Notes
Sunday 28 March 2021 - Saturday 3 April 2021
[Notebook: DB 86: Hilbert / Minkowski]
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Sunday 28 March 2021
Cobar to Nowendoc 692 km.
Since the quantum of action is so small and the universe is so large, we need a way for quanta to multiply and diversify. We take a lead from the Christian doctrine of the trinity in which on god becomes three persons, all identically god. Aquinas, following Augustine establishes the multiplication via relations and we, developing a network model, do the
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same, proposing the relations are real substantive realities established by communication [using physical tokens, sound waves or ink]. We propose further, conceptually at least, that a quantum of action is a discrete entity, a particle, and that all the events of a network, both sources and messages are particles. This is consistent with one of the fundamental quantum theoretical classifications of particles into fermions and bosons [this reificiation of the quantum is reminiscent of Einstein's interpretation of Planck's E = ℏω as a particle, the photon]. Albert Einstein: On a heuristic point of view concerning the production and transformation of light
In quantum theory we associate a 'state' or state vector with every particle but there is more information in the state than we can . . . observe when particles interact [where we only see one element of a spectrum of possibilities]. We find that bosons have integral spin and fermions have odd half integral spin and these qualities cannot be superposed on each other. [Nevertheless] bosons, the messenger particles, can be superposed into the same state but any attempt to superpose two fermions leads to an empty state [the Pauli exclusion principle]. Pauli exclusion principle - Wikipedia
Driving hundreds of kilometres through this immense and complex landscape I wonder how to create it out of quanta of action. It is of the nature of quanta of action to act, and insofar as they are completely simple, they have no means of controlling the timing of their action so that we observe throughout nature that quantum events are random everts drawn from some complete space of events. This observation provides us with an origin for time and energy, since energy is the [time] rate of action. Insofar as the action of quanta is a random event in time, we can expect a wide spectrum of energies to arise in this way. If we imagine that the
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simplest possible particle is a boson, the photon, we thus imagine a spectrum of photons differentiated by their frequency and energy and existing prior to space. This suggests an origin for the quantum vacuum in time division multiplexion. Now we need to introduce space and fermions. Space serves to differentiate identical fermions and is often considered to be created by them. We also need a mechanism to create massive particles which are differentiated both by their states and their location in space-time. Here we introduce the quantum harmonic oscillator as the dialogue between bosons and fermions facilitated by the introduction of potential [energy]. Quantum harmonic oscillator - Wikipedia
Quantum field theory seems to come with lots of fudge. Why do we have to give photons spurious mass to make computations work and four degrees of polarization when we only see two? Is nature really this kinky? It is almost certain that the real natural processes do not need these weird fixes. A lot of this may arise from putting too much faith in 4 space. The first bifurcation we see in Hilbert space is splitting it into two orthogonal subspaces corresponding to bosons and fermions that cannot be superposed. We may not need to find a reason for this beyond the creative tendency of the divine universe to complexify by bifurcation.
The idea of six degrees of separation seems to imply that every person on the planet is complicit in my sixth order perturbation [via a global hum of 'news'].
Monday 29 March 2021
We are building a universe out of a quantum of action - a big god out of
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little gods. Aquinas repeats the belief, traced to Pseudo-Dionysius and others, that god is absolutely simple, without parts. From a formal point of view, we may see quanta of action as 'parts' of the universe, but from a dynamic point of view we may see them blending seamlessly so as not to break the dynamic simplicity of the universe. Modern mathematics proposes to define geometric continuity by putting points ever closer together, trying to resolve the contradiction that continua are by definition continuous whereas points are by definition discrete. Aristotle's definition of continuity avoids this problem by saying that things are continuous insofar as they have ends in common. This definition of continuity is commonly implemented in logical communication in computers where two entities communicate by sharing one 'end', a memory location, both reading from and writing to the same address. Aristotle: Physics V, iii: Continuity etc
How do we implement this algorithm in physics? We are looking, in the first instance, for a mechanism for the interaction of photons and electrons. We know that particles with rest mass have internal processes since, for instance, neutrinos with mass can undergo a change of flavour in transit from the sun without interacting with any other particle. The interaction between electrons and photons, we suspect, must be continuous, that is they share some logical state in the interaction process.
I know you fear me because you want me dead: 'I hope you die in gaol'. Fear of the other is probably the fundamental reason for murder in all its forms: if I do not kill them, they will kill me. You know that I know the truth and your only escape is to call me a liar and wish me dead. I will die in the end, but never lie. The Roman Catholic Church asked me to lie [by preaching doctrines I knew to be false] and I declined and left. I would not lie to you, my beloved child, and you will have to accept that in the long run.
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In the world of photons and electrons, all communication seems to be related to frequency - an electron and a photon will interact if the electron can change its potential by an amount corresponding to the frequency of the photons. Is this feature universal in quantum mechanics, everything depending on quantities of potential and kinetic energy? The whole business of gauge fields is about phase and frequency and so it seems reasonable to imagine that time, frequency and energy are sufficient to describe the mechanism of quantum mechanics. Space enters this mechanism because, given the finite velocity of light, it takes time for s signal to move through space and so distance becomes an input to quantum processes.
Tuesday 30 March 2021
It is often repeated that gauge particles should be massless. While this is true for photons it is not true for W and the Zs or gluons [?], and so mechanisms have to be devised to account for the masses of these particles, the final discovery being the Higgs boson. Once again this seems fishy to me but at present I do not understand the reasoning. What does seem clear is that pure unadulterated gauge theory demands that messages move at the velocity of light and so, from the point of view of massive fermions like electrons, they are in effect frozen in space and time moving on null geodesics in Minkowski space. This seems to be an interesting point since the information carried by a particle travelling at c does not evolve in time and so delivers the message initially encoded in it without change. It is true that photons travelling through a gravitational field have their energy changed but perhaps their phase and polarization is delivered unchanged from source to source. Higgs boson - Wikipedia
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Wednesday 31 March 2021
Determinism is a very serious defect. God knows and acts with infinite precision and control, having oversight of all events in the universe. We see this as a set of ℵ0 of quanta of action. We maintain that it is not possible to control such a large set of events. There are five basic limits to control: Cantor's theorem [which provided us with new numbers by ordering old numbers], Gödel's theorem, showing that some propositions are undecidable, Turing's theorem [showing the limit on the power of computation], [the cybernetic principle of] requisite variety [which defines limits to control] and Shannon's theory of communication. Cantor's theorem - Wikipedia, Kurt Gödel I: On formally undecidable propositions of Principia Mathematica and related systems, I, Universal Turing Machine - Wikipedia, Variety (cybernetics) - Wikipedia, Claude Shannon - Wikipedia
Gödel's original proof established a mapping between logical statements and numbers devised so that all the numbers (like all the propositions) are unique and uniquely coupled to one another. Shannon saw a new metric for complete systems of events: entropy: the logarithm of the number of combinations and permutations of a set of events. Boltzmann produced an abstract path from the random interactions of particles in space to the entropy measured by thermodynamics and statistical mechanics.
An essay on the [five] dimensions: Cantor, Gödel, Turing, Wiener and Shannon assembled into a formal mathematical model for theology and therefore the world. Norbert Wiener; Cybernetics or Control and Communication in the Animal and the Machine
. . . the disappointment of seeing my house wrecked is offset by writing things that look good, each new sentence representing a step in a long and random process that has taken me from monk to concerned old man, convinced that the young ones are doing stupid things (young meaning that their Weltanschaaung is long out of date). The world is beginning to assert its right in the form of limit to growth. We want growth of the spirit within a sustainable system of necessary production. The vile
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distortion of theology practiced by trumpist and fundamentalist Christianity has completely missed the point of the revolution in human communication brought about by [the] engineering and theoretical discoveries facilitated by world wars. D H Meadows, Randers & D L Meadows: The Limits to Growth: a report for the Club of Rome's project on the predicament of mankind
There is great pleasure in discovery, that is finding a way to portray a discussed feature of the universe in simple and accurate language, a fact only possible when the phenomenon has gradually become well understood, so every new writing is representing an aspect of this understanding. My hypothesis is that the previous sentence can be rendered into quantum mechanics. To make room for our story we treat the quanta of action of the universe as a version of the natural numbers and then treat these numbers by 'Cantor's algorithm' to generate the transfinite space of possibility in which we exist. From a probabilistic point of view the universe is thus modelled as a transfinite system of events. Gödel connected the world of events to the world of logical computation and computation by his numbering system which produces a unique number for each outcome of a [trial on a] set of events.
The next step is to map these ideas onto quantum mechanics. Talking science, we are talking about the deterministic and predictable processes in the universe. These processes are built from deterministic and predictable sub-processes which are joined together to make an overall process and there is in principle no limit to the number of layers of process generated from simple constituents ultimately measured by a quantum of action, an information content of one bit. At its most fundamental, an action turns a state of affairs p into not-p by changing elements in p. At its most general, it is simply a change of state. In the deterministic part of the world we should expect such changes of state to be causal. Like Aristotle, we must seek out the causes. All this is based on the existence of discrete
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identifiable elements in the universe that can be built into maps of the world, at all sorts of layers of complexity from fundamental interactions to the globally distributed complex network of interactions which keep what I call civilization running. Civilization we see as the development of a fundamental suite of relatively deterministic processes that can form the basis of civil engineering whose target is the development of peaceful happy communities that have a satisfactory and respected place in the world. The root of all this is orthogonality, that is discrete processes. One can move North independently of moving East. Understood in terms of action, each orthogonal dimension represented in Hilbert space corresponds to a discrete and identifiable process. Communication is invariant with respect to complexity so that we can imagine that similar rules establish to structure of atomic electrons and complex political and cultural structures mediate how we treat one another in civil society. We contrast this with non-civil society where violence rules and the way to deal with a dissenting opinion is to kill or imprison the individuals trying to promote civility out of uncivility and vice versa. Civility is more than politics. It reaches right down to water supply, drainage, sewerage, transport networks, communication networks, and so on. We would like to extend these benefits as fast as possible given the political and financial constraints. These matters take a lot of talk and adaptation to become realities.
My website will serve as some sort of anti-Q-anon. What is the antidote? Mostly people mostly want amazing things which require the conquest of some difficulty. God is, by definition, the most amazing thing there is. It is just a matter of spreading the details of this possibility, based on thousands of years of speculation on
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the wonders of divinity.
I am working on the engineering side, looking for constructs on reality.
The journey is from fundamental constraints on the universe to everyday life: don't waste; don't pollute; in every way reduce your footprint on the planet.
Thursday 1 April 2021
The network model seems quite secure on both common sense and technical grounds. The question is, how does it work? How do we design a network that works just like the real world? We make this network out of messages and sources. The sources are particles with spin ½, fermions. We assume that each particle is in fact an item of embodied software, like a person, which plays a specific role in natural processes. The most common are protons and neutrons, electrons and photons, the principal players in atomic life, but as we dig deeper we find neutrinos, gluons, quarks and so forth and the rather mysterious fact that we cannot produce an isolated quark or gluon. They are all found together apparently essential components of the processes we call proton and neutron. The works of a baryon, in other words, rely on each other for their mutual existence and any attempt to cut one out of the system simply causes a duplication of the system if there is enough energy available. This is a key to the constitution of particles: they are all made of energy. Energy is needed to make them; energy is released when they are destroyed. Energy is rate of action, so each particle [is dynamic inside]. Although high energy is needed to create [heavy particles]. We imagine the energy of a composite particle being the sum of the frequencies of the processes within it, and the functioning of a network structure depends on its components interacting with rational frequencies.
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In a proton, which is exceedingly long lived, the basic frequency, the inverse of its lifetime is very close to if not exactly zero, and the higher energies involved approach significant proportions of the mass of the proton.
Through the squared amplitude |ψ|2 quantum mechanics predicts the relative frequencies at which events occur, the rate of communication. It also predicts, through the eigenvalue equation the exact nature of the events whose frequency is it predicting, and these two features, the structure of the complete set of events and the rate of action (the rate of observation) of events in the system [constrain the quantum world]. This would appear to be near the heart of quantum theory, the relationship between frequency and structure. We see it in nature: a well structured creature is fitter, will breed more thus increasing its frequency relative to other species given a fixed quantum of resources. I am an artist, in my own little way, writing websites about theology.
The overall evolution of particles is constrained by the five mathematical theories associated with the names of Cantor, Gödel, Turing, Wiener and Shannon. At the root of all this is the fact that quantification and logic are mutually consistent. Deterministic natural processes require gears with teeth which do not slip rather than continuous friction connections like belts and plate clutches that provide variable coupling drifting frequency.
Happiness - making progress toward whatever. Thomas is right when he says the vision of god fills all the senses and the intellect: this is just day to day existence, a process that fully occupies us at some moments and maybe lets us relax in others (how long is s moment - a continuous bit of time bounded by everts).
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Looking at the lion whose eyes are black and the pupils white, the opposite of nature. The teddy is the same. If I was being empirical I could go through the whole basket and check their eyes.
Friday 2 April 2021
Christie, Mirror, page 152: 'Miss Marple: ". . . its always interesting what one doesn't see". She added. "If you don't see what a thing means you must be looking at it the wrong way, unless of course you have not got full information. Which is probably the case here." She sighed. "It's a pity she did not go straight to the police." ' Agatha Christie: The Mirror Crack'd from Side to Side
Cantor revealed the power of ordering implicit in the symmetric group snd showed how to create unlimited complexity modelled by the transfinite Cantor universe, or, as Hilbert recognised, Paradise. Symmetric group - Wikipedia
We expect the universe to fill the space of mathematics, which is to say that for every theorem in mathematics there exists some computational structure that matches that theorem, the turing machine that proves it. Here Gödel and Chaitin and cybernetics enter, telling us that the conclusion of a proof cannot be more complex than the ingredients that go into it. Proofs are deterministic and do not create entropy. They are analogous in this way to the unitary evolution of 'unobserved' quantum systems. There is limit to determinism, however, pointed out by Turing: there are uncomputable functions. A Turing machine is an ordered set of a finite number of actions and so there are at most the same number of turing machnies as there are of natural numbers. We know that ℵ1 is the number of mappings of the ℵ0 natural numbers onto themselves, and we are led
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to conclude that the vast majority of sequences of actions in the universe are incomputable and so random. In other words, our formal universe is a deterministic core represented by proofs executed as computable functions surrounded by a transfinite cloud of possible structures (ie new technologies and arts) from which it is the role of science to pick out the deterministic paths which account for the dynamics of the universe as we find it. The glory of this scenario is that it sets the scene for evolution by incorporating random variations in reproduction with selection within the environment in which the reproduced entities must survive. Maybe this algorithm applies as much to fundamental particles as to animals.
Our current standard model of the universe begins with an absolutely structureless initial singularity which somehow contrives (through a cosmic explosion, the big bang) to convert itself into the universe we now experience, particularly, for us, our planet. So we imagine the big bang to be s process where the initial singularity reproduces itself at random and the random variations of the initial singularity compete for the fundamental resource of the universe, action. The result of this competition is a system in which the use of a scarce and precious resource is optimized with respect to the deterministic processes in the universe and so fulfills de Maupertuis's dream of a perfect physical world. The physical world has in fact evolved toward determinism and serves as the deterministic core of the processes that have led to our own extraordinary existence, beginning to understand where we truly came from. Big Bang - Wikipedia, Pierre Louis Maupertuis - Wikipedia
My modus operandi for this year: begin from a study of quantum field theory to build a theological interpretation of the origin of the universe.
My first marihuana for three years. Does it work? Is it helping me to
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put my ideas into print? The silent treatment will not silence me because I am in my childhood dream, trying to find the realities behind the traditional theology reflected in our current knowledge of ourselves and our world. The political lesson is that heaven is an asymptote of human peace and security toward which we have shown what we can [move] by good management that respects our individual values by enabling us to create a space for an 'ideal life', the life enjoyed by the rich and powerful, or some other more complex and durable civil structure. The structural engineers of the world made mistakes and things fell down, but we can now manage things so that mistakes are detected and quality is controlled. It is now the turn of software engineers to go through the same discipline of conforming to reality. The problem is security and so far it seems that the hackers at all levels have been having a field day and many are devising malevolent uses for the ubiquity of social networks. A loudspeaker for everybody which requires us to renew our critical instincts separating truth from falsehood. I always return to the point that the most massive preacher of falsehood is the Roman Catholic Church but it is such a comprehensive network of falsehood that it provides an alternative intellectual ecosystem in which ideas are tested to see if they can survive.
I would not be surprised to learn that as many as half the workers in the science industry believe that in one way or another the universe was created by an omniscient and omnipotent being that is very much smarter than we are and whose mysterious ways are beyond our ken. The other approach is that the world itself is divine and created itself, the first act of a creative divinity.
Good to be working on physical problems again. The flood overtopped the pump killing the electric motor and washing all the oil out of the semi-open gearbox. On Tuesday I took the motor to town to a very helpful man who took
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it apart, cleaned it, dried it out, gave it a coat of paint and some new pieces of cable all for $90. A few minor difficulties with a lost screw and getting the bolt holes to line up in the motor base. Cleaned the gearbox, filled it with new oil, tightened the gland on the piston rod and turned it on, primed with about ten litres of water and it started to pump briefly and then stopped, losing its prime. I suspected that the footvalve was jammed open with debris and set up some ropes to get down the river bank and took a rope down to snare the footvalve and haul it ashore. But the problem was more amazing. The foot valve was in a tree about 4 metres above the present water level and it looked very hard to get it down since the suction line is 50 mm hard PVC and cannot bend sharply without kinking. In the end I decided to cut down the small tree that was holding the suction line up.
Sharpened the chainsaw (electric), ran a lead down the bank, scrambled down with the chainsaw, cut the tree and the suction line fell into the water, picked everything up, started the pump, primed it without twenty litres of waster I had carried down and it began to pump and that is another job done. If I decide to stay a bit longer I may replace the leather buckets on the piston which must be about 5 years old, 2500 hours of pumping.
Civil and mechanical and electronic engineers have enough knowledge of the physical systems they deal with to produce safe, reliable and economically sound physical structures ranging from highway networks to microchips. In the more complex worlds of love, politics, diplomacy outcomes cannot be specifically planned and much of the work is rather quantum mechanical,
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trying to arrange things to increase the probability of a favourable outcome for us where us may be the population of the world or a clandestine criminal network. Here we find the software engineers and lawyers who draft laws trying (and often failing) to devise laws which act as algorithms to ensure the desired outcome.
Measure theory: no matter how you chop up a set the sum of the pieces is always the same because the elements of a set are discrete identifiable individuals. Cantor theory: we can make ever larger numbers [more complex structures] by permuting the numbers we already have [recursively].
From metaphysics to mathematics and back: Whitehead and Russell. Whitehead & Russsell: Principia Mathematica (Cambridge Mathematical Library)
Should we rely for our salvation in impossible dreams? Certainly a dead end, like building bridges without being aware of the strength of concrete and steel.
Looking for an algorithm that can promise 1040 times speedup between gravitational and electromagnetic interaction. Gravitation does not need particles. It is a continuum theory based solely on the density of 4-momentum (energy -momentum) at various points in spacetime. The arrival of particles greatly increases the entropy of the universe (the outcome of the big bang) since they represent independent degrees of freedom which we take to mean turing computable transformations. We see a particle as a unit of embodied code whose execution requires one quantum of action.
All mathematics is discrete mathematics because it is written in discrete symbols which may nevertheless represent continua. This leads us to presume that the universe proceeds by discrete quanta of action. Action is the esse. The code within the action is the essentia [scholastic talk]. In the initial
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singularity esse and essentia are identical, as the medieval theologians said of god.
Saturday 3 April 2020
I have eschewed disciplined study since I left the order because I have been on the path of discovery, searching for a new theology to replace the obviously flawed and imaginative theologies of the past. Now I have come to a resting place I call quantum-theology which is in fact a critique of science from a theological point of view with the overall purpose of building a theology consistent with my assumption that the universe is god and created itself from the initial singularity to the present.
Zee's mattress: we are going to model the world of quantum amplitudes as a lot of coupled harmonic oscillators coupled by a set of continuous complex (periodic) fields. Particles are imagined as excitations of a field. There is a field corresponding to each [type of] particle and the art of quantum field theory is to describe the nature of these fields and their couplings, taking into account the velocity of light which imposes some limitations on interactions between what we can see, that is a network of interacting particles whose actual interactions are described by some theory, perhaps this one. The big problem is how to interface the discrete world of particles with the continuous one of fields [Dirac's delta plays a role here]. Dirac delta function - Wikipedia
Mathematicians faced the problem in the nineteenth century - how to build continua from mathematical points and how to name the points with numbers which will serve as a reference frame to keep tabs on them. The result is the real numbers which also serve to construct the complex numbers as components of points
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or vectors in the complex plane. Periodic complex functions, built from e-iω are the backbone of physics and we must consider carefully why they play such a large part in our description of the universe. The real and complex numbers are nevertheless fictions, and may not in fact serve as good models for the universe because the universe as we see it is quantized and appears to us in the discrete quanta of action and energy that we see about us at all scales from fundamental to galactic and universal.
My problem is to find a digital description of the world that accounts for all phenomena, in other words to make particles rather than fields primary and describe interactions between particles facilitated by networks of communication and computation which are very closely related at the level of encoding and decoding. From the quantum mechanical point of view this communication is carried by phase and in particular by the rate of change of phase which we call frequency or energy E = hf, mediated by the mysterious constant h which provides an invariant measure of events in the universe. The quantization of the world is our starting point because it provides a firm logical foundation upon which to build a picture of the world based on real logical continuity rather than the slightly fictitious continuity revealed when we apply the law of large numbers to huge numbers of events.
The path here is opened by the Nyquist-Shannon theorem which shows that any continuous function can be represented exactly (in the limit) by a sufficiently long string of binary digits. Almost all signal processing is done in the digital domain using the fourier transform to translate from continuous periodic functions to a weighed spectrum of discrete 'points'. We should not therefore be surprised to find that the deterministic processes of the universe that yield exact values also operate in the digital domain. Nyquist-Shannon sampling theorem - Wikipedia
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CSIRO WiFi algorithm Colin Ward: CSIRO: Wireless LANs
