Notes
Sunday 5 March 2023 - Saturday 11 March
[Notebook: DB 88 Salvation]
[page 320]
Sunday 5 March 2023
Quantum symmetry, as noted by Von Neumann, demands that quantum sources be normalized in the same way as communication sources, and this established the identity of the Schrödinger and the Heisenberg formulations of the theory, Schrödinger's in continuous mathematics, Heisenberg in discrete matrix mechanics. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics Chapter 1.2: The original formulations of quantum mechanics
The answer to despair is hope. Von Neumann established the hope that a consistent theory of quantum mechanics could be developed without the need for Dirac's delta by showing that Schrödinger's observation, [which unites the two formulations], that the fundamental requirement on quantum mechanics is that the observables obey the statistics of a communication source. What is the equivlent insight that I need to unite physics and theology? The insight that makes my story plausible, I feel, arises from Cantor's observation that all the steps in the generation of the transfinite numbers are a 'unitary' operation (not in the quantum mechanical sense) and that this operation underlies the principle of symmetry with respect to complexity which takes us all the way from the initial singularity toward the final state of the universe when its entropy, like the transfinite numbers, approaches a maximum Principle 15: Symmetry with respect to complexity. Perhaps this is the story I want to tell in cc20_memory, which has been holding me up since 18 February (notes page 291). Tomorrow we get it right (I say for the nth time). Now back to an evening with The Constant Gardener whose personality I like to compare to my own as I witnessed when my favourite woman was killed in a road accident, and again when my family called me a pedophile.
[page 322]
Le Carre page 244: ' "Sandy mistook my flirtations for a promise, exactly as he mistook your good manners for weakness." John Le Carre (2005): The Constant Gardener: A Novel
page 366; Montesquieu: ' "there have never been so many civil wars as in the kingdom of Christ".' Why? Because there is no data. Like all theologies to date it is make believe and the faithful must be made to believe or otherwise be killed.
We build up the world as we build up mathematics using (may be) set theory and Cantor because it is so simple and animating it with computation all built on a foundation of Hilbert space [motivatd by divine action].
Augustine and Aquinas had already tacitly used the symmetry with respect to complexity when they compared the structure of the Trinity in the omnino simplex divinity with human intelligence and love in our incredibly complex physical bodies. Aquinas, Summa, I, 3, 7: Is God altogether simple?
Driving along in the usual traffic of trucks and tradies and thinking about the heuristic of simplicity and wondering whether the foundations of the world were any more complex than this, and how to apply the idea of symmetry with respect to complexity and contemplating a new beginning for CC20_memory in terms of laws and symmetry a la Noether and Feynman, but in
[page 323]
some replacing mathematical continuity [in a topological space] with layered logical continuity as part of a bridge leading from transfinite Minkowski space via fixed points and memory to quantum field theory, expanded by symmetry wth respect to complexity to carry me from the fermionic nature of traffic (avoid collision) implemented by bosons (watch where you are going snd everyone around you). Emmy Noether - Wikipedia, Richard Feynman: Lectures on Physics III:17 Symmetry and Conservation Laws
Le Carre's books about spying and deception are a good example of a human situation more complex than traffic when all the participants are using various forms of body language to ascertain what the others are doing or going to do in a mix of cooperative and adversarial situations which might very well be described by path integrals and Feynman diagrams, the dance of the fundamentals orchestrated by the almost absent constraints of operators in Hilbert space.
Monday 6 March 2023
At some time in my violent youth I dreamt of having a nuclear weapon to blow up the Church and all its partners in human oppression. Not a real weapon, of course, but a version of the weapon that the Church has used to control the world, propaganda, but not false propaganda but true scientific propaganda, the true biography of God.Now I am getting close[page 313]
to it and I have assembled enough bits and pieces to make a story that I am happy with. Slowly, I want to ooze it into the public consciousness, not as a best seller but as a scientific attitude to theology based on reality, cognitive cogmogenesis is an obscure alliterative alternative to Jack Miles' book. Yahweh died in the hands of the writers of Job. Jesus died in the hands of Constantine, joining the imperial forces that have slowly destroyed the world in their search for money and power. Jack Miles (1996): God: A Biography, Constantine the Great and Christianity - Wikipedia, In hoc signo vinces - Wikipedia
I am, in a way, at a low point in my life, but my hopes are high and growing because awareness of the destructive effects of theological corruption and corporate greed is spreading precisely because the propagators of evil, Putin, Trump, Xi and their ilk, think they are in control and are exposing themselves to ridicule. The ground seems to be becoming fertile for the scientific revolution to embrace theology and step from supporting the warlords to supporting humanity and Earth.
Can we map symmetry with respect to complexity onto the Hilbert oscillator, so bringing cc20_memory into line with the essay on the divinity of money? From this point of view, the Hilbert oscillator is a kinetic implementation of the symmetry. Am I game to believe this? Jeffrey Nicholls (1992): An essay on the divinity of money
[page 325]
It seems to me that the essay on the divinity of money was a moment of inspiration which occurred to me about the same time as the essay on value which led to Nicholls v NPWS, although the essay was not mentioned. Memory, the simple symmetries of life like the quantum of action ≡ unit of currency, energy ≡ rate of work = rate of expenditure of currency last the longest. Later we find genetic code, citric acid cycle, chemical signalling, synapses and neurons and so on up to the human symmetry which is the foundation of economics, ethics and politics. Land and Environment Court of NSW (1994); Biodiversity cases
The structure of the Universe is also a structure for knowing the Unverse which makes sense if we work from the bottom up, from simple to complex, wheres it is almost unintelligible if we take the finished complex product head on as traditional theology does and finds itself preaching that things may look bad but the all seeing God has a plan and everything is for the good and what is not is the wages of sin, our own fault which we have to grin and bear in faith, hope and charity until we reap our eternal reward in heaven in the sight of god.
Le Carre page 472: ' "You want to turn to God, you gotta be a sinner first . . . everybody in this place is a convert to God's pity, man, believe me".'
[page 326]
My dream is to put all this together and make it work, ie produce a consistent story that fits the facts. "To look at a thing is quite different from seeing a thing. One does not see anything until one sees its beauty." An Ideal Husband (1999 film) - Wikipedia
To love oneself is the beginning of a lifelong romance (ibid)
So I still have to see where the Hilbert Oscillator fits in. Quantum mechanics is kinematic, complex not real, whereas the Hilbert oscillator is real. Some how the null geodesic makes quantum mechanics real vis the mechanism of operators with real diagonals, is Hermitian. Does this make sense of is it a meaningless form of words. Quantum mechanics runs on complex time with no space which is why zero sum bifurcation works when quantum kinematics becomes Minkowski dynamics, is kinematic ≡ periodic ≡ complex. Dynamic ≡ force ≡ real. Hermitian adjoint - Wikipedia
Tuesday 7 March 2023
To say that Hilbert space is independent of Minkowski space is to say that it can go to places where Minkowski space cannot go. This is a consequence of the fact that Minkowski space is the space of observation and we can only observe fixed points, so all we observe in Minkowski space are
[page 327]
the fixed points of dynamic processes in Hilbert space [particles?]. This suggests that the quantization we observe in Minkowski space is in some way not indigenous to Hilbert space but is nonetheless diagnostic of fixed points in the motion of Hilbert space which are represented by real eigenvalues associated with fixed eigenvectors which are fixed points of the Hilbert motions. Does this help us? The quantum of action is a real measurable quantity. Once again we are in the zone of measurement [communication] and Minkowski space and, since our derivation of the Hilbert Oscillator is related to communication theory and the quantization involved there we can see that the clue is that the velocity of light and null geodesics are in some way involved in stopping time to create space, ie the action in Hilbert space is bifurcated into space-time, energy-momentum ie it is intrinsically action, that is energy × time, momentum × space.
The velocity of light, like the velocity of a runner, is the product of the length of their stride by the frequency of the strides.
The primitive variabe t which we use in the Schrödinger equation to represent the unitary [mapping of Hilbert space onto iteslf] we might call action, and we see that it is quantized as the uncertainty principle when it appears in Minkowski space, a fact that we represent by the equations ΔE.Δt ≈ Δp.Δx ≈ h where t measures time, x measures
[page 328]
space and in Minkowlski space x2 + t2 = 0, the definition of a null geodesic and an example of zero sum bifurcation. This, I think is all so simple that it is hard to understand, but perseverance will prevail. The quantum of action is the fundamental fixed point in the Universe, but the fixed point of what set? This is clearly related to logic [and knowledge and communication] so let us guess that it is a fixed point in the dynamics of the Hilbert oscillator and the primary physical realization of the bit of information, the measure of the quantum of action as the not operator.
Al-Khali page 103: The history of 0 (zero) gives a good idea about how long it takes a quite basic idea (like maybe the wheel) to take root and become common. There may be a whiff of this history in the relationship between Hilbert and Minkowski space which is still blocking me from something I do not know but want. Jim Al-Khalili (2010): Pathfinders: The Golden Age of Arabic Science
The algorithm is the fixed point in dynamics is the quantum of action is the primary algorithm in the universe, analogous to the nand operator in classical computation and it is represented by a Hermitian operator (?). Self-adjoint operator - Wikipedia
Wednesday 8 March 2023
An algorithm is a fixed point in a process expressed by physicists as an equation and by
[page 329]
software engineers as a program to be stored in memory. It is the memory which makes a computation what it is, its essence. What about its existence? What is the memory that holds it. We say that in God essence and existence are identical? Why? As Aquinas puts it, they are confined by the simplicity of God, what we might call logical confinement. God is so simple its essence cannot be different from its existence. This is the property of a formal Turing machine, defined by a memory encoded in the initial part of the tape of a universal Turing machine that we might equate with God. The quantum initial singularity we identify with the traditional god, and like the traditional god of the Trinity, we give it the power to reproduce itself generating more gods at random which are distinguished by their relationships of origin as children of the initial God. In the quantum world we attribute these differences to the no cloning theorem, and we attribute the kinematics of god to this power of God which increases the number of Gods, that is the entropy of the divine universe (see Cognitive Cosmology, page 9: The active creation of Hilbert space)
A photon carries a quantum of action from its point of creation, which we take to be a god, to its point of annihilation, which we take to be another God, a model of the Trinity, two divine sources and a messenger between them. If divine essence and existence are logically confined
[page 330]
to be identical we must say divine dynamics is identical to divine kinematics. The technical problem in the development of practical computers was to devise a dynamic system which would reproduce the kinematics of the Turing machne. As we have discussed, this was achieved with the clock which turns a dynamic process off and on to isolate the kinematics from the dynamics. (see page 19: Fixed points, laws and symmetries). The clock is an oscillator and the intuitive key to the universe as a computer which occurred to me in 1992 was the "Hilbert Oscillator". I have ploughed ahead since them, perhaps with this machine in the back of my mind, and now I have come a full circle trying to understand how to fit the Hilbert oscillator into the picture I have developed so far in cognitive cosmology. I have all the pieces of the jigsaw before me, but I am now three weeks into trying to fit them together and still waking in despair but still full of hope that today will be the day, building on Einstein's description of his search for general relativity which I modelled as a Carnot cycle built on Hilbert's questions:
[The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding are known only to him who has himself experienced them. Pais page 257]
Now I hope to recapture that moment. But first check the finances. Bad. But intuition feels good. Abraham Pais (1982): 'Subtle is the Lord...': The Science and Life of Albert Einstein
Danielle Lee Tomson on political vibes. When my vibe is right I stop work and just sit and enjoy. Post orgasmic high. Danielle Lee Tomson: Opinion | The Vibes Are Off With the Republican Party
[page 331]
Maybe the Hilbert oscillator is the vibe necessary to get my show on the road, but it is proving a bit difficult to understand wha it means in the cognitive cosmology scenario even though its emphasis on knowledge an creation is central to the story. One step in a good direction would be to link it to Lonergan's Insight, pointing out that insight is not merely a matter of knowledge but a matter of implementing creative evolution by selection out of a plethora of possibilities. Bernard Lonergan (1992): Insight: A Study of Human Understanding
Vibes: transcendent appeal: ens, res, aliquid, unum, verum. bonum. Transcendentals - Wikipedia
Have I lost my faith, or am I just having a rest, looking for more depth? In my old age I feel that I may get better results by cruising rather than striving, conserving resources and not getting too pissed off with my lack of progress.
The memories in Minkowski space serve to control processes in Hilbert space as, for instance, we design transistors [and experiments, eg Wu]. More broadly, natural selection requires memory and is a feature of Minkowski space which we have outlined on page 18: Transfinite Minkowski space. So the point of cc20_memory is that dynamics controls [kinetic] formalism becasue it rewuires quantization to achieve eror free communication and therefore computation and control — all three are the practical aspect of Minkowski: memory, communication [via null geodesics], computation, control, stationarity [enabling observation, see page 25: Principle 9: We can only observe fixed (stable) states,
[page 332]
observability, particles, states, entropy. We atrribute a lot yo Hilbert space which is not because we map it onto Minkowski space where all fixed points and memories reside die to the conversion of pure kinetic action into controlled quanta of action. So we leave gravitation as the home of [divine] potential which is shaped by [classical] dynamics and so we say that gravitation is in fact the unfettered, uncoded, unscripted pure action of god. We see the quantum of action created by the quantum mechanical creation of Minkowski space, a fixed point in the divinity [page 12: The quantum creation of Minkowski space. Wu Experiment - Wikipedia
The demand for Hermitian operators is imposed upon Hilbert space by Minkowski space since the observables (which are particles) exist in Minkowski space. [von Neumann's axiomatic abstract] Hilbert space itself places no constraints on its operators [ie mappings of Hilbert space onto itself] since every complex polynomial has solutions in the complex domain, ie not all solutions are observable, only real quantities are observable. Another word salad, but a good one I feel [once I understand it]. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
Thursday 9 March 2023
A justification for the existence of page 20 Space_time: Cosmic memory and operating system is beginning to emerge and provide a bit of clarity for cc18_Tranfinite Minkowski space, which in turn may explain the need for the Hilbert oscillatorwhich describes dynamic transitions
[page 333]
up and down the layers of the transfinite computer network that we are proposing as a model for the divine universe, and brings us closer to the Turing vacuum to be proposed in cc23_quantum field theory. This step may justify the three week delay it has taken to see what I can do with page 20.
Lunch with Auntie and a good insight on the way out realizing the full variety of Hilbert space unconstrained by the Schrödinger equation, that eigenvalues, normalization, snd unitary operators, all of which features, it seems, are imposed by the theory of communication and computation in Minkowski space. Afternoon rest time now and then think about it some more, but it certainly provides a role for spacetime in the constraints on [abstract] Hilbert space which is, like Cartesian space, limited only by [von Neumann's] axioms.
Fixed point theorems define fixed points in continuous, convex compact sets. On the contrary, fixed algorithms define sets, such as the set of all symbols which obey the axioms of Hilbert space.
Friday 10 March 2023
Rovelli, Helgoland Carlo Rovelli (2021)
cc20_memory has become something of a pons asinorum for me. I am not clear about what I am trying
[page 334]
to say except perhaps that Hilbert space like music, has no memory and no stationary points except the axioms of abstract Hilbert space (and all the history of mathematics implicit in them) and that memory is necessary in order to hold the immense structure of the universe as encoded in particles in Minkowski space, which is itself a quantum mechanical construct. These particles each carry with them operators on Hilbert space which encode their interactions with one another. This idea is implicit in pages 16, 17, 18 19, and the real question is have I anything to add in page 20? If the answer is no, I should leave it out and edit 16-19 to make sure that they make their points clearly. At the moment my mind is quite fuzzy, no Cartesian clear and distinct (ie quantized) ideas to work on. One idea may be that quanta do not exist so much in Hilbert space as Minkowski space where the real theory of communication exists in spacetime, whereas, since Hilbert space exists prior to space-time, communication is by contact and the transmission of messages through space and time does not become meaningful until the Minkowski metric and null geodesics appear [this is consistent with the idea that gravitation, the symmetrical image of the particular universe, is not quantized]. In a way I am failing to logically implement my postulate that Hilbert space is independent of Minkowski space, ie it is the space of God and the angels, a lot of material long since erased from cc20_memory.
[page 335]
Perhaps I should think of my mind (and minds in general) as a dynamic system going through various historical phases marked by different line of communication, centres of activity and accumulations of wealth that behave overall like the politics of a nation going from autocratic stasis to democratic creativity and I am currently in a period of creative drought which will hopefully end soon so that I can get cognitive cosmology back in my grip and perhaps compress it into a clearer and more distinct form as cognitive cosmogenesis, the political history of the mind of the universe, the [new] biography of God. Jack Miles (1996): God: A Biography
Rovelli page 33: XP - PX = iℏ von Neumann page 8.
Saturday 11 March 2023
Superposition requires degree of freedom which are not [readily] available in Minkowski space. We cannot superpose motor vehicles, they exhibit fermionic behaviour but we can superpose multiparticulate fluids like air and water so in these media, like vibrating strings and surfaces, we can observe superposition visually or aurally to gain insight into the quantum realm which acts like a continuum as water or air do because their scale of quantization is imperceptibly small. Ie we can superpose fluids but not solids because fluids have more degrees of freedom, as Hilbert does relative to Minkowski.
[page 336]
Active Intellect re Plato: 'since a thing is actually intelligible from the very fact that it is immaterial.'. What could be a modern interpretation of this ancient and rather simplistic axiom which is used to attribute omniscience to an absolutely simple God? 'We must therefore assign on the part of the intellect some power to make things actually intelligible by abstraction of the species from material conditions. And such is the necessity for an active intellect.' Ie the agent that creates insight. What is that in our model of creative evolution?Is it the variation and selection that creates species. An extractor of fixed points, a solution to the eigenvalue problem? Aquinas, Summa I. 79, 3: Is there an active intellect?
Let the Hilbert space, the heart of the divinity, associated with each particle or source (eg electron, me) be its active intellect which constitutes its intellectual integrity, its orbit or neural circuit (Eccles). Hilbert music. John C. Eccles (1958): Innovation in Science: The Physiology of Imagination
I have two views of my mind. One is neurophysiological, the complex picture of neurons, axons, synapses etc which serves as the dynamic representation of my mental processes rather like a physical computer realizes the dynamic version of a formal computation [with the intervals of change excised by a clock]; and the interior introspective view I have of my conscious mind as I compose these lines and am aware of all the information coming in through
[page 337]
my senses as I sit here writing and thinking. As ever I am trying to apply symmetry with repect to complexity to compress this picture down to the realm of fundamental particles and expand it to the size of the Universe. What I am feeling is that the most general version of my conscious experience is like music which is ideally suited to representation in Hilbert space, and the outside physical view exists in Minkowski space where the functional units, cells, synapses, atoms etc control the interior space to give me that conscious picture which I experience while working, and which has just dragged me out of bed to write this little essay. Now back to bed and hope that no more ideas will keep me awake. We'll see.
My local sensory picture of the world is in effect an item of local consciousness of the world. My knowing the world, given that I am part of the world, is in effect the world knowing itself, just as my local contact action on my little bit of the world is analogous to the contact actions in the spaceless and timeless Hilbert world which operates the observable world. This is a two way flow of information between the Minkowski and Hilbert spaces.
