vol VII: Notes
2013
Notes
[Notebook: DB 76 Liberation]
[Sunday 6 October 2013 - Saturday 12 October 2013] [page 161]
Sunday 6 October 2013
What is religion anyway? We tend to associate religion with the activities of the old established religious institutions that
[page 162]
surround us, not least the Roman Catholic Church. But the dictionary definition gives a much broader canvas: 1. The quest for the values of the ideal life, involving three phases, the ideal, the practices for attaining the values of the ideal and the theology or world view relating the quest to the evolving universe. Macquarie, Delbridge 1981. Delbridge
OED: the belief in and worship of a superhuman controlling power especially a personal God or gods.
Movement is a consequence of discomfort or pain, real or imagined, eg green movement, tea party movement[, rolling over in bed].
LOGIC = DYNAMICS
So we imagine transfinite quantum computation and then turn to set theory and the theories of Gödel, Turing, Shannon and Brouwer to explore the properties of this network.
Monday 7 October 2013
Back to Feynman with transfinite quantum mechanics in mind. Via the path integral method? Feynman
Tensor product generates transfinite Hilbert spaces [?] Tensor product - Wikipedia
The first is to establish that quantum mechanics is based on digital computation, based on the algorithmic information notion that a continuum carries no information, only discrete symbols. (as required by communication thoery) can do this, and the uncertainty comes from the low resolution of memory free computation.
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We want to understand the Feynman diagram of the whole Universe, ie the universal network.
Emotion : energized form
It is frustrating that one has only probabilistic control over the onset of an insight, and in this respect quantum mechanics and human insight can be measured in a similar way, as the rate of various individual elements of a spectrum of events. This similarity is suggestive of the symmetry with respect to complexity which is to be found stretching from quantum mechanics to cosmogenesis at all scales.
What is the insight I want: how to establish a consistent relationship between quantum mechanics as we understand it now, a deterministic process controlling the probabilities of events through the Born rule (the phase overlap rule) and a digital computer network in which there can be a continuous spectrum of phase differences between two independent computers. We distinguish a computer from a network insofar as all the elements in a computer work in phase whereas discrete machines in a network may be out of phase with one another. Have said this many time before, but the idea is becoming clearer that out of phase computers in a network can model the data of quantum mechanics. Born rule - Wikipedia
Once we have gone digital (ie implemented Shannon's theorems) we can just follow set theory as far as it takes us (Jech). Jech
What we are saying is that a one bit computer can only resolve p and not-p, and a linear superposition of two
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such computers with random relatie phase explains the utility of the overlap integral, ie the dot product.
We are just shifting the uncertainty in quantum mechanics from the interface between a system in contnuous deterministic evolution and the random events which this evolution controls (to a certain degree) to a digital deterministic computation system with limited resolution. We have a general version of the equations ΔpΔx ≈ ΔEΔt ≈ ℏ, insofar as we can trade a continuum (no definition) for a digit (perfect definition) and the information carried by the definition is equal to the entropy of the continuum, ie the information carried by one element of a permutation group is equal to the entropy of the group.
We study continua by artificially digitizing them using epsilons and deltas as a measure of the chunks into which we break the continuum and then let the number of chunks tend to infinity and their measure to zero, assuming that the relevant algorithms work no matter what the measure of the variables.
Feynman 6-1 Transfinite amplitudes.
'Any state ψ can be described in a set of [orthogonal] base states by giving the amplitude to be in each of the base states.' Amplitude is a complex number normalized to 1.
ψ is an 'angle' [orientation] in a Hilbert space.
'The amplitude to go from one state to another can, in general, be written as a sum of products, each product being the amplitude to go into one of the base state times the amplitude to go from that base state to the final condition.'
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a dot product or overlap integral which abstracts all the data in the initial and final states ψ and χ down to a single complex number. A lot of data is said to be lost here, the collapse of the wave function, but perhaps it was not there in the first place due to limited digital resolution.
'The amplitude to get from one state to another directly is the complex conjugate of the inverse <χ|ψ>* = <ψ|χ> We multiply these two amplitudes to get the probability of the transition.
Tuesday 8 October 2013
Here's the rub. Quantum mechanics, like classical mechanics, works on the hypothesis that continuous mathematical functions are deterministic. According to this view, the wave function evolves deterministically and we can readily compute its values at ti given a value at t0. But information theory tells us that error free information must be digitized, and given our information in digital form, we can implement algorithms to transmit it error free. Digitization introduces orthogonality and reduces confusion (error) to as close to zero as we like. The continuum, on the other hand, is fully confused, at most just one symbol, and carries no information so it cannot be deterministic. In the Platonic world we purport to study the nature of the continuum by digitizing [it] with epsilons and deltas and assuming that this digital precision [holds] in the limit of symbols with measure zero. In the quantum [physical] world, however, the minimum measure of a symbol is Planck's constant and there are real continua which carry no information, commonly known as symmetries.
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Physics by symmetry is physics by the via negativa.
Cantor symmetry [= symmetry with respect to complexity].
Christie, Chimneys chapter XI ' "We went to bed early. Somehow or another the party didn't seem to 'go', . . . " '. This is the judgement of God, things work or do not work, a clear test, although it often takes a long time [time step] to see if a policy is working or not, and the decision becomes more difficult of the data is [either] not collected or suppressed [or falsified]. Christie
Wednesday 9 October 2013
Motion implies distinction, moving from one state to another. Motion is seen to be continuous, and the fact that the physical world is a moving world gives us a strong incentive to think the world is continuous. However detailed examination at the quantum level shows that this is not so, and it is obviously not so at the macroscopic level where we are all individuals (Brian). Monty Python's Life of Brian - Wikipedia
We might say that the deepest problem in mathematics is the relationship between geometry and arithmetic as it has worked itself out in number theory, calculus, algebra, etc. The Platonic continuum: infinite in information density. The real continuum: no information. Something like Lonergan's empirical residue where this whole story started for me, denying the existence of empirical residue (it is a member of the empty set) and so asserting the failure of Lonergan's argument for the difference of God [and the world]. Lonergan: Insight
Commonweal founded 1925, circulation 20 000 Commonweal Magazine
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Haight Haight: Jesus, Symbol of God
America founded 1909, 45 000 readers. America (magazine) - Wikipedia
Subscribe to Commonweal.
Cantor symmetry: the fundamental symmetry, everything observable is a distinct object, no matter how large or small. This is the empirical foundation of all science and a definition of observable = communicable.
Have been gradually upping the ante for myself since this project started on one of those mornings when I got up at 3 am to puzzle my way through Lonergan's Insight and ultimately see where he has gone wrong. He wanted to prove that God is not the Universe, but opened the way to proving the opposite by letting me see that the Universe is a completely intelligible network of causality at the same time as being radically unpredictable (Gödel and the dynamics of logic).
Thursday 10 October 2013
Friday 11 October 2013
Saturday 12 October 2013
Gittins: SMH Adam Smith: 'Consumption is the sole end ans purpose of production and the welfare of the producer ought to be attended to only as it may be necessary for promoting that of the consumer.' Ross Gittins, Adam Smith
What we need to do is map Dirac's canonical development of quantum mechanics and Feynman's path integral
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onto a digital computer network.
