Notes
[Notebook: DB 59 Draughts]
[Sunday 6 August 2006 - Saturday 12 August 2006]
[page 108}
Sunday 6 August 2006
Monday 7 August 2006
Tuesday 8 August 2006
Uncertainty is a result of the limits of local (in spacetime) processing
All this is a result of 40 years trying to imagine how the world could be divine. Fides quaerens intellectum
[page 109]
general covariance = communication bounded only by consistency
Since time is of the essence of everything except photons, a certain amount of energy (mass) is necessary to define a system of a certain complexity and error rate.
Universe = nothing outside = group. (nothing accessible outside, all interior permutations possible). All possible permutations define all possible mathematics, on the nothing outside possible [principle].
We model the Universe as a transfinite group whose group operations are achieved with computable functions. To make a formal system dynamic, we apply it to itself. So we propose that the Universe we see is the result of a recursive process of self reflection, which has brought the Universe from the initial singularity to the present and will carry it into the future.
The fundamental creationist view is that no matter how much the Universe may look like an evolving system, it is not responsible for its own evolution, but is simply the unfolding before human eyes of a divine plan conceived in the mind of a being that existed before the Universe and continues to create and sustain it now. Ultimately this is a question of taste. Theology is the traditional theory of everything, and so includes both god and the world in its ambit, whether they be distinct or the same. Here we go the same way.
A brief history of god.
[page 110]
The creative power of order.
God, as we know, is a human creation. A point at infinity that provides the ultimate answers to all our questions and guarantees the stability and reasonability of the human ecosystem ad least for the chosen ones of a given god. The first records we have of the Western Christian God [are] in the work of Parmenides and the Book of Genesis. Parmenides, Genesis These two gods coalesced in Christianity and after a millennium of intellectual ferment, roached a definite statement in the work of Aquinas. Aquinas
Quantum mechanics and the Cantor Universe a mapping: first cardinality. Then ordinal.
Perfect locality = initial singularity
Quantum mechanics is a formal system based on function space which is isomorphic to the Cantor Universe.
Function space divides into computable and incomputable. The computable functions form a set of dynamic basis states to build the [observable] Universe.
Capitalism makes clear the interaction between capital and cashflow., long term goals vs day to day exigencies. Size pays off, in that fluctuations may have less effect on the big ones.
Wednesday 9 August 2006
Thursday 10 August 2006
Friday 11 August 2006
[page 111]
One stands always poised between heaven and hell. Some fate has launched me on a lifelong quest to explore the notion that god and the world are one, ie that the world can account for its own existence as well as god can. Sometimes the job seems possible and little snippets of progress fill me with joy; at other times it seems hopelessly impossible and I am inclined to follow sound advice, forget it all, get an honest job . . . . Yet on the whole I press on, both because it is exciting and in the hope that even if I die deeply in debt, I might have contributed something to peace and understanding which will, in a tiny but often repeated way, make life more satisfactory for my children and all future generations.
The essence of my method is to apply the theorems of mathematics to mathematics itself, so arriving at a picture of the world. Beginning with the Cantor Universe, a formal creation which can be derived from the axioms of set theory [provided the formal Universe is consistent]. Behind this (a la Misner, Thorne and Wheeler) we find a sort of pregeometry in the axioms of predicate calculus, which give us the laws of logical continuity. Misner, Thorne and Wheeler We can then apply the theorems of Gödel, Turing and Shannon in the Cantor Universe and hope to come up with something resembling quantum field theory, but without the contradictions and infinities arising from he poles in the harmonic paradigm. All the while we try to proceed only on the assumption of formal consistency, which can only be judged in deterministic systems.
Gieres page 1: (note) 'We will generally use the terms 'rigid' and 'flexible' superspace instead of the familiar ones 'flat' and curved' . . . '. Gieres
[page 112]
Such a small change (mapping) n terminology seems to open up a wealth of insight, emphasizing that space itself is dynamic ('geometrodynamics'), so that we need to understand it in a dynamic context. Motion shapes the world.
All change is accompanied by communication, eg change of the internal state of an atom s accompanied by the emission or absorption of a particle (transmission or reception).
The Cantor Universe functions as a potential which tells all the things which could be. The potential is reduced to actual by the process of natural selection seen as the development and pruning of networks, as in the development of the mammalian neural network.
The Cantor Universe contains all possible functions (mappings, permutations) of all cardinalities. We hope to derive a picture of the Universe we inhabit by certain plausible constraints acting on the Universe. In particular, we are interested in the constraint that gives us four-space. Intuitively it seems to be the smallest-dimensional space in which every point can communicate with ever other along paths that do not cross. So, when circuits reach a certain complexity they can no longer be realized in flatland, but we need to enter the third dimension so wires can 'cross' without contact.
The question of consistency only arises on communication.
[page 113]
Quantum mechanics is the measure theory of universal interaction, yielding cardinal numbers (scalars) as the coupling constants between various states. Time is scalar, so n the real of quantum field theory we interpret quantum theory as a field theory in 1+0 (or 0+1) dimensions, ie all time no space, no communication, no delay, no relativity.
General covariance" every entity experiences the same world., There are no real reference frames except reality, ie we get our references from one another. Relativity is invariant.
Pais, Einstein, page 256: 'Any physical theory that obeys special relativity can be incorporated into the general theory of relativity. The general theory does not provide any criterion for the admissibility of that physical theory. . . . Finally the general theory of relativity is closed as a logical structure.' A Einstein Pais
Energy-momentum conservation is an almost immediate consequence of general covariance. Pais page 275.
Saturday 12 August 2006
General features of the transfinite network as a formal entity:
general covariance
requisite variety
complexity invariance
permutation definition of infinity
schemes of recurrence
Gödel and Turing
natural model of intellectual search
logical continuity
[page 114]
Recursion
The common early morning despair: will this ever lead to anything, which in practical terms means make me a living by contributing to world peace and beauty.
Pais Einstein page 257: 'The years of searching in the dark for a truth that one feels but cannot express, the intense desire and alternations of confidence and misgiving until one breaks through to a clarity and understanding are known only to him who experience them.'
Which is everybody in their own way and a feature of the capitalist nature of nature, that we must invest in hope to be rewarded with profit; but not all succeed as Einstein did, and die with their hopes unfulfilled despite their courage and ability. So in the evolutionary scheme of things many d not score the basic goal of reproduction, and at least I have done that, so that some of my attributes will carry on!
This is where the Christian fiction (scam?) has its role of maintaining morale, cohesion and cooperation is a society with false promises, like heaven for the good and hell for the bad in an eternal afterlife.
If quantum mechanics is rigorously linear and unitary and yet subject to uncertainty, we must postulate some sort of control process to maintain the linearity
[page 115]
and unitarity.
So what is really going on with me? I operate within a space of constraints defined by my ecosystem, and I am continually trying to manipulate the constraints to my own advantage (and to the advantage of parts of my ecosystem (plants, people, [buildings, ideas]) that may later advantage me. The better I play this game the better I survive, but what of my mental state, the source of many anxieties centered around my mental state, the source of many anxieties centered around potential loss of advantage, insolvency and eventually death. The Buddhist view tells me not to worry; Christianity tells me if I be good it will all come right in the end. For myself I seek a religious view that is realistic about my position and provides a means of deciding my next step. So keeping my dreams in mind, I do what I have to do to live and use any free energy to move closer to my dreams (realizable or not).
Panic comes from ignorance, like not knowing which valve to operate on the fire truck to operate the overrun sprays. Relaxation, on the other hand, some from experience and knowing exactly what to do to achieve the desired outcome. Working the truck is a deterministic process based on 'local' knowledge. What the wind and the fire are going to do, however, is only partly predictable however, so continuous feedback and response is required to avoid loss of life and equipment and bring the situation under control.
The integration involved in the inner product erases the detailed information about the relative directions of state vectors and gives us a complex number whose absolute square we interpret as a probability.
[page 116]
If we therefore accept that the processes going on behind the graphic user interface are hidden for us. Nevertheless we can guess at them and a person with the necessary skills observing the pixels can work out how to write a system which will give identical behaviour. Reverse engineering. Of course, the actual methods used may be different but we accept that there are a relatively limited number of possibilities when all aspects of the graphic behaviour are accounted for. Word processors. Computer books discuss the best way to do things, and the whole software community.
Got carried away. What I was going to say was if we accept hidden processes we can accept as an hypothesis that the appearances of the world in 4-space are driven by quantum processes that cannot be observed, but have been found to conform perfectly with the algebra of Hilbert space.
The complex integers are the roots of 1. Let us consider the ℵ0 ℵ0 th roots of 1 as the foundation of our system. They form a cyclic group and we might like to say that one cycle corresponds to action 2 pi h bar = h.
Let us assume that all our constraints come from outside, ie from more complex systems. Then we can understand quantum mechanics as something imposed on us (and presumably all subsets of the Universe) by 'the whole'. [natural law = divine law]
What us an equation: a statement about cardinal numbers (including 'reals' (decimals)).
[page 117]
I think the problem I have set myself to solve, to develop a theory of everything from theological ideas, is completely beyond my power, yet on the other hand I seem to have no choice but to go on. . . .
