vol VII: Notes
2012
Notes
[Sunday 29 July 2012 - Saturday 4 August 2012]
[Notebook: DB 72 Energaia]
[page 167]
Sunday 29 July 2012
Martin's book takes me back to the days of my monastic youth when John XXIII's Ecumenical spring lured me into speaking my mind and receiving my marching orders. But I have kept up the pressure and now a theological spring seems within my grasp, and in the most powerful possible way, through physics to theology following the steps of Parmenides, Plato, Aristotle and Aquinas but armed with a clear knowledge f the boundaries of mathematics which are also the boundaries of the fixed points of the Universe, so the boundaries of what is observable. From the fundamental problem of theology as formulated by Parmenides to the Turing machine which sets the limits of deterministic process, that is proof. I am worried that I will never think this again, but I can relax in the knowledge that it has gradually become p[art of me. From the Thomistic point of view, the proposition that the Universe is divine is absurd and unthinkable. Fifty years of tinkering, however, have slowly revealed to me that it is obvious, a matter of clear principle like the theories of relativity.
The 'God Particle' has been in the news lately.
[page 168]
The ultimate output from the dynamics of the scientific community is the literature. The literature is picked up by the technological community seeking profitable ways of combining the fixed features of the Universe revealed by science.
Information is a physical thing. Particles are things, and so the carriers of information.
The Church prospers because people believe that what it says, and they believe what it says because it tells quite an interesting story about sin and salvation which it has propagated very profitably for two thousand years, There is no doubt that we need stability in our lives and this stability is founded on a set of beliefs that form a basus (in the quantum mechanical and communication theoretical sense) for communication of value to one another.
A mild mannered theological manifesto.
The Christian story resonates (like all the other ancient stories) because it explains the difficulties of life (the problem of evil) and promises that it will be alusright in the end because God loves us. The natural story also explains our condition, but it also tells us that we are responsible for our own salvation because the God in which we live judges our actions with their consequences, which may be death or exteinction.
You only see what you know. Greek?
Aquinas' model must be the starting point for this investigation: we reopen the question of the existence of God after a 700 year hiatus.
[page 169]
Monday 30 July 2012
Money / love makes the world go round -- actuality / potential
How do we cast this in computing terms. Start with quantum mechanics. Whatever else, it describes the functioning of the Universe at its simplest and broadest level.
physics / theology -- initial singularity / classical God / Trinity.
Current big problem - quantum mechanics / gravitation. Solution? We move to a bigger space, discrete rather than continuous. Strongest possible observational evidence, the whole observed Universe is discrete. Why? Because the continuum is not observable.
Secular = dynamic. Secularity - Wikipedia
Catholicism vs Marxism Martin page 545 Marxism and religion - Wikipedia
Life requires continued and active construction and error correction (destruction) to continue.
A differential equation expresses a symmetry, the unmarked void between fixed points. The collapse of the wave packet happens at the fixed bounds of the void, one boundary generates it, the other receives it and replies, creating a 'standing wave'. All this can be visualized in 3 space, but quantum mechanics describes processes in Hilbert space a hybrid of orthogonal instances of a complex exponetial function of time, the universal affine parameter measured by phase. What is the overall picture represented to us by mathematics, the boundary
[page 170]
between determinate and indeterminate revealed by Gödel and Turing.The mathematical literature represents fixed points in the dynamics of the mathematical community which spreads out from the prizewinners to the users of cash registers and other embedded forms of mathematics. An abstract fixed point, like Pythagoras' theorem, is instantiated in an infinite number of right angled triangles.
The big moral question is what should we realize of all the possibilities. This is the art of quantum computation, designing systems which execute the desired algorithms.
What is potential in the time dimension? What is the force that drives time on? Numerus motus secundum prius et posterius (Aristotle: Physics 219b1). Can there be potential without distance, a function without a domain? All of our useful knowledge is functional: do this, get that. Some of these functions are quite deterministic: hammer finger, feel pain; others are less so, send flowers, get a phone call . We also understand the Universe as functional, some deterministic, some stochastic. Aristotle, Stochastic - Wikipedia
Interactopmn - dot product Tomonaga page 34.
The fundamental source of all the trouble in banking and consequent error in the player's estimations of one another (mediated by the rating agencies) [is secrecy].
[page 171]
The principal power of a network is resistance to damage. Ina hierarchy, bad leadership from the top can lead to bad behaviours, as we frequently see. A peer network, on the other hand, by being conscious of itself and self critical (like the scientific community) can relax itself to a stable relationship with its environment.The world is rent by different theologies. On this site I wish to offer a diagnosis and some ideas about a cure. The problem is that the traditional Gods are invisible, so anyone may choose to describe them in any way they choose. The result is the large set of often incompatible theologies that inhabit the world.
The alternative is to accept that God is visible, and that in fact all our experience is experience of God. This approach makes it possible for theology to be a science, experience and evidence based.
There is quite a distance between these two positions and this site is intended to document my long wandering journey from Catholic Scholastic theology to natural theology.
Tuesday 31 July 2012
All the quantum mechanical stuff is something of a side issue, but a powerful one, since we want the Universe to be as big and as powerful as God and we demonstrate this by modelling.
So the model is the essential expansion of the initial ansatz.
The transfinite computer network shows us that a computer is a network, admittedly highly constrained.
[page 172]
The divine properties of the Universe, size (Cantor) and power (Turing). Demontrated by cosmology and quantum information theory.
A New Theology website released
Martin page 690: 'First: how to reestablish the incompatibility of Christianity and Marxism, . . . '
For a peer network to be self correcting, all public statements should be visible to every one, Since money is a public good, significant movements of money should be made visible.
Theology can be a matter of life and death.
Hilbert space has built in fixed points, the dimensions which are parametrized to create a signal. The computing network also has fixed points, the logical elements, (algorithms) that process the messages, creating and annihilating them.
That monastery was a very strange place, as I can begin to admit to myself now.\, a thoroughgoing adaptation of day to day human life to a certain set of beliefs about the nature of the human enviromnment, God in other words.
The sentence 'in the beginning God created the world' serves as a definition of these four words.
Martin: '[Lansing] is totally and exclusively Christ's man.'
[page 173]
Maybe his own man. Trouble begins when organizations pull people off their geodesics.
Wednesday 1 August 2012
Martin: Who controls the money controls the world insofar as the realization of any potential requires transfer of action to that potential and action is conserved (reduction of the wave packet) so one form is realized at the expense of the others.Tomonaga page 37: Thomas: 'If the electron has acceleration, there is a complication.'
page 14: g = | magnetic moment| / |angular momentum|.
The whole business of quantum mechanics is to measure the energy equivalent to a quantum of action. This is measured by a frequency E/f = h. In 'practical' terms, the energy measures the interval necessary to perform the action, as in a computer, the faster the clock, the less time the computation takes. The actual time taken for a process is measured by complexity of processes / energy. The complexity of the process is measured by the size of the Turing machine (embodies algorithm) necessary to execute the codec involved. The simplest codec (described by quantum mechanics).
Assumptions
1. The processes of the Universe can be modelled by a transfinite computer network, so the theories of computation and computation apply. Shannon.
[page 174]
The most important point about the theory of communication is that one can only eliminate error by making messages discrete. Error arises in a communication of one signal is mistaken for another. etc.
Quantum mechanics, like traditional theology, is an attempt to explain what goes on behind the scenes. Traditional theology, a result of a period of thought of unknown length, proposes an invisible, omnipotent, omniscient eternal being which creates and sustains the visible world which includes all our lives. The properties of God are devises to ensure that it is deterministic. God being able to foresee and control every event, even though 'acts of God' appear to be completely random to us.
Quantum mechanics is based on the unobservable [invisible] mathematical formalism of Hilbert spaces and vectors and operators in this space. The complex mathematical functions are believed to evolve deterministically, but they are only loosely coupled to observable events.
Given a certain physical setup and the corresponding quantum mechanical equations of motion, the best we can do is predict the probabilities of various outcomes using the Born rule p = |φ|2. The outcomes themselves are clearly defined by the quantum 'eigenvalue equation', Aψ = aψ where A is an operator ['observable'] and a is a real number.
Boson - singulary
Fermion - binary
Boltzmann's method shows that there is order in a classical gas, since it relies on the realization of distinct permutations.
[page 175]
the eigenvalue equation defines both a function and a value associated with that function which measures the probability that that function (of all the functions in the superpositions defined by the energy equation) (Hamiltonian equation, matrix, set of linear simultaneous equations with a guaranteed solution).
The transfinite computer network has all the features of real networks like the internet, but the only limit on its computational power is represented by a certain transfinite number (peer group, peer layer) of Turing machines, Such machines can have their process changed by a signal from another machine.
All information is physical (Landau) so all communication is based on a physical layer of sound waves, electrons, photons, etc. Since all [operations] are in effect computations, computations are also physical, and we study them in quantum information theory.
Christian theologians had to deal with the fact that a large body of exegetes of the New testament, and, presumably, living tradition, maintained that Gopd, while On, had three distinct persons and personalities, a very subtle of not self contradictory statement. [on the other hand, the Universe as we see it has a countable infinity of personalities]
Tomonaga 38 Thomas' theory is purely classical.
page 52: The energy is the solution to an equation, n other words the equation puts bounds on the energy, that is the rate of exchange of quanta, the two way flow of units represented by a function like φ = e-iEt/h. The dimensions of
ET are the same as h and so we might say that this equation sees only pure numbers, ein, n = Et/h
Time is quantized (parametrized) by the steps in a computation. The parameter is emergent, so the actions count the time or does the time count the actions? Both. They are duals that must be related as p and not-p to keep the splitting dynamics of the Universe (like spectral lines) balanced so that the Universe remains in effect omnino simplex.
Newton produced an observable horizon [surface] of God, space and time, God's 'sensorium'. What did he mean? Sensorium - Wikipedia
Sounds mystical, but can be worked out in terms of arithmetic, conserved currents flowing in opposite directions so there a centre of momentum, zero net momentum before and after the interaction. In 3-space momentum is a vector, in 1 space it is indistinguishable from energy.
We think of abstract as metaphysical, but the metaphysical is concrete. Physics describes the properties which are common to all events in the Universe, the physical layer of the universal network. So it is physics that is abstract, relatively simple and straightforward, describing the basic features of the Universe upon which our lives are built. I perceive my life as the birth and growth of a complex network, followed by an inevitable breakdown in my network due to accumulated fatal error. Maybe we can make death technically palatable through the term fatal error.
This is the rub? A, I happy to die, knowing why it
[page 177]
must happen to me. A few new winter aches remind me that I am nearly up to my threescore and ten, although I am hoping for a hundred so I can finish this project and hand it in for marketing.
Be cool. Diplomatic. Do not oppose the old, just build the new, as has happened in the other sciences (with a few clashes here and there [to be resolved by collecting more evidence]). However, theology is recursive in that the subject mattter of theology is partly physics and partly metaphysics. The Cantor world suggests that the only constraint a layer places on a higher layer is the multiplicity of states and the speed of execution [parallel = multiple serial].
Another 'axiom': a stable Universe requires error free communication which requires quantization. Eigenfunctions / standing waves / processes (whose details are invisible to us because they are deterministic).
If the evolution of the wave function is deterministic, it too must be quantized because a continuum carries no information, like a blank sheet of paper, a plane wave. Does each node of a standing wave mark a computational step? Standing waves in Hilbert space. Everything that happens in Hilbert space depends upon phase, that is the measure of 'distance' (interval) in time.
How do we digitize wave functions, whose existence is defined by continuous mathematics? The question is what does the 'reduction of the wave packet' mean? It is a break in symmetry, a weighed random choice between vrious possible outcomes. So are there really was m,any state vectors as the continuous model suggests, so that we need Hilbert spaces of ℵ1 dimensions to work in?
[page 178]
All this seems to be a bit hard to understand if the Universe really did begin as an omnino simplex.The notion that the First Mover or God is pure activity is quite consistent with the quantum mechanical view of the world, which sees all different events happening with energies and frequencies which fit together in harmony as the solutions of sets of linear simultaneous equations (constraints) represented by a quantum observable (operator). So we see observability as marking the end of a computation. The machine halts in a state which is its output, no doubt to be taken in by another network of machines and processed some more.
Radioactive decay is an example of the reduction of the wave function, and it is our basic way of observing the world, either by patiently watching things decay naturally ort setting up experimental states which are then allowed to decay so that we can observe their output and compare it to the input state which we created for this experiment.
A continuum 'parallel transports' a state, since it has no means to interact with a state and so change it. We may think of a Turing machine as such a logical continuum, deterministically generating a certain output given a input from its domain.
Identify the rebirth of 'old' ideas in 'modern' science. The scientific process is structurally sound since it maps itself onto the world, which has proven to be structurally sound over 13 billion years.
Dirac's equation is linear in time and space [Klein-Gordon quadratic and therefore real?]
Thursday 2 August 2012
A memory (location) is a degree of freedom which can be loaded with a certain amount of data [a symmetry waiting to be broken]. It is sufficient for theoretical purposes to consider binary memories with transfinite addresses.
Networks naturally reflect on themselves, you see me, I see you. I comment on your looks, and so on.
Tomonaga page 93: 'Therefore the subtle property of electron spin appears directly in the everyday macroscopic phenomenon of a magnet attracting iron, and this is related to wholly transcendent facts [in the standard model] such as the symmetry properties of wave functions and the electron being a fermion.
How do Hilbert space and 4-space communicate?
page 92: '. . . it was established that the concept of a matter wave actually existing in space is just as valid as a light wave existing in space.' or space existing in a light wave,. The quantum space of timings antecedes the real space of memories.
At the human level each of us lives and moved in the superposition of potentials arising from our interactions with the people around us. Not necessarily linear, as falling into love (or hate) show.
New notebook Spring2012, DB 73.
Friday 3 August 2012
Saturday 4 August 2012
Tomonaga page 122: Interaction energy = communication rate in actions per unit of time, E = ds/dt
