Notes
[Notebook: DB 62 Interpretation]
[Sunday 25 November 2007 - Saturday 24 November 2007]
[page 45]
Sunday 25 November 2007
Monday 26 November 2007
Sydney, a hive of motion. What we see is the circulatory system. My vehicle mostly carries me in circles, away from home and back again, into my home frame = inertial frame = frame in which I am at rest and not continually having to be ware of my environment [because] it is foreign to me.
At the heart of Google is a deterministically controlled search designed to be the most efficient. Is this by speeding things up or using large amounts of memory rather than faster processors. What is the tradeoff function of investing in memory (algorithmic complexity) vs investing in processor speed. [the expansion of the Universe suggests that memory outweighs speed].
Mathematics is rendered dynamic by mathematicians. The mathematics, as recorded in journals, lectures and conversations is the alphabet of particles that mathematicians exchange in the course of their trade.
ALGORITHM = SPACE endowed with a potential
[page 46]
that guides the calculation as desire breeds / creates courtship the need to please, to pray, ultimately to beg and when all else fails, to die for love.
The Church policy is to separate love from desire so creating a formal love deprived of its dynamic motivators, lovers. All this manifestation of the flow of action.
Tuesday 27 November 2007
. . .
Life and death are necessary if the set of physically realized systems is to be free to explore the space all logically possible systems.
[diagrams]
KNOWLEDGE - ABSTRACTION - INTEGRATION
TRACTABLE = COUNTABLE = COMPUTABLE = RATIONAL
INTRACTABLE = UNCOUNTABLE = INCOMPUTABLE = EMOTIONAL
The emotional system, nevertheless, seems to operate at a lower level of resolution.
[page 47]
DUPLEX = MUTUAL CHOICE (NOT RAPE)
Wednesday 28 November 2007
We note that the initial singularity has many of the properties of the classical god, starting with the notion of pure act, ie it embraces ℵ0 quanta of action. It is not a body, outside space and time, eternal, omnipotent, omniscient, completely simple and so on. The classical view places creation outside god, but here we see the Universe as god and so that creation takes place within rather than outside god. We are all processes within god, dynamic parts of a dynamic god.
The theory of the trinity is the subtlest product of classical theology, and our assumptions allow us to use it as a starting point for the unfolding of the Universe.
We may think of the initial singularity as an inside out black hole (Time reversed, Hawking and Ellis) Hawking & Ellis
Thursday 29 November 2007
The mathematical development of Einstein's insight into free fall defines geodesics, paths through the four dimensional spacetime manifold along which an observer feels no force. Spacetime is said to have a singularity wherever geodesics end or are incomplete, ie the geodesic begins or ends in a point which is not part of the continuous differentiable manifold that we use to represent spacetime.
[page 48]
Quantum mechanics (and the Hilbert Oscillator) is one dimensional, but this is a countable dimension, and, as in the harmonic oscillator, every number is represented by a frequency (or inverse momentum) whose power is a function of temperature alone, as shown by Planck's law.
Phys04Normalization
The network model has built in normalization via the conservation of action and the full duplex nature of communication which requires two virtual operations (question and answer) to complete an action. In effect a permutation which was to change has to find a mate which will make the inverse change. [In a two state Universe this is no problem, but as the number of states increases, the chances of finding a mate decreases]
The CPU and memory of a computer are the physical (deterministic) [features of the communication network]
phys05Uncertainty
Uncertainty is also built into the network Universe, since al measurements are discrete and there are gaps which can only be estimated by statistical treatment of a large number of discrete events.
Why does wave mechanics work:? because amplitudes simply add in two channels (complex numbers) transforming functions in a manner that can be represented by superpositions of periodic functions. Time here is the ordering parameter which decides what is added to what. In one dimension things are added of they
[page 49]
exist at the same time.
Wikipedia Mathematical Formulation of Quantum mechanics. Mathematical formulation of quantum mechanics - Wikipedia
'Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant, h, is now called Planck's constant in his honour,'
Wiki: 'similar equations can be written for any one parameter group of symmetries of the physical system. Time would be replaced by a suitable coordinate parametrizing the unitary group (for instance a rotation or a translation distance) and the Hamiltonian would e replaced by a conserved quantity associated to the symmetry (for instance angular or linear momentum).'
'The quantum harmonic oscillator is an exactly solvable system where the possibility of choosing among more than one representation can be seen in all its glory. There apart from the Schrödinger (position or momentum) representation we encounter the Fock (number) representation and the Bargmann-Segal (phase space or coherent state) representation. All three are unitarily equivalent.'
[page 50]
Recursive function theory builds complex processes out of simple processes. The complexity of a process is measured by its total entropy = bandwidth x time = action ? So we have time, 2D spacetime, 4D spacetime.
Quantum mechanics operates independently of the number of states involved, that is of the dimensionality of the vectors, which in turn controls the number of basis vectors that must be superposed to represent a state. Now the collapse of the wave function is a transition from a superposition of many states (a space of a certain entropy) to a unique state whose information value is equal to the entropy of the superposition from which it was drawn, ie from a many state system to a single state system. So we have a sort of natural transition from amplitudes to probabilities since a one state system has both amplitude and probability of 1 (?).
We say the Universe is quantized by the need for error free communication and Shannon's theorems. A quantum mechanic might say the Universe is quantized because certain operators with which we observe the world have discrete spectra. We say that things happen when there are no inhibitions, and calculate the probability of this situation in a system with two sources each with a set of eigenstates by the transition probabilities between eigenstates.
Einstein's problem, once he got onto differential geometry, was juggling all the tensors until everything fitted together. This is, in a general (abstract) way the same with
[page 51]
any construction job, fitting the building to the constraints oat every level of abstraction, that is every level of complexity.
What makes a computer go is what we serve up to the nander, the 'spatial structure' in which the nander is reading, moving and writing.
At the fundamental level, to read is to annihilate, to write is to create.
Insofar as something is bound, it has discrete states [Brouwer].
Quantum mechanics operates at all scales.
My ideas have been incubated in the womb of Catholic Theology, but since the days of Lonergan I have been aware that one day they would have to be born and become a free living entity. This might have happened when I started the web site and started to feed off more modern science, but it also became increasingly more obvious that there was not much sustenance in quantum field theory as we have it and my continued existence requires revision of the whole model of the world which I am trying to achieve by the scale invariance of ideas presented in natural theology.
Lurking in the back of my mind is the idea that the quantum of action (= solution to a problem) is effectively the same at all scales and that possible entities that do not exist (ie have no energy) do not have a 'zero point energy' and so we can solve the divergence problem
[page 52]
that plagues the world of physics. Feynman Gravitation. Feynman
It is tension / potential / desire / lust etc that move me. We are encased in a sea of potentials (fields) and we yield to them when we can. In some cases (eg normal hunger) yielding to the potential dissipates it. With inverse square forces, however, the closer we get to the source the stronger the attraction or repulsion. I have a strong attraction to a new vision of god, which every now and then becomes a bit closer because I manage to capture a feature of it in writing, thus making it communicable, a vision that can reproduce itself.
So Foundational Questions in Physics and Theology (Nature 1/11/2007 page recruitment 40) Following ancient Mediterranean tradition, this project has its roots in theological considerations, that is an attempt to create a unified model of the whole of reality rather than just the physical aspect.
Traditional theology distinguishes god and the world. A consequence of this position, relevant to cosmology, is that the world is an arbitrary creation of a superior being and could have been otherwise. A further traditional view, deeply ingrained in the Christian psyche is that this world is in a damaged condition consequent upon the divine displeasure created by an ancient human act.
The alternative proposed here to the traditional view is that the terms 'god' and 'Universe' point to the same reality. We define a Universe as a system with nothing outside. This
[page 53]
has the cosmological consequence that the Universe has no external constraints, leading to the heuristic principle that all the constraints observed in the Universe are a consequence of one initial condition: structures in the Universe, insofar as they are in contact, must be mutually consistent.
To model such a Universe we begin with a Cantor Universe populated with Turing machines (the transfinite network) and try to map this structure onto the observed Universe.
Like [a] physical computer network, this structure has a physical layer overlaid by a hierarchy of user layers, which include ourselves and culminate (in imagination) in the ultimate User which correlates with the various Deities that have been created over the millennia.
We construct the world from deterministic transformations strung together in an indeterministic way, like a card game where the cards are randomized but each card played puts certain deterministic constraints on the following play (and player). What we have here is a cellular automaton with next moves random but constrained, ie only a subset of all possible plays is allowed by the rules.
Non-perturbative = communication protocols (Turing machines)
Perturbative = message (machine) probabilities). More probable machines are more frequent that less probable: How tautological can you get?
Friday 30 November 2007
[page 54]
Saturday 1 December 2007
Feynman gravitation page 8: 'We must keep in perspective what it is we are doing, simply to put forth some wild peculations in order to see whether we get any real ideas.'
What chance does my hypothesis [have] of carrying cosmology forward? Let us say that planet wide we spend $E11 per year on physical research. I am asking for $E5, so if my idea has E-6 probability of revolutionizing the field, its cost benefit is of the same scale as the rest of the physics industry.
