vol VII: Notes
2014
Notes
[Notebook: DB 78: Catholicism 2.0]
[Sunday 28 December 2014 - Saturday 3 January 2015]
[page 73]
Sunday 28 December 2014
Feynman III 2-8; '. . . disturbance is necessary for the consistency of the viewpoint.' Feynman
Feynman pag 2-2: 'uncertainty comes naturally from the wave picture'. [and from the digital picture].
A story: from wave mechanics to computed dynamics. We observe discrete events whose form (eg electron-ness) appears to be defined with infinite precision, ie it is a quantum or unit.
[page 74]
The determinism suggests the presence of a deterministic machine like a computer executing an algorithm. This suggests that we identify the eigenfunctions of wave mechanics with algorithms or computers, and understand the messages emitted by quantum events to be the outcome of these computations when they are halted, so the eigenvalues of an observable [embodied as particles] are the set of halting eigenvalue computations.
We may think of a communication channel as two pairs of to algorithms, each the inverse of the other, processing strings of symbols from clear to code for transmission and code to clear for reception. Shannon coding can render messages strong against corruption, but not absolutely incorruptible as this takes infinite time for a source whose output rate is finite. The only foolproof method is full duplex: the receiver reads the received message back to the transmitter who acknowledges that the returned message is identical to the original. Claude Shannon
Quantum mechanics embodies the 'echo' method of verification symbolized by the computation of probability P = |ψ|2 = ψψ*, the complex conjugate being interpreted as the return message and the probability of a successful communication being measured by the product of the forward and return messages represented by ψ and ψ* respectively, which could equivalently be written ψ*ψ since ψ** = ψ. The computation of the probability is deterministic, ie the computation of the dot product, although the choice of eigenfunction to execute would appear to be a random event. Here, however, we note the observation that a well coded string has maximum entropy and is indistinguishable from noise, except to the transmitter and receiver of the string.
[page 75]
It may be that at the quantum level the Universe is so simple that Shannon coding is not possible because everything is processed one quantum at action at a time and so the only way to see if a communication is successful is the 'echo' method, and this succeeds between various eigenvectors of the measurement operator and the unknown quantum state being measured at a rate given by the Born law. Born rule - Wikipedia
Measurements are normalized because measurement operators are unitary which means that every measurement has one or another outcome whose probabilities, given by the Born law, add up to 1, so that we can treat a quantum measurement as a communication source whose language is determined by the measurement operator in use.
The notion that the observables are the stationary points in the divine dynamics is gradually gaining weight as it becomes more concrete. The world is held together by logical continuity because it is embedded in the one and consistent God. We understand the stationary points by understanding the dynamics of which they are part. In wave mechanics we see the dynamic process as the superposition of infinite dimensional waves, of which we get an occasional snapshot by making an observation. Now we see that there is nothing special about physics, logic or intelligence, it is all part of the logical continuity of the observable fixed points of the logic being manipulated by creation and annihilation of different species at different points in spacetime.
Can we say the fixed points control the dynamics or the dynamics control the fixed points? Both are true. We design the dynamics by designing the fixed points, since it is generally the dynamic process that we want. We set processes in morion by removing the inhibitions so that potentials can act.
[page 76]
My writing flows when I have a sequence of stationary points to record and a clear road ahead. Then we come to the end of the road where new understanding or new creation is required to continue. In time a new step forward will probably appear. I began this story with faith that God and the World are one. The demonstration by fixed point theory that a world complex in fixed points is nevertheless compatible with the completely simple dynamics of the traditional god has opened my faith to a path to understanding. Now I am beginning to see how this can be all fitted together with the theories of computation and communication which tell us how fixed points logically relate to one another, all built into the Cantor universe which shows how large and complex structures can be made by joining smaller points together, as I am a community of atoms, distinct from but mingled with my environment.
Making the observable world out of the fixed points of the divine dynamics carries echoes of Newton's decision to build his celestial dynamics in a space (god's sensorium) fixed by God. Patrick J Connolly
Everything we observe [is] an act, something prior to space and time which we nevertheless experience as embedded in space and time. Quantum theory requires only time, that is sequential ordering to function (?). Periodic functions step out the process of time. An act occupies space and time, as I do. I am a complex act comprising many smaller quanta of action .S, the total quanta of my life, is mc2 . l /h, where l is my lifetime. This works out to about S = 1053.
Entropy is a count of action [complexion]. An act is a fundamental unit, a state, with no dimension other than orthogonality to the rest of the Universe. What is the Cantor universe, a formal
state space, ie a phase space. A space is the set of all its states. The information carried by a point in the space is equal to the entropy of the space ie the number of points it contains. So log(ℵn!) = ℵn.
Monday 29 November 2014
We can only talk about what is observable and speculate about what is invisible. Currently quantum theory posits a world characterized by the deterministic continuous evolution of wave functions which occasionally 'collapse' when they are observed. Because it is continuous motion, we model it with sets whose cardinal is the cardinal of the continuum, which we assume to be ℵ1. The mechanism that makes all these points behave as they do [is mysterious]. Continuous mathematics has been developed over millennia an is thought to be logically sound tat is bound together by logical continua = proofs.
Here we propose a simpler alternative, thst the invisible dynamics is logically rather than geometrically continuous. We do this by assuming that eigenfunctipns are computable functions, so that instead of there being ℵ1 of them there are only ℵ0, that is the number of Turing machines whose algorithm is expressed by a finite ordered set of symbols. Such an algorithm may appear to a casual observer, if it is maximally compressed [by a suitable coding algorithm], as a random sequence of symbols all of which are equiprobable, so maximizing entropy.
If the whole Universe is a computer network, our next task is to see how computer networks create themselves, beginning with nothing from [an] observable point of view (ie the omnino simplex,
[page 78]
continuous) God.
Neuenschwander page 4: ' "Invariant" means a quantity's numerical value is not altered by a coordinate transformation. "Conserved" in contrast, means that within a given coordinate system the quantity doe snot change throughout a process. NeuenschwanderChaplin, Biography, page 210: 'I did not have to read books to know that the theme of life is conflict and pain.' Not always, there is also harmony and pleasure, which I imagine occupies 90% of my life. Chaplin
'. . . humour . . . ; is the subtle discrepancy we discern in what appears to be normal behaviour.'
Tuesday 30 November 2014
Neuenschwander page 25: Jerry B. Marion: 'In Newtonian mechanics a certain force on a body is considered to produce a definite motion; that is a definite effect is always associated with a certain cause. According to Hamilton's principle, however, the motion of a body ma be considered to result from the attempt of Nature to achieve a certain purpose, namely to minimize the time integral of the difference between kinetic and potential energies.'
Wednesday 31 November 2014
Thursday 1 January 2015
Our human relationships are represented as field of 'force' that guide our behaviour, deciding in a crowded situation who we will dance with, kiss, etc etc. All of tis would seem to be directed by our judgement of whether an interaction will be 'attractive' or not, or maybe productive.
[page 77a]
Neuenschwander page 40: 'The concepts of potential and kinetic energies came along after the concept of force (eg Thomas Young was the first to use the term of "energy" applied to mv2 in 1801-03).
page 46: 'The generalizability of Hamilton's principle to the widest scope of physics , even far beyond mechanics, and its presentation of conservation laws, gives Hamilton's principle a depth and versatility not shared by other mechanical principles.'
Friday 2 January 2015
Albert Camus: Intellectual: 'someone whose mind watches itself '. Bruce Grant
The Lagrangian describes the action. If there is no action, ie the Lagrangian = 0, nothing happens and we have a symmetry, ie a NOP.
The wholeUniverse is one pure act which we see time division multiplexed into the action we see around us, which looks like a massively parallel process but all our local perception of it is time ordered (= serial) communication.
When we say ∂μjμ = 0 we are algebraically adding the flow of action in each dimension to get the total 0, ie the measure of action collapses the structure of spacetime down to a single scalar parameter.
Neuenschwander page 126: "In this chapter we study local gauge invariance. In the analogy it corresponds to rotating the pointer needles by different amounts on different gauges. It may be hard to see how such a transformation can leave anything invariant. But if the gauge needle emits some kind of signal to compensate for its
[page 78a]
rotation, then the coupled system 'gauge + signal' might exhibit some kind of invariance.
Saturday 3 January 2015
Physics uses coordinate systems to study physical systems, but insists that the physics exists independently of the coordinate, so that changing the coordinate system should not change the physics, only the way we look at it. Different coordinate systems may reveal different features of the physics and may hide other features. This notion is supported by the theorem of quantum measurement that tells us that what we see are the eigenvalues of measurement operators, so different operators will reveal different eigenvalues corresponding to the eigenvectors of the operator used. We may think of the observable operator as a reference system. We see a similar sort of behaviour in the senses of different creatures which are sensitive to different features of the environment. In a universe where everything is looking at everything else from its own point of view, can we claim that there is a true point of view that exists independently of observers? Einstein appears to have felt that this is so, but it seems hard to believe in a universe which can be modelled as a layered communication network, since the meaning that a layer may give to the elements of the layer beneath it seems to be pretty much arbitrary. Only at the very lowest level can we expect to find no interpretation effects introduced by the observer, ie we can expect the gravitational structure of the universe to be independent of observers, since gravitation attributes no meaning to actions but sees only their frequency as energy.
Coordinate system - language. As language expands it develops the ability to record more subtle features of human experience and at the same time propagates these experience, increasing their frequency.
[page 79]
Noether Wikipedia: 'Noether's first theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.' Noether's theorem - Wikipedia
Conservation of momentum is a consequence of Newton's third law: action and reaction are equal and opposite. We might se this as an example of duplex communication where we represent the forward and reverse processes (echoes) of a message to be φ and φ*. The probability of the communication succeeding is the product of the forward and reverse probability amplitudes, P = |φ|2 = φφ*.
A large proportion of the mathematical machinery of physics is concerned with the transformation f coordinate systems while preserving the integrity of the physical systems they describe. The aim is to obtain a coordinate free insight into what is happening, ie determine the relationships of elements of the universe to one another without being led astray by coordinates.
The tour de force in this enterprise is the general theory of relativity which identifies the reality and te coordinate system using the metric to translate between actual distances and coordinate distances.
