic picture. The second order (consciousness) is beginning to become observable.
The world is constrained by consistency. The potential which drives my writing is the result of my becoming aware that Christian theology, while immensely powerful politically has no scientifically demonstrable foundation and so is literally 'out of this world' in that it contradicts reality. My task, well under way, is to remove this inconsistency (cognitive dissonance) from my own thought and hopefully sell my work as a 'self-help' project for everybody else. Meanwhile back to plumbing [where divine judgement is often instantaneous; bad joints leak].
Barrow page 138: 'All theories of physics that have ever been proposed as fundamental—Newtonian particle physics, the electromagnetic equations of Maxwell, Einstein's general theory of gravity, and even quantum mechanics—all of these are ontologically deterministic theories.' Ie computable. The incomputable stands above the physical layer.
page 139: 'The theory of quantum mechanics itself tells us that it is impossible to get the necessary information to predict the future wave function even though the wave function is in fact determined.' (?)
page 146: 'One can never be sure tast future development in physics will not show that the supposedly independent properties of matter are in fact subtly related, and that only one particular collection of material properties are (sic) logically possible.
page 154: 'A program can be regarded abstractly as a map f: N → N from the set of natural numbers N into itself.'
