vol VII: Notes
2016
Notes
Sunday 24 July 2016 - Saturday 30 July 2016
[Notebook: DB 80: Cosmic plumbing]
[page 153]
Sunday 24 July 2016
Public secrecy: those who act on behalf of us all have no intrinsic right to secrecy. Wikileaks and the Democratic National Convention Tom Hamburger and Karen Tumulty
Much of the answer to making a computer network behave like quantum mechanics (ie match inputs to outputs) may revolve around the absolute simplicity of the turing machines involved, ie we start in the 2D space explored by quantum computation. Nielsen & Chuang: Quantum Computation
von Neumann page 3: '. . . the general opinion of theoretical physics had accepted the idea that the principle of continuity ("natura non fecit saltus") prevailing in the perceived macrocosmic world is mere simulated by an averaging process in a world which in truth is discontinuous by its very nature. von Neumann: Mathematical Foundations of Quantum Theory
My main task is to explain my idea to myself by mapping it to quantum mechanics. Classically, energy is a function of the coordinates and their time derivatives (in a conservative space where kinetic + potential = 0).
Classical mechanics gives us a series of transformation equations all of which are constrained by the conservation of energy.
v N page 7: 'In both theories we must now learn as much as possible from this Hamiltonian function about the true, ie quantum mechanical, behaviour of the system.
[page 154]
The science budget must provide equivalent support to both research and the communication of the results of research to the voting public.
v N page 7: 'Primarily, therefore, we must determine the possible energy levels, the find out the corresponding "stationary states", and calculate the transition probabilities.
Matrix = computation (operator).
page 17: The fundamental problem of the matrix theory was to find the matrices Qi, Pi such that first the commmutation rules are satisfied, and second that a certain function of these matrices H(Qi, Pi) becomes a diagonal matrix. Natural Sudoku.
page 21: 'The fundamental problem of the matrix theory is the solution of the eigenvalue equation Σνhνμxν = λx μ.
The 'holism' of quantum mechanics is captured by the relationships between the orthogonal basis vectors encoded on the observation operator which is self adjoint with real diagonal and in fact diagonal, all the complex off-diagonal numbers zeroed out.
By the time I have worked all this out maybe I will understand quantum mechanics. Is this a big problem or not? Depends how you look at it This depends on the tools you have available.
We have to work it out as software in a machine which is itself software maintained by machines in a higher layer which need this layer for survival.
[page 155]
v N page 22: 'Eigenvalue problems of the type E3 [integral] have been investigated extensively in mathematics and can in fact be handled in far reaching analogy to the problem E1 [Matrix version of eigenvalue equation].
What we are looking for as a coupling between networks and matrices ie a correspondence. The entries in a matrix encode the probabilities of different orthogonal vectors interacting with one another.
v N page 29: Normalization limits the field of admissable functions to those with finite sums or integrals [as dimension increases without limit]. . . . we call the totality of such functions FZ and FΩ respectively. Now the following theorem holds: FZ and FΩ are isomorphic (Fisher and F Riesz). To be precise this means that following: It is possible to set up a one-to-one correspondence between FZ and FΩ. . . . The two sets of functions are equinumerous [ℵo or ℵ1?].
page 31: Z and Ω are very different, and to set up a direct relation between them must lead to great mathematical difficulties. On the other hand FZ and FΩ are isomorphic, ie identical in their intrinsic structure (they realize the same abstract properties in different mathematical forms) — and since these (and not Z and Ω themselves) are the real analytical substrate of the matrix and wave theories, this isomorphism means that the two theories must always yield the same numerical results. Riesz-Fischer theorem - Wikipedia
FZ = Hilbert space. Next step from Hilbert space to computer network [think about tensor products].
Monday 25 July 2016
Series: the sum of a sequence of terms [with a metric]. Sequence - Wikipedia, Series - Wikipedia
[page 156]
A turing machine is a sequence of operations which do not sum but each of which changes the process toward the last operation, which is for the machine to halt with an output. This difference changes the whole game of applying infinite series to Hilbert spaces.
Why am I so hooked on digitizing the universe? Is it because I am subconsciously convinced that this is the only path to declaring the universe divine, that is constrained by no outside force or power.
Following Aquinas, beatitude is the fundamental attractive potential (Heaven) and hell is [the opposite].
We are getting to the target by cutting through a jungle of ideas, opinions, proofs and observations, but a clear path to an observable target does not yet seem open. Before I can preach authentically, I must convince myself. This is why I left the Order of Preachers. They, like the Catholic Church everywhere in propaganda mode, wanted me to say things I did not believe. The pressure to do this is the principal power of the ruling class, because once they can get you to say you believe something you are committed, like a member of a political party. One must toe the Party Line, which is an exercise in human entropy reduction with a view to gaining power. The creative nature of the universe tells that this approach may work locally if enough violence is available, but it is unstable. So the principal interest is in creation rather than annihilation Creation requires the advent of something new and that cannot come from an impossible deterministic system as imagined by Catholics.
[page 257]
The Catholic Church maintains that we are embedded in a fully deterministic system [Free will?]. God has total knowledge of every event, past, present and future, and absolute power, able to totally control every event. This is a comforting thought if you believe God loves you, and it has served as the core of Church propaganda for 2000 years. In the past, they have attracted little criticism of this idea, but the fores of reality are beginning to build up against them. The roots of this movement are in the logical and mathematical developments over the last few centuries that show that the this model of deterministic divine control is self contradictory. It becomes clear when we consider God the creator. To create is to being something new into existence. But god cannot create because it is already the fullness of being. The whole space of reality is (allegedly) filled by this God. The created universe is not new since it already existed in God in the form of complete knowledge and power. The rot in this sort of argument is ancient, first stated by the Cretan who asserted that all Cretans are liars. Since then we have learned that things that reference themselves are very dangerous territory, all the way from the self energy of point masses to the fact that my reference to myself includes my reference to myself ad infinitum. as we see in the invisibility theorem that bans god from looking at itself under pain of getting nowhere — attempted self-reference leads to incomputability and trouble. Physically the self reference problem created an infinity out of dividing by zero. Hence no divide by zero. The smallest possible divisor is the quantum of action. Development, chapter 2: Model: page 6 Invisibility
All quantum communication occurs in shared orthogonal bases.
[page 158]
The set of Turing machines covers the space of deterministic processes.
Do we ever observe continuous spectra? Only as a random superposition of a very large number of discrete spectra shifted by random time delays.
The execution of each Turing machine is move in the game of life.
Tuesday 26 July 2016
The invisibility theorem tells us that we cannot watch the universal computer network in action at the hardware level, but we do know the eigenvectors of the operators we use to observe the outcomes of observations, and we will know which ones of them have been executed when to read the eigenvalue we observe. This suggests that the key to this project, of it is not to be hopeless, is to devise a method of translating eigenfunctions into executable code and then executing the result to get (hopefully) the same eigenvalue. This further suggests, since each element of an eigenvector is an energy, ie a changing phase that the multiplication of ordered strings of phases changing at different frequencies explains the effectiveness of the inner product for producing probabilities. Gaps here but a but of sculptural adjustment may improve the outlook.I think one reason for my feeling that I will get there in the end is that the whole story begins with a god who is omnino simplex, and our observations of the history of the univers suggest that this simple dynamics complexified by the mergence of fixed points. Some take time, like the decay of a uranium nucleus.
[page 129]
Tellurium-128 half life 7.7 × 1024 years for double beta decay. Bismuth-209 - Wikipedia
The biggest problem we have yet to face is the vast numbers of identical particles in the universe. Although identical the have unique identities or else it would make no sense to talk about numbers of them. Conventionally (and pretty obviously) they are distinguished by their position and momentum.
Here it is very simple, phase is the measure of action, and although we conceive of this measure as a complex number and so continuous, in reality phase can only change by full quanta, ie 2π.
Political navigation and the theory of everything.
Spatial navigation used to be a difficult issue. Early sailors suffered severely from not knowing where they were, and the history of navigation encompasses many inventions in the area of timekeeping and astronomical measurement. For many of us, these days are over now. Every active smartphone knows exactly where it is by receiving signals from one of the sets of GPS satellites that surround the globe. They are like active stars, telling the phone where it is through the phasing of wireless signals. Satellite navigation - Wikipedia
Navigation tells us how to get around in geographic space, but there are many other spaces to be navigated. Here, by space, we mean a set of places that may be defined by some condition, rich, poor, happy sad, hot, cold, whatever. To a mathematician any set of distinct things can be fitted to an abstract space.
[page 160]
A practical navigation system requires a map, a means of finding out where you are and the mean of moving in the real world from one point on the map to another, all you really need for navigation is a metric.
The observable structure of the linear manifold is induced by the metric which in gravitation is determined by the local energy. The basic metric unit is the quantum of action. The action, we assume, can be any computable function.
A marvellous morning (to me). Terris. I am a messenger. We are all messengers. [McLuhan: the messenger is the message?] Ben Terris
Many a ship has been lost through inaccurate navigation.
A complete theory of everything must deal not only with fundamental particles but with everything that comes after them We get from physics to politics by the complexity invariant symmetry of networks. A network is a set of communicants.
The invisibility theorem means that we cannot look inside a quantum of action. Feynman's path integral method and most of the rest of quantum theory assume that we can differentiate and integrate phase, which requires looking at infinitesimal subsets of the action. The application of calculus works because nothing happens within the
[page 161]
primordial quanta of action that are treated by quantum theory. In effect it is the theory of 'empty' (ie meaningless) quanta and in this respect it antedates gravitation which involves time since it sees the rate of action, E = ℏω [= ℏdφ/dt].
Cantor's insight is that order is the source of complexity, that is the increase of entropy. The idea that entropy is the opposite of order needs a little adjusting, entropy, which brings stability, is a consequence of ordering, the vey opposite of Stalin and other dictators' plan: break society down to naked people. They disappear easily if they are not bonded to a social network.
Complex systems must be peaceful if they are to survive because violence destroys complexity, even though at a different level it creates rubble.
The product is a new theology, a new instrument to navigate everything.
NAVIGATION: Navigating the ship of state is [traditionally and still in many places] a task for theologians.
Wednesday 27 July 2016
An idea: a sequence of actions, eg how do we build the Sydney Harbour bridge?
How does the statistical nature of quantum mechanics arise from deterministic computations? By network timing - space gives a metric to phase [which is not available in time].
Work, which I do not like very much, helps me to buy time to read, think and write, the process of progress.
[page 162]
Does 'quantizing the field' mean restricting phase to multiples of 2π' = 1 quantum of action?
The minimum action is identical to god with no content. The omnipresence of god is equivalent to the omnipresence of action.
Act is the fundamental symmetry and it matches symmetry with respect to complexity in that all acts are identical regardless of their complexity. Action has no metric except a number. There have been n events.
Dynamic entropy = bandwidth is measured in energy, ie acts per unit time.
An event is the superposition of dynamism and stasis, so act exists before dynamics and stasis bifurcate into kinetic and potential energy.
Space: a set with some sort of metric which enables us to define [address] positions and paths [maybe a manifold is more primitive than this, addressing but no metric?].
Squeezing out words. Building I do the same thing over and over again according to a prearranged plan. Writing every word needs to be new or else it simply become repetitive. I say the same thing over and over again in these notes, and although the words might be similar, each return to an old idea usually brings a new point of view or context that adds to the historical trail I have followed in my response to studying Aquinas and Lonergan in my youth. The principal
[page 163]
impediment to declaring the universe divine is the deeply embedded notion, no doubt dreamt up by those who had servants, that dirt is dirty and inferior, rather than an exceedingly complex structure on scales down to the fundamental particles. The key to this is that the computing power [of the universe comes up against the theoretical limits].
Blowback: paradoxically the attempt to suppress various forces of life tends to increase selective pressure on them so that they evolve faster to escape the forces of suppression. Is this happening in our understanding of terrorists and terrorism? Should we listen to these people more so they do not feel the need to do violent acts to attract attention?
Turing's theorem places a limit on the number of different Turing machines available to use. The other resource of importance to computation is memory and Cantor's therem tells is that by creating more complex structures we are creating more memory, that is more states, more entropy. The quantum mechanical and network way for this to happen is by communication, by the creation of pairwise tensor products of all the systems in the universe.
We are looking for the physics that makes itself.
Computer network is a tool to create awareness of the creative power of the universe.
[page 164]
One product of this line of thought is the application of physical ideas to the creation, annihilation and flow of money on the planet. At present the system seems very leaky and corrupt.
Baez and Story John C. Baez and Mike Stay: Physics, Topology, Logic and Computation: A Rosette Stone
Ahmed page 6: 'It is precisely this correspondence between Islam as a theoretical object of analytical category and Islam as a historical phenomenon that is considerably and crucially lacking in the prevalent conceptions of the term "Islam/Islamic".' Ahmed
Locally the transfinite network is countable and so suitable input and output for a computer.
Thursday 28 July 2016
Honour thy parents. This is a subtle control insofar as it means do what you think they would want you to do. Now that my mother is dead I feel a reduction in this constraint (ultimately a shift in a wave function). She lived and died a devout Catholic. I took Catholicism seriously when I was young, but found it wanting. They found me wanting, and let me go. Mum thought that this was bad behaviour on their part, but she could not understand, immersed in her faith, how radically I have rejected Catholic theology by redefining god. So I could not convince her that my rejection was a blessing that has filled my life with the pleasure of exploring a new theology and slowly sculpting is to a publishable level of perfection.
[page 165]
A quantum mechanical superposition is a superposition of numbers of identical operations (2π) phase which if they are superposed at random phases will yield a constant probability of halting (completion).
Mathematics is incomplete meaning that there are unending functions. We can classify functions by how long they take to execute which is a function of complexity (entropy) and energy (processing rate).
Normalization is blind to time, in other words the normalization integral is not a function of time but the sum of the infinite series of probabilities associated with the infinite space in which we find φ, von Neumann page 197.
. . . Playing with the very energetic grandchildren and seeing myself at play when I was that age. Since then I have spent a lot of time thinking about the woes of the world, their causes and cures. This can be depressing but there is hope in the creative power of a divine universe if we just get into the real game, abandoning the ancient fantasies of our rulers trying to justify their dictatorial tendencies, always gratefully assisted by the arms and allied industries. This all builds on fear which is rife because the old gods are failing and the new ones are yet but dimly realized.
Prophet - whistleblower. Prophet - Wikipedia
Friday 29 July 2016
Keep circling back to the fundamental point in this essay, illustrated by Cantor's idea, that structure creates entropy, and maximum entropy gives peace, where every particle has a voice.
[page 166]
This insight, only vague understood, showed that we bring peace by the creation of space, in the human sense noetic space, and all attempts to restrict control of noetic space to a self interested few are acts against reality, since against God.
Relax and travel at a sustainable speed for the long haul.
Mapping overlap to interruption. Two identical processes may be said to overlap if they are running in the same system at the same time but with possibly different starting and endpoints and different energy levels. What is an electron doing in an atom? Responding to the fields [messages] that it feels as it moves. Solving the relevant equations enables us to visualize the probability densities of electrons in 4D space-time. These are many body problems only approximatable by repeated solution of constituent two body problems [since each message between two charged particle is a discrete event].
A common enemy is leaky pipes [failure of conservation].
We need not worry about the details of digitization / software engineering given that we know quantum mechanics embodies the power of a turing machine [but would nevertheless like to see how it works, which, on the omnino simplex assumption should be at root fairly simple].
Everything is a theological problem because theology is the theory of everything.
[page 167]
How are the inputs to quantum systems coupled to the outputs? By observation. We only observe the inputs that we send to the system as outputs with a certain probability structure, an alphabet. An observation is a transformation of an alphabet ψ in, ψ* out, |ψψ*|2 probability. In the simple quantum system, we get back exactly what we put in [but going in the opposite direction, <p|q> = <q|p>*].
Reconceiving the universe as a network makes no difference at the quantum level, but opens the way to the Cantor hierarchy of energy / complexity.
Dark energy: maybe this is processes that do not halt (like an operating system) and therefore produce no output ie they are dark. Maybe take no input either because they cannot interrupt themselves to take in new information from the oracle [operating system is a symmetry inherent in the network].
I love to watch the solder wet the pipes and fittings as I weld them together. We love fluidity and flow, a clue to the world that made us that conserves flows and densities of probability. How do we couple these flows to the transfinite network, via the ur-metric, the quantum of action, the creative orgasm of god?
Watch the nude wrestlers seriously, in their full [social and political] context, and not just salaciously, where lust rules all.
Saturday 30 July 2016
Walking in the forest looking for directional clues — navigation in an unknown space, using hints from the past to work out the future. Quantum uncertainty arises from the quantization of action which means
[pag 168]
that it cannot form a continuous past that moves deterministically into the future, as the continuous complex wave function is believed to do.
von Neumann page 207: 'The statistical statements which we found in quantum mechanics have a different character. Here, for k degrees of freedom the state is described by the wave function φ(q1 . . . qk) —, ie by a point φ of the R∞ suitably realized. . . . Although we believe that after having specified (φ) we know the state completely, nevertheless only statistical statements can be made on the values of the physical quantities involved.' Born rule - Wikipedia
The statistical predictions of quantum mechanics are deterministic insofar as the law of large numbers suggests that they approach a fixed point (eg the half life of an event) and so, we assume, they are fixed by something computable ie by the formalism of quantum mechanics itself.
'We know the state completely'. ie it is determined at every moment by an infinite series of complex numbers, How can this lead to uncertainty? By the reduction of all this data by forming the inner product of two such vectors and requiring that the vectors and the product be normalized to 1 so that all the information being processed is contained in the angle of the resultant vector. Does quantum mechanics really take place in infinite dimensional Hilbert space or in ordinary 4D space-time? Our study of the behaviour of particles suggests complex set of rules as we find in applications of quantum field theory. In effect most of these rules are symmetries, the boundaries on spaces of structure, and effectively 'nothing'.
We are working on the assumption that perfect causal coupling (ie computability) is relatively rare (ℵ0 / ℵ1) but is powerful enough to bind the
[page 169]
world into a logically consistent structure which is bounded by incompleteness, incomputability and uncommunicability all of which are features of symmetry and leave the world open to creation. The PNP suggests that even though the route to the discovery of a new turing machine may be uncertain, the result so obtained becomes certain by the truth of the proof that establishes its existence, So evolution proceeds by discovering new deterministic processes (like reproduction) that give more power to the computable side of the system, resulting in structures like myself which are deterministic enough to prevent fatal errors for a century or so. P versus NP problem - Wikipedia
Rick Morton: 'Failure to fit in' breeds crime. Rick Morton
Equations compare two metrics of the same phenomenon to give us a broader understanding of what is being conserved in the observed operations.
God does not laugh because he already knows all the punch lines. But this is not true. In a truly creative system the past simply cannot control the future, nor can all time exist simul as the definition of eternity goes because there are only ℵ0 different resources (orthogonal turing machines] from which to construct all possibilities so timesharing with consequent annihilation and creation) becomes necessary to maintain logical consistency (outside time?) (local and 'instantaneous') ie a fixed state, a completed step in the logic. We have to think of the universe as embodied mathematics. What constraints arise from embodiment? The constraints associated with computability, ie something a consistent machine (like an engine) can do, ie all machines are embodied symbolic computers, distinguishable into formal theory and actual construction - approach to thermodynamic
[page 170]
perfection. Aquinas 45: Eternity: "The simultaneously-whole and perfect possession of interminable life"
Reality check: we cannot go on seeing ourselves as specially created angels inhabiting vile bodies. We must recognize that we are part of the same universe and most of the technology implemented in our bodies is common to other animals and plants, and even the mineral of which we are composed.
von Neumann page 210: 'This concept of quantum mechanics, which accepts its statistical expression as the actual form of the laws of nature, and which abandons the principle of causality is the so-called statistical interpretation. It is due to M. Born, and is the only consistently enforceable interpretation of quantum mechanics today, ie of the sum of our experience relative to the elementary particles,'
Elementary abstract quantum mechanics operates at every level of complexity but it is only concerned with abstract events at any level ignoring the smaller events which lie within the higher level event [think Einstein and specific heats]. This may not make sense. More superficially, the algorithms of quantum mechanics are indifferent to the complexity of the system to which they are applied.
