vol VII: Notes
2012
Notes
[Sunday 28 October 2012 - Saturday 3 November 2012]
[Notebook: DB 73 Spring2012]
[page 126]
Sunday 28 October 2012
I have no idea what will come next.SLOW = RARE = IMPROBABLE
Distance is pythagorean. Overlap is an exponential function of distance. SLOW = SMALL OVERLAP
'To happen' is to overlap. We visualize this in Hilbert space. Shannon is concerned with establishing orthogonality = zero overlap = zero confusion = complete resolution = no error.
Brower predicts the existence of fixed points,. Cybernetics describes their realization.
To map the transfinite netowrk to the world, we must map it to quantum mechanics.
In the network an observation is the transmission of a message which may be analyzed in terms of encoding and decoding. In quantum mechanics we model observation with
[page 127]
a unitary operator possessed of a certain set of eigenfunctions, each of which can be represented as an algorithm or computer, so we guess an operator corresponds to a set of computers in the network which operate with a frequency proportional to an eigenvalue.
Can we say that in quantum mechanics encode and decode are conjugate?
The unitary evolution of quantum mechanics conserves energy, but distributes it in different ways modelled by the time derivative of the energy matrix. We may see this as a longer process comprising the subprocesses represented by the eigenvalues each of which is 'called' at a certain rate. Harmonic analysis will yield a similar spectrum of species in a conventional computer, as when we set our debugger to find out where all the action is happening with a view to optimization.
Quantum field theory is an elaborate structure for determining fixed points,. Does the transfinite computer network provide a shorter path to the same results?
We assume that quantum systems can do anything a Turing machine can do and vice versa. This is to be contrasted with the view that quantum computers may be more powerful. It seems this that view (and most of hte trouble in quantum field theory) arises from treating the continuum as a geometric rather than a logical object,. The life of a photon is a logical object. Its mapping onto spacetime (a null geodesic) is a vestigium of the very simple Universe in which photons as such exists, as opposed to the 'meaning' they obtain when spaces and particles emerge.
CONSERVE - CONSTRAIN - FORBID
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We say in quantum mechanics that anything can happen, but a lot of quantum field theory is conservation laws which tell us which things do not change.
Symmetries tell is what can't happen, incomputabilities.
SYMMETRY = INCOMPUTABLE (UNDECIDABLE)
Embodied message = particle.
Network explanation of neutral K meson: Feynman III pp 11-12 et sqq.
Hamiltonian equations can only be solved for certain values of E (remember E is the obnly adjustable thing we have in the ewuations).
Given that fixed points exist, how do we find them? In physics the Lagrangian, in mathematics eigenvalues of operator.
Communication theory is concerned with independence, quantum mechanics with action.
What's the matter with matter. Matter has had a very bad press over the ages, keeping company with the world, the flesh and the devil. We still treat it like dirt but it is time we changed our feelings about matter to match the reality revealed by science.
Earthmates: grounded on planetary harmonies. [taken]
The fixed points of the Universe are the axes around which it rotates, where by rotation we mean a periodic
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function.
A periodic function is closed and defines a fixed point or set of fixed points, a group.
Normalization preserves particles: there is no creation and annihilation, or at least particles annihilated are recreated, unlike as in relativistic theory, E = mc2.
Amplitudes represent the invisible processes of the eigenfunction computations.
Feynman page 17-5: 'Classically, if a state is symmetric under an inversion, the operation repeated gives back the same state. In quantum mechanics, however, there are two possibilities: we get the same state or - the same state. When we get the same state . . . even parity. When the signs are reverses . . . odd parity.'
Monday 29 October 2012
The invisible computers compute the wave functions according to the simple rules: add indistinguishable alternatives, multiply sequential processes, halt is equivalent to observation.
Amplitudes are two dimensional cardinals, the parts we call real and inaginary, and may be thought of as elements of an incomplete computation which will yield a message on completion.
Sine and cos 'emerge' from the complex exponential
[page 130]
eiθ = cos θ + i sin θ
The 'virtuality' of a particle is relative to who is watching: it is real to the system that sees it ('measures' it).
What I am looking for is a nice complete story to encapsulate a theology. We begin with the classical God and then imagine that the world 'emerges' within this divine state of pure action. That this is possible is suggested by fixed point theorems. The point is that the fixed points (forms) are part of the action, not distinct from it. The distinction pioneered by Parmenides which descended to us via Plato and Christianity between the eternal forms and the moving world is no longer necessary, we can identify God and the world. The next step is the analogy between the emanation [procession] of the trinity and quantum mechanics which we develop in terms of a computer network, physiologically very similar to the neural networks within us that do the processing necessary to project our conscious minds to ourselves.. etc. To Theological Studies.
'Wave functions' are the [invisible] subconscious of the world.
Quantum mechanics shows us how to pick out the stationary points inthe world when combined with the Lagrangian method.
Although the words of God and selected commentators have been endowed with great emotional [and political] power by the majesty of the Roman Catholic Church, their truth remains a matter for scientific judgement, takng into account formal correspondences between the text and experience.
[page 131]
INTERFERENCE = PROCESSING (INVISIBLE)
Observation comes when the process halts; there is no more 'interference'.
Each transfinite number represents a complete set of functions on its domain, the complete set of functions from the layer before. When we model that as an infinite product of infinitesimals, we get the exponential function.
The memory in quantum computation is the state vector and operators change the values in the cells of the memory, which are paired, z = x + iy [a vector equation].
Tuesday 30 October 2012
Quantum mechanics is all about timing. When amplitude is at a maximu,, probability is at a maximum. p = |ψ|2. What does this mean? We look at timing in our own lives, where it is seen to be very important in day to day life, in everything from getting the kids off to school, humour, music, planting and reaping and almost everything else. Spatial distribution is secondary to timing, since with a global communication system operating near the speed of light we can converse wherever we are on earth. Fixed points in timing are regions of phase coherence when two or more
[page 132]
processes work in step, points we detect using the lgrangian and the action principle.
So I have learnt by piutting the timing belt on wrongly in my car.
Quantum mechanics is about pure timing.
Quantum field theory adds the complication of spatially distributed processing and communication delay, which complicates questions of timing but makes certain interactions impossible (outside the communication cone).
Have I bitten off more than I can chew? Today has been a day of doubt. I continue with this project because I have faith in it, so I see my work as an investment which may not pay off for me, but for my children and their children ad infinitum. One cannot half jump the chasm between Christianity and science, it is either be content with two truths of go all the way.
The divine world is a brilliant idea that can change the world if people understand it.
Although authors like Aquinas and Lonergan advance proofs for the existence of God, Christianity is deeply rooted in faith, and those with the faith may not be swayed by arguments against it. Nevertheless we have faith that such arguments, if they are good, will eventually prevail and the scientific approach to God based on contemporary evidence will sweep the field as well established disciplines like physics, chemistry and biology have done, and become a sound basis for engineering.
[page 133]
By God we mean the source of all our experience, the Creator. Aquinas, following Aristotle, produced the definitive Christian model of God based on the hypothesis that God is pure act.
Traditionally God is the realization of all possibility. We explore this idea using Cantor's transfinite cardinal and ordinal numbers as a backbone for a model of God,. This leads us to the question of the relationship between model (kinematic) and reality (dynamic).
The core of the story is that mathematics is so useful because the fixed point in the dynamics of the mathematical community is generated by the same process as generates the fixed points in the physical world, so that it is not surprising that they show considerable isomorphism, beginning with counting and arithmetic, measurement and geometry [a;; quantum mechanical measurements are counts of bins].
We structure of the proof in a layered network, beginning from pure act and developing through the establishment of fixed points in a way similar to the growth of the transfinite numbers. The link is symmetry with respect to complexity, the basic functioning of creation which brings new fixed points into the dynamics. The idea is that each fixed point is itself a convex bounded set which generates a new fixed point within it, and so to worlds within worlds to God.
The principal difficulty with the classical God is how it encodes its knowledge, since it is omnino simplex, no physical representatives of information.
Since this position flies in the face of Aquinas, we will follow Aquinas' development of the theory
[page 134]
of God, pointing out the differences induced by out contradiction of his Christian hypothesis. A commentary on the Prima pars.
The foundation of my faith is that the alternative is worse because it is arbitrary, devised by the elite to enforce their power.
Wednesday 31 October 2012
Religion helps us deal with emergencies: rare but significant events which cannot be accurately predicted, wars, storms, fires, but also falling in love, conceiving and other good emergencies. Prudence suggests that we budged for emergencies, having a bit put aside for a rainy day. How much to put aside as an actuarial problem which lies at the foundation of a properly funded insurance business. Actuarial science - Wikipedia
The commentary on Aquinas, question by question. A big job? Worth doing? In a way it can be a record of my breaking the bonds of historical theology one by one. The key now is the fixed point theorems breaking the symmetry of the mystical conception of the One that has been promoted by the mystical literature.
Our problem has its origin in Ancient Greece: Parmenides no doubt representing the consensus of his colleagues.
Elected Silence: Thomas Merton, thinking one's life through. I am in a period of revision now, having found a resting pl;ace, I can look back on my path and see
[page 135]
how to optimize it.
Copy = become continuous with, ie logically bound, as the the product space of two interacting systems. The entropy of the product space is greater than the sum of the entropies of the interacting systems.
Christianity is a mystery religion and the fundamental mystery is how an omnino simplex divinity can contain all information about past, present and future, since in our experience all information has physical markers,. Thus we represent the text of the Bible as a string of distinct symbols given meaning by writers and readers.
In the quantum world things just are, there is no distinction between writers and readers, no distinction between messages and senders and receivers because there is no memory, that is symmetry with respect to time, the mere passage of time does not change a memory, and event is needed.
The division of reality into two, God and the World, seems to have two motivations, one political and one scientific. We are principally concerned here with the scientific but must take not of the political. By taking possession of an invisible God, political elites have been able to entrench themselves, as we see with the modern Papacy and its power over a billion or more people.
The scientific problem is the reconciliation of stillness and motion, and its is first documented by Parmenides . . . .
[page 136]
We turn proofs for the existence of God around by assuming the existence of God and proving the creative expansion of fixed points = memory.
Long ago, somebody decided that reality could be divided into two entities, God and the World . . .
Quid est hoc quod est esse? Videre Deum. Aquinas was deluded by his Church, as was just about everybody else in the territory of the old Christian Roman Empire.
The Old God wants suffering even for his own son. The new God wants present pleasure.
We can safely say that Christianity was the dominant religious paradigm in the West, and still maintains its power in the US [which has failed to keep up intellectually with the development of the concept of humanity in other parts of the world]. The waning of the US empire is to some extent the waning of the Christian empire in the face of local natural religions, instances of a global religious cosmological symmetry, the scientific method, the democratic method, where being a member of an elite is no guarantee of superior power.
Christianity is a black religion motivated by the fear of death and a promise of eternal life of bliss if you toe the line [despite the pain it may cause], pain if you defy it. A throwback to the days of absolute monarchy [when it was expected that the sovereign had power of life and death over the subjects].
" 'Look at me,' she ordered, 'and tell me if you think of me as filth, wantonness and falsity . . .' " Benzoni 434 06605 2 page 28. Benzoni
[page 137]
Silent Spring - Theological Spring. The US is as much in need of a political / religious reform as the other countries which it aspires to reform,. Physician heal thyself etc.
The lust for life must eventually break free of the Christian prison which sees sexuality only as a means of breeding more followers, sheep.
I believe the Universe is divine and I want to be one of its many prophets.
God has been silent for a long time and all we hear is the cacophony of its self appointed prophets telling us what God wants.
Having repeated the divine Universe to myself for nearly fifty years, I am beginning to believe it.
If the divine Universe is an idea whose time has come plenty of other people will be working on it and if I do not get it out somebody else will and it we will see the embryogenesis of scientifc theology once the egg is fertilized.
Thursday 1 November 2012
Another smoky dawn. And my local clock ticks on, the affine parameter of my life. The passage of time gains meaning from its relationship to form or eternity, something that does not change with time, like (we assume) the total energy of the Universe or the energy of a completely. . . isolated subset of the Universe. ßGeodesic - Wikipedia
[page 138]
The contrast of 'spiritual' and 'material' order is repeated between each layer of the universal network, in which order it is hat to tell. Is the initial entity of pure act more or less spiritual than the energy that emerges from it? Undecidable.
TSEliot, Death, 'The darkness declares the glory of light.' The potential makes possible the kinetic, a duality established by a fixed point.
Computation: a determined series of steps, eg walking [we can interrupt (halt) our walk at certain points in the stride].
The Church is in breach of the Universal Declaration of Human Rights if it legislates to punish people for thinking differently from it and expressing their opinions. United Nations
Friday 2 November 2012
Call the book [159] Articles [Summa qq 1 - 26]The global financial crisis is a manifestation of the global survival crisis, just like Sandy being a sign of the results of global warming.
Wall Street steals your money, Christianity steals your life. In both cases, plundering elites practising effective slavery.
Saturday 3 November 2012
Unreasonable effectiveness of mathematics leads to a new theology.
[page 139]
ETERNITY - DEFINITE ENERGY - FIXED POINT
It seems to me that i am slowly moving from the excitement of discovery to the labour of documentation. The remedy for this may come with the propagation of the theory, the excitmeent of communication withy other people replacing the excitement of communication with myself, which includes the Universe that created me as a sexy little beast with a strong urge to reproduce body and soul.
My body is to a large degree transparent to me the user except in cases of error where the pure pleasure of integrity is replaced by the pain of error. We see this in the body politic where the elite (the cancer) enslave the rest causing the pain like that induced by Wall Street in the US body politic. The rest of the world, the whole body of humanity, is also feeling this pain to varying degrees.
We can go about reimagining all the doctrines of Christianity in terms of the divine Universe. Among these we can see the mystical body of Christ (mystici corporis Christi) as the human network, the bdy of humanity. When did the idea originate? We see much emphasis on the body of Christ: hoc est enim corpus meum, seen first murdered and then risen in glory. Insofar as we can draw an analogy between Earth and the body of Christ, we are n the murdering phase now, skinning the place alive, raping and burning all in the name of the economy. Pius XII
It is about fifty years since I became heavily engaged in Christianity and am beginning to see now how to understand the appeal of its story of pain and suffering through a divine act
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of pain and suffering becoming through the grace of Gods) the fiat of the sovereign) a life of eternal bliss. The elite have firmly established in our minds the concept that pain is a necessary precursor to bliss, and so we should seek pain, martyrdom etc in the service of the elite, as our sole sure path to heaven.
Pain, martyrdom and religion, Christianity deconstructed, ie the true dynamics revealed. How do networks save themselves from elitism?
For the good of the world Romney has displayed the true nature of the elite for all to see, if they could but see, To see anything we have to cook up the correct measurement operator [point of view].
The step from Cantor to quantum mechanics is via function space, which is a way to represent the space of all Turing machines. We can only talk and reason about the computable points in function space, is the Turing machines.
The Essence of the Roman Catholic Church is the notion of an elite hierarchical order derived from the idea of a sovereign lord. Luther's reformation broke this to degree by sending people back to the Bible, the historical fiction that justified the elite, bit this is no a powerful source of truth as reality, and so the Reformers have yet to gain power, as we can see in the relationship between the Roman Catholic Church and the World Council of Churches. World Council of Churches
Feynman III 16: 'The Dependence of Amplitudes on Position., or is it the dependence of position on amplitudes? Like Newton, quantum mechanics takes a space and time or space-time as
[page 141]
the God-given continuous background for all universal process, and we do not question where it came from, what sustains it or what role it plays in the overall process, ie the function of the fields that we map onto it. The network theory wants to treat time and space as emergent symmetries in the Universe of pure action.
A new story built on the concepts of Christianity as Christianity was built on the concepts of Judaism.
Boson - 1 state - process - energy signalling with no meaning
Fermion - 2 states - message, or vice versa, the beginning of meaning.
In the 'pure' condition before they are assembled (bonded) into meaningful structures bosons and fermions can be associated Pythogoreanly with 1 and 2. Then we have the introduction of stationary energy levels by fermionic behaviour. The structure of the quantum harmonic oscillator depends heavily on the quantum of action, a fixed point that 'confines' a system from a formal point of view or 'emerges' from it from a dynamic point of view.
Time = phasing is of the essence of quantum mechanics: boson - 'in phase', fermion "out of phase'.
Cleanliness is next to Godliness vs cleanliness of the denial of Godliness.
