vol VII: Notes
2012
Notes
[Sunday 21 October 2012 - Saturday 27 October 2012]
[Notebook: DB 73 Spring2012]
[page 111]
Sunday 21 October 2012
Cool and smoky. What do I want vis a vis the Catholic Church? Not so much revenge as vindication. I think I was right to identify God and the World, but until I get some public recognition of that rightness (if it be so) it is just a private fantasy that keeps me happy but has no public consequences. Since that time I have been on a long intellectual journey that always seems to be going somewhere but never seem,s to come to an end: the end I want being a publication of some sort that stirs public interest. The best i hope for at the moment is that my self published website, that will ultimately contain these words, will ultimately be complete and attract some constructive interest, Meanwhile press on, every day is both beautiful and a few steps forward, driven by the power of the revelation that seems forever almost within my grasp. As I saw at the beginning, the task requires a revolution in both physics and theology.
[page 112]
The bonds of ignorance are strong, and one is always trying to break through them by insight and understanding. Agatha Why didn't they ask Evans? What does it mean? read the Book. [Context] Christie
Unreasonable Effectiveness: Conclusion.
Physics faces a dilemma: how can the initial singularity with no structure represent the precise initial conditions necessary to constrain the Universe ion its historical line of evolution? The explanation proposed here gathers ideas from two thousand yeas of human intellectual development starting from Parmenides fullness of being, through Aristotle's unmoved mover to Aquinas God of pure act. to the manifestation of fixed point theory. We have sketched this journey and leave it to the community to see of there is merit in this model of the world.
The evolution of the world is guided by fitness: of all the possibilities those that go forward are those that are sufficiently consistent with the story so far (ie their environment) to survive. We may see this as analogous to the Judgement of God that we read so much about in (eg) the Old Testament.
What to do today? Write, it seems, and keep on writing until everything becomes clear. This I have in common with all individuals from quantum systems to the Universe, express myself/ But why? Why do wave functions 'collapse' and things do thinks. We say it is because certain computations halt, giving us the eigenvalues of the computed eigenfunctions. The rate at which this happens is related to the eigenvalue which measures the (normalized) rate of emission of the corresponding symbol. One could go through all my
[page 113]
notebooks and count the occurrences of each word to give an analogous probability, each word corresponding to a basis vector in my language.
Why do things act, ie send messages, do things? I am quite energetic and would always be doing things, but am inhibited by two things: One is lack of energy, tiredness. The other is the lack of a way to do what I want to do, a situation usually resolved by thinking time, modelling the result and possible processes to achieve it in my mind until a course of effective action becomes clear. One may imagine that the universal process itself is inhibited in a similar way, that a uranium nucleus does not decay until it finds a way to decay and because the barrier to decay is so high, it may have to wait about four billion years until it finds that way, a very long search and computation.
We are pushed into the future by the irresistible force of time, whose source we expect to find at the beginning of time, which is possible because locally time is represented by an ordered set of events which must have a first element in the order for the idea of order to make sense in the wider world of mathematics.
We can attribute the fact that the Pope thinks his story is truer than the story that history actually tells us as an example of sovereign arrogance, the two-year-old stage of human ontogenesis.
Space is field, that is invisible computation.
Monday 22 October 2012
Communication = bonding = correlation
page 114]
Given that space is the field of invisible computation, we now wish to map the transfinite network onto space sop that the network becomes the equivalent of the field of complex amplitudes which we can analyze a message at a time using Feynman diagrams.
Non-relativistic quantum mechanics 'preserves' 'particles' [messages] (but not states, which can change). Relativistic quantum mechanics creates and annihilates particles but conserves energy, momentum and angular momentum [the fundamental properties of space-time].
We are always looking for explanations in terms of something, ie an explanation and a language are inseparable (Misner, Thorne and Wheeler page 76 again). Ultimately all explanations are messages and messages are digital, and so it may seem to explain the world in terms opf continua is no explanation at all, ie Noether's theorem picks out the non-events which correspond to non-explanation of the world [abstraction]. Misner, Thorne & Wheeler, Neuenschwander
So we want to show that the network explanation is equivalent to quantum field theory. All this requires is 1. quantization; 2. computability.
Feynman III: 8-9: Non-relativistic world dynamics
ihdCi / dt = ΣjHij(t)Cj(t)
Two computers can be said to communicate if they are reading and writing the same memory address. Two computers are independent if each stays inside its private partition of the memory. We see this structure in an ordinary computer with one processes but many users and applications where the operating system divides the computer's
[page 115]
time between working in different portions of memory whole the operating system itself (in charge of communication) has access to the whole memory so that separate processes may communicate.Invisibility theorem: The Dirac style scientist who is so busy imagining how the world might be that s/he tends to taciturnity. Farmelo
The dynamics of a halting, deterministic, discrete computer are not observable. For a system to be observable by another system, both systems must share a memory locarion through which they communicate, the sender writing to the location and the reader reading from it. The data written to memory is the output of as halted computation. We hope to find that the extra work required to write to this bit of memory means that the computer being observed will not halt. We use the debugger analogy. [the proof is recursive, the machine having to explain the operations it needs to communicate its state, and then explain each operation of this operation, etc etc so it can never halt].
Halt. Dynamically we are interested in 'halting ithin a given time from starting', making time of the essence of the proof, to observe the dynamics of a process we must slow it down.
So we might say that the dynamics of a h, d, d computer cannot be resolved in that machine's real time.
Physicists find fixed points using the Lagrangian method and we can see how Feynman's path integral method explains the digital nature of state changes.
Tuesday 23 October 2012
[page 116]
We communicate by reading and writing from the same memory [or a copy thereof], as I am now communicating with you by writing this sentence and you by reading it. The conversation here is a bit one sided, but maybe one day we will meet and you can write and I will read. It is the memories that are the fixed points in the network system and we see a deterministic computer stepping from fixed point to fixed point, each step determined by the one before it.
Zurek's paper may then be considered as elucidating the conditions on reading and writing a memory, that reader and writer should share an orthonormal basis, that is a discrete alphabet. Wojciech Hubert Zurek
In the old faery tales the boy must make his fortune before he can marry his true love. I have never made a fortune, but have been married a few times on slender means, and although these marriages produced beautiful children at the 'reproductive' level, they have not fared so well at the social level. Nevertheless the dream stays with me that one day my theological fortune will be realized and the resulting fortune will set me free to find and marry my true love. This dream is a potential that carries me on., but one may suspect that it is 'incomputable' and so may never be observed to happen, but 'hope springs eternal.' Hope Springs Eternal - Wikipedia
Next step: Plato to Landauer. So far we have modelled the world in terms of the classical Platonic view of mathematics in which ℵ0 is a really big number. Cantor was criticized in his day for claiming that infinity and transfinity could have formal mathematical existence, that involve no inconsistencies. Set theory was found to lead
[page 117]
to paradoxes but has been cleaned up in various ways. We know, nevertheless, that because all information is represented physically, the Platonic set of the natural numbers cannot be represented physically. Instead we rely on certain symbols such as N = {0, 1, 2, . . . , n, . . . } and card(N) = ℵ0 etc which by convention represent the set indicated. We can then make arguments which include such axioms as an infinite set is one that can be mapped onto a subset of itself and so on.
Bell page 195: 'When we invent worlds in physics we would have them be mathematically consistent continuations of the visible world into the invisible . . . even when it is beyond human capacity to decide which, if any, of these worlds is the true one.' Commutation = simultaneous eigenvalues = common bases.
Reversibility ==> determinism Bell page 177: 'The reversibility of the Schrodinger equation strongly suggests that quantum mechanics is not fundamentally stochastic in nature.'
Wednesday 24 October 2012
Aquinas and co thought the human 'intellectus agens' to be a spark of the divine light of intelligence, which idea seems perfectly consistent with the idea that all actions are acts of intelligence [and acts of God]. The interesting thing for me was that when this thought crossed my mind i was instantly depresses. Maybe an example of Aristotle's dictum 'omne animal post coitum triste est', which is a bit hard to understand if true, since a successful mating is high on the list of animal successes. Maybe it is my ancient religious indoctrination biting back as
[page 118]
it receives another damaging blow. Active intellect - Wikipedia
Farmelo, Dirac
One of the many ideas that need to be overcome in the construction of a scientific theology is that the modern scientific view of the world completely destroys the ancient views, ie that Plato, Aristotle, Aquinas and co are so completely wrong that we can forget them entirely, rather than that seen from the right angle (in something like Hilbert space) these ideas are a foundation for further work, eg that the persons of the Trinity are fixed points in the divinity, as I am at my own scale.
Farmelo page 75: Orwell 'Good prose is like a window pane.'
page 75: Dirac: 'I never knew that parents ought to care for the children but from [my brother's suicide] on I knew.'
page 83: Heisenberg: 'The present paper seeks to establish a basis for theoretical quantum mechanics founded exclusively on relationships between quantities which are on principle observable.' Van der Waerden 1967. van der Waerden
Dirac commutator paper 1 December 1925. Paul Dirac,
We may think of theology as science for religion, rather than science about religion, that is a form of sociology. The ambit of theology must be wider, since this is the traditional theory of everything. For physicists to think that a fundamental theory of the physical world is a theory of everything is perhaps a blunder bigger than the cosmological
[page 119]
constant problem. Stephen Weinberg
I feel myself beginning to get more excited about theology after fifty years of penny pinching and slog. It has been worth it. No regrets.
The properties of a system of pure action was studied in the detail available by Aristotle and Aquinas. Their result led them to posit a power beyond the visible Universe, unmoved mover, quintessene, God, and now the quantum field. What has been overlooked is that pure dynamics has stationary points, and the ensemble of temporary and permanent fixed points in the Universe is the observable data not only for science, but for the whole of sentient life = life.
Perhaps it was just my theological curiosity that precipitated me into the Dominicans. I could not have gone to a better place, as I can see in retrospect and have no motivation to blame them for their conscientiously held errors. Order of Preachers
How does the invisibility theorem account for the loss of interference if we know through which hole the electron went? Is it relevant?
Fixed points and cybernetics. We control the world by controlling its fixed points,. A malleable world subject to selection will optimize, as we see the optimum action as stationary, maximized (in general relativity).
Space is memory which is a fixed point arising from the interaction of two systems (what quantum mechanics calls measurement) which produces physically embodied output, a particle in space particle / space duality - general covariance.
[page 120]
Everything we observe is a particle. We do not observe fields, we conjecture them.
The next step is to establish a correspondence between quantum mechanics and the transfinite computer network. We can do this in a binary way, assuming that each address contains one bit of information.
The reduction of the wave function reduces a continuum of frequencies to a set of lines, The wave function only reduces when we communicate, and for error free communication we need an orthogonal basis.
. . .God is a continuum and a continuum carries no more information than a point [information in point = entropy of the space].
Space is a consequence of the exclusion principle, or vice versa, a phase thing.
Thursday 25 October 2012
Quantum mechanics starts by postulating a wave equation with a continuum of frequencies which are invisible. When we come to observe such a continuum, it collapses into a series of 'lines', the spectrum of the operator used to make the observation, Zurek explains why this is necessary.
[page 121]
Democracy is empirical in the sense that it provides an opportunity for everyone to contribute their experience to the management of society although the very abstract means of a vote only carries a few bits of information at most.
We can see the world as a set of broken symmetries. Emmy Noether showed us the close relationship between symmetry and continuity. We may see a symmetry as a line, open or closed [infinite or periodic]. In geometry we define a point by crossed lines, breaking the symmetry of both lines. Conversely, in geometry, we can define a line by two points [so that the two ideas are duals of one another] In general two fixed points define a line, which we may interpret as a dynamic continuum, and two lines define a fixed point. Emmy Noether
We can cast these ideas in terms of computation. A computer, like a Turing machine, is a deterministic process with a beginning and sometimes an end, We may see a computer as a logical continuum, every step being determined by the outcome of the step before. Like a continuum the dynamics of a computer is invisible. We see only the output and we can only ever see a source when it emits a signal. Feynman was first to conjecture that quantum mechanics represents a computational process, so initiating a large areas of contemporary research in physics and logic. Feynman
Symmetry, entropy and information
State the proposition and then bring out the proof.
An algorithm = computing machine is a symmetry [same algorithm, infinite inputs and outputs].
[page 122]
A Brian notes, we are all individuals, discrete points in human space, but we share a vast number of symmetries with one another through the physical, physiological, genetic, epigenetic and cultural foundations upon which we are built. Our individuality comes from a superposition of breakages of these categories and symmetry = abstraction.
The Lagrangian and the selection of algorithms. Algorithm (ie computer) us a fundamental symmetry in the Universe, ie algorithm = form - software (something of a misnomer since deterministic algorithms are invincibly strong and hard, formally error free. Although mathematically there are ℵ0 Turing machines the actual alphabet of processes that we see are quite few, outputting less that 100 fundamental messages (particles).
Algorithm,ic information takes orthogonal states as its alphabet,. Physical information theory deals with the actual creation and stability of physical states suitable for mapping to formal logical symbols. Logicians write in their logical alphabet, the Universe writes using its alphabet of particles.
effective mathematics is my next baby, seventeen years later [than the 2BOB lectures, which are based on the notion that the Universe is so divinely big that we need the transfinite numbers to describe it].
From the point of view of making a religion, it does not so much matter if this is true as that it is plausible enough to attract people to develop it further. Effective documents (songs, etc) are self propagating [like viruses], attracting people into a boson (symmetric) state. Broken symmetry gives fermions, isolated points in message space.
[page 123]
The symmetric tree. each new branch being a fixed point in the symmetry represented by the branch before it. Ambiguity meaning both the multifurcation and each of the states (lines, new symmetries) that come out of it.
Human symmetry and a-symmetry = groups with different sewxual cultures.
When we apply the Lagrangian method to computation hat do we take to be the kinetic energy and what potential? The candidates seem to be computation = kinetic, memory = potential and systems are optimized when (computation - memory) is a maximum or a minimum. [maximum for gravitation because all computation, no memory, pure isolated quantum mechanics].
Friday 26 October 2012
Saturday 27 October 2012
Farmelo: Dirac chess analogy: ' "Each chessman has a characteristic way of moving, and this is all that matters about it. The whole game follows from this way of moving the various chessmen." ' [two processors (players) shared memory]
The 'solution' to an equation is a fixed point.
Always the big question: what should I be doing now? Usually there are simple local answers: make a cake; write; get ready to go to work; associated with day to day life. On the wider scale the answer is always the same: get closer to natural theology, realize my dream. This is the potential that shapes me, embracing my family, friends and the whole planetary condition.
[page 124]
Farmelo page 399: Einstein and Dirac both spent their later years in disagreement with contemporary theory. E with quantum mechanics, D with quantum field theory and renormalization. It may be that the network model vindicates their position.Fir E's case, it makes quantum interactions represented by algorithms (eigenfunctions) deterministic, but the actual choice of eigenfunction [is] a network function that appears random (like an ideally encoded message) but is actually determined by the local communication requirements of the network [ie what I want to say to you]. For D's case, we have the fact that the continuum is a logical rather than a geometric entity, so that the zeroes in the bottom lines are an artefact of the model rather than the reality, and changing the model might make delta functions and renormalization obsolete.
One might guess from Cantor's theorem that stationary points spawn new stationary points by generating new convex bounded sets within the dynamics where the fixed point theorem holds again, leading to recursive complexification within the pure dynamics of the Universal system.
To be excited is to be in a state of higher energy which can reach a lower energy state by emitting as message or particles (ie a photon, or for me a sentence, or even an essay). Once the essay is emitted I enter a low energy state which ay be excited once more by a new idea for an essay coming to me, leading me to begin writing and reading in order to find the optimum string of words to represent the message which will once more carry away the excitement, and on we go. [the excitement may also come from outside input]
Feynman III 11-4: 'matrix vector', vector whose components are matrices.
[page 125]
It is sometimes said that to each quantity in classical physics there corresponds a matrix in quantum mechanics. It is really more correct to say that the Hamiltonian matrix corresponds to the energy, and any quantity that can be derived via energy [rate of action = rate of completed computation] has a corresponding matrix.
Energy is conserved, he total rate of action is constant but it ismultiplexed between different states at rates measured by the element of the Hamiltonian which must be normalized to represent a classical source as described in communication theory (information theory = algorithmic information theory.)
The inputs and outputs to information processing are information and the transformations on the input to make the output are also information measured by entropy.
Feynman page 11-4: 'It just happens that there are certain correspondences [between classical and quantum physics] which are hardly more than mnemonic devices—things to remember with.
page 11-5 '. . . there is no mystery in the fact that in classical mechanics there is a shadow of quantum mechanical laws—which are truly the ones underneath.'
Operator - computer
Vector - memory
1hd / dt = H = 'the dynamic law of nature—the law of motion—for a quantum system. What does this mean in terms of some underlying logic - energy of a given process = rate of computation, ie rate of halting at a fixed point, a message or signal encoded by computation, as we do.
[page 126]
Christianity is a fiction, some based on fact, much based on imagination unconstrained by observation or experience,. For this reason Christianity heavily discounts everyday experience and tries to promote its own peculiar view of the nature of the world and human existence.
Computer electrodynamics.
rate of action = rate of change. ß
