Notes
Sunday 21 May 2023 - Saturday 27 May 2023
[Notebook: DB 89: Cognitive Cosmogenesis]
[page 54]
Sunday 21 May 2023
High energy physics and deep inelastic scattering. Deep inelastic scattering - Wikipedia
The zero energy bifurcation of action in Minkowski space gives us the relations ΔE.Δt ≈ ΔE.Δt ≈ h which is an implicit representation of the quantum of action in Minkowski space represented as energy × time, or momentum × distance.
This morning I see lights at the end of my tunnel and I still hope to make 2023 a good year. I am hoping to eventually write as good story in a theological vein that I can stand by.
Murphy, Washington Post, Amis: ' "This is literature's dewey little secret," Amis wrote. "Its energy is the energy of love." ' Brian Murphy: Martin Amis, British writer who cast caustic eye on society, dies at 73
In Hilbert space there is no distinction between hardware and software as we find in Minkowski space where the software is formal and kinematic and the hardware is physical and dynamic and the clock serves to time division multiplex their roles. The divine initial singularity plays the physical role, creating and driving the kinematic Hilbert space, in effect writing and exciting the software and manifesting as gravitation, using its potential to create the dynamic energy that makes the kinematic world real when it fulfills the selective criterion of end to end consistency.
Gravitation is unmoved, represented by the Einstein equation, as inertial space is unmoved, represented by the Lorentz equation, the Minkowski metric.
My dear chidren, the viciousness with which you have attacked me is a measure of your own insecurity, rather like Putin's genocidal invasion of Ukraine. I am renting a room in a household of high tension caused by the persistent violence of a son against his mother who has turned to alcohol and is collapsing under the stress. Fortunately I have been strengthened by my 60 year struggle to eliminate the imperialist streak from theology and physics so I am thriving on your attack against me and subtly thanking you for providing a concrete realization of the problems I face: a church with a history of war and torture against those who would draw attention to the false mythical foundations upon which it is built.
The zero-energy universe seems to make sense on the cosmic scale where the average density of the universe is a hydrogen atom or so per cubic metre. What about locally? We are suggesting that the mass of an electron. m = E / c2 is balanced locally by the gravitational potential, which does not seem possible. The equivalent gravitational potential ocupies something of the order of a litre. So we can imagine an early time when the graitational potential and matter are much denser than now. So how do we deal with this idea now? Maybe only about 1 part in 1040 of the energy in a local event is represented by local
[page 56]
potential and the rest is simply transformed from one particle to the next. Gravitation is so weak that it can change very little of the quantum mechanical structure embodied in the average pendulum.
Gravitation is relatively delocalized to the wavelenth of gravitational waves, MTW page 955: 'the stress-energy carried by gravitational waves cannot be localized inside a wavelength . . . . However one can< say that a certain amount of stress-energy can be contained in a given "macroscopic" region (region of several wavelengths' size) and one can thus talk about a tensor for an effective smeared out stress-energy of gravitational waves T(W)μν'. Misner, Thorne & Wheeler (1973): Gravitation
Monday 22 May 2023
Can my story be saved? Is the zero energy universe a red herring? Where do I go from here? The eternal initial singularity, like the traditional god, is a necessary beginning. In the last six months the Trinity has metamorphosed into a countably infinite Hilbert space with the evolutionary power of variation and selection by the quantum mechanical eigenvalue equation. Seems to work quite well. Now we are working on the origin of Minkowski space, gravitation, the transition from kinematic to dynamic, the role of gravitation as the divine potential that makes matter possible in a zero energy universe, and a new question: why is gravitation so weak? Or why is elecromagnetism so strong?
[page 57]
The clue seems to lie in the relationship between the gravitional continuum and the quantum mechanical logic, a slippery belt versus deterministic logical gears. How do we get this into the story? Logic, computation, quantization, applications of Gödel, Chaitin, cybernetics and information theory, all of which need to be lined up and made coherent by exploiting the method, rather than the content, of mathematics to explain the world using the genetic content of the theory of evolution as expressed in Hilbert space and translated from music in Hilbert space to code in the universal network. Today try to sort out gravitation and zero energy as the feedback loop that stabilizes spacetime and matter. Gregory J. Chaitin (1982): Gödel's Theorem and Information
I am looking for two things: something approximating the truth, and a good marketable story, so I am not allowing myself to mix in too much fiction, which means in practice trying to stay closer to the truth that my chosen opposition, the Roman Cathilic Church and its descendants, as described in Hopkins 2001. Keith Hopkins (2001): A World Full of Gods: The Strange Triumph of Christianity
Tuesday 23 May 2023
Take your time and hurry up. My enthusiasm for this project is maintained by little steps forward [just like walking]. Now I am up to cc19_fixed points in my revision of cognitive cosmology and wondering again what is the point of this page. There are two points: The first we owe to
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Parmenides: If we are to have permanently true knowledge (and a permanent world) we need a fixed core which he learnt about from a goddess and passed on to Plato. The second is that fixed point theorems tell us that fixed points are derived from fixed points by logical processes which are also fixed points, as Turing showed. In Brouwer's case the primary fixed point is a continuous, convex compact set. From a theological and physical point of view, provided that we accept that nothing comes from nothing, there must be an eternal fixed point, an entity with no beginning, at the foundation of the Universe, and we can then assume that all subsequent fixed points are derivatives of this primordial fixed point. John Palmer - Parmenides (Stanford Encyclopedia of Philosophy), Brouwer fixed point theorem - Wikipedia
When I finally get something preachable I can finally begin to talk. Writing is formal without the presence of the author. I used to give talks in my early days, lecturing my brethren in the monastery, trying to add modern understanding of mind and sight to the vague utterances of Aristotle. But when the Order rejected me I lost my voice and I have yet to get it back. The reason, it seems to me, is that my story is too complex and undercooked to explain in spoken words. The beauty of writing is that I have before me a panorama of every thought that has ever crossed my mind over the sixty years since I entered the order and it still has not settled down to a coherent story. I am revising cognitive cosmology now. I did cc17_gravitation and cc18_networks
[page 59]
yesterday and cc19-fixed-points today and now I am getting to the hard bits.
From the religious point of view the basic ethical and moral tone of my work is not to be built around sin and guilt and the inefficacy of divine mystery but [on] the reality of the evolutionary process that brought us to be, softened by the fact that our bodies of trillions of cells with a well developed immune system and a life many times longer than the lives of the cells of which it is composed. This provides us with a model for [a] peaceful and durable community based on rhe physiology of multicellular species. Here we see that cognitive cosmogenesis should embrace lust-4-life as well as cognitive cosmology, rendering the kinetic theory of cognitive cosmology dynamic in cognitive cosmogenesis, so in the end it is a work of politics driven by a theological view of the world. At the root of the politics is a physiological economy protected against intruders and freeloaders by an effective immune system. Jeffrey Nicholls (2019d): Political dynamics: Rousseau, Rawls and the Physiology of Contract
Wednesday 24 May 2023
Lust-4-life brings cognitive cosmology into the religious and political domain, but I do not like the domain name I have chosen for this. [I] would prefer to fold this work into cognitive cosmogenesis framing peace as a dynamics process of development implicit in the evolutionary trend
[page 60]
toward complexity which envisages the human species becoming a single organism based on a common theology as the cells of my body have become a single organism based on their common DNA. How do we combine cognitive cosmology with this idea in mind? What role does quantum chromodynamics and the stability of the proton have to play in the hinge between cognitive cosmology and cognitive cosmogenesis?
Thursday 25 May 2023
There are many variants of human DNA which nevertheless inform people who are identically human and we can see the same setup applying to human theology which nevertheless informs stable religious and political organisms comprising human beings. Here we are looking for the human symmetry which can be applied to the formation of human communities. We get our clues from the space-time structure of the tree of life which is ultimately rooted in god, the initial singularity.
cc21_transfinity.What is the relatonship between the transfinite and the infinite? What is this page about? First we have to talk about the relationship of transfinity to infinity: read Daubin. And then we are interested in the way that the transition to Minkowsli space increases entropy driven by the hypothesis that actual quanta of action are preserved / conserved forever
[page 61]
and the increasing entropy of the universe is simply a count of the number of quanta of action actually in existence at any moment. This we take to be the driving force of creation, driven by the process of observation by the selection of fixed points by quantum mechanics in Hilbert space, which become attached to the real particles created by observation and communication and determines the behaviour of these particles when they come into contact with one another and bond to create complex structures. I feel something good coming on. Will it 'materialize', ie become observable, tactile, performable? Now that the household has calmed down I am able to take my time again. Joseph Warren Dauben (1990): Georg Cantor: His Mathematics and Philosophy of the Infinite
Friday 26 May 2023
Dauben Cantor page 40: axiom: 'to every number there corresponds a point of the line whose coordinate is equal to that number.'
' [Cantor] was at last in a position to introduce one of his most innovative concepts: derived sets of the first species.'
page 41: For Cantor "point" means primarily the numerical value of the point. He is working from arithmetic / algebra to geometry, 19th century analysis, Bolzano-Weierstrass theorem. Set has set of limit points 'first derived set of P', P is set of rationals, P' is set of reals → ν th derived set P(ν) of P.
P(ν) comprises only a finite number of points fom which we can work back to via P(ν - i) to original rational set. He has given it a structure [of discrete levels of infinity].
[page 62]
Dauben page 47: 'What soon brought transfinite set theory to life was Cantor's discovery that the set of all real numbers was non-denumerable.'
1872-1879 Cantor established the existence of different magnitudes of infinity and that space of arbitrary dimension could be mapped into a one dimensional line of real numbers.
My feeling is that Cantor and the transfinite numbers interpreted as the structure of the real line is a bit mistaken and what we should be looking at more closely is the relationship between the transfinite numbers and multidimensional ordered structures like myself. Even though I am made of elements which are in fact integers, ie quanta of action, the multidimensional ordering of these integers, like the position sensitive ordering of digits in decimal numbers, opens up a transfinite domain of entropy which can serve, through the hierarchy of layers of the computer network, to represent a transfinite structure like myself, the planet or the universe. The articulation of this idea is the task of cc21_transfinity [recogising that the physical number of quanta of action in the universe are always countable, and the "transfinity" comes (as in Cantor's later proofs) from the ordering established by the layered computational network which is driven at (the physical level) by quanta of action. From an information theoretical point of view, the entropy of a quantum of action (symbol) is a function of the distribution of its peers emitted by the particular source from which they come. Maybe we can identify quanta of action with the execution of Turing machines interpreted as complex (but singular) actions].
The mapping of complex multidimensional spaces onto a one dimensional time line, my life, is a logical hierarchical network process. Reread cc21 and see if it captured this at the beginning of [this] year.
[page 63]
Daubin page 49: 'What was the nature of the continuum? The search for an answer to this question was to haunt Cantor for the rest of his life.' And it seems the answer escaped him. The continuum represented by the transfinite numbers [may be] in fact a logical nework, each layer in the nework representing another layer of complexity, as in myself.
page 50: 'The rationals were dense but not continuous.' Both rational and algebraic (and computable) numbers are countable. But Liouville had established the existence of non-algebraic numbers, the transcendentals. Answer: 'It was impossible to establish a one-to-one correspndence beween the natural numbers N and the real numbers R'. Transcendental number - Wikipedia
page 51: Proof by conradiction corroborated Liouville. if the real numbers are countable, they must correspond to a sequence of natural numbers. He then set out to find one real number not in the interval enumerated by this sequence.
psge 54: One-to-one correspondence is the key to counting infinite collections. Then to lines and planes, planes to cubes . . . ..
page 55: Because the cardinal of a subset of an infinite set is equal to the cardinal of the set, we can break a real interval into any number of sub-intervals that represent new dimensions. Cantor: ' "I see it but I do not believe it". ' A mathematical ideal / dream.
[page 64]
The hardware does not know what the software is doing. It simply steps along [footsoldier] reading instructions and data and writing out the answers. In this sense it is very like kinematic natural numbers, stepping along like a clock. Each tick tock is a quantum of action, and the structure is contained in the memory of the network which serves as a store of instructions, input and output. The meaning of each operation lies in its context, anything from ["do nothing"], "add 1" to "go to nuclear war".
Saturday 27 May 2023
It is interesting to see that Cantor's interest in transfinite numbers grew out of a study of Fourier representation of functions / alorithms.
[back to the beginning of Dauben]
Duben page 6: 'Functional analysis, in fact, spurred Cantor's interest in point sets and inspired his discovery of the transfinite numbers.' Cantor used the Euclidean definition of point, something that had position (named by a real number) but no magnitude [so an infinite row of them gets nowhere, ie all correspond to the same number!]. My idea is to bring this point to life by identifying it as an operator, a quantum of action which we identify as a logical operator [having intrinsically nothing to do with space-time] an active rather than a passive point. My feeling is that these quanta of action are permanent fixtures of the universe which account for its increasing entropy and so act as both memory for the construction of the transfinite (not infinite [not finite (?)]) computer network. Fourier series - Wikipedia
Dirilichet on convergence of Fourier series:
[page 65]
Dauben page 6: 'Fourier had established that arbitrary functions could be represented by trigonometic series with coefficients of a specific type.'
page 7: Cauchy 1823 on convergence problems.
page 120: 'The essential element of proof invoked Dirilichet's introduction of what would today be termed accumulation points and sets of zero measure.
page 11: Singular points have zero measure.
Function: any correspondence between given domains. Dirilichet needed little bits of continuity.
Riemann 1826-1886:
page 12: Riemann wanted to go beyond physics and into pure analysis. Dirilichet dealt with necessary conitions, Riemann was looking for sufficient.
Riemann wanted to sharpen the definion integral - He wanted to introduce many or all discontinuous functions to Fourier analysis.
' What could be said for functions that have infinitely many discontinuities between two limits, however close they might be?'
page 5: Auxiliary function is continuous and convergent.
page 17: '. . . one of the major stimuli to refinements in analysis during the nineteenth century were discontinuous functions, and Riemann was the first to give them any sort of systematic treatment.'
'page 19: Cantor: Uniqueness of Fourier reprsentations. Lipschitz:
page 28: 'Cantor was among the first to realize that there were differences in
[page 66]
magnitude that had to be identified among infinite sets and this discovery proved to be a turning point in his study of infinite sets as a subject wholly independent from the theory of functions. . . . .. Cantor was able to modify old ideas and to forge new ones in order to establish the uniqueness of functional representations by means of trigonometric series.'
The ideas here will hopefully enable us to interpret the trigonometric series implicit in Hilbert space in terms of the algorithms driving the construction of the Turing Universe. From the point of view of reality all of Cantor's work, insofar as it deals with point sets, is a mathematical ideal, a constructed delusion but as suggested above, it can be given real meaning if we read 'quantum of action' for 'point'.
Dauben page 30: - are trigonometric representations unique? Heine problem; Heine Theorem: 'A function f(x), continuous in general but not necessarily finite, can be represented only one way by a trignonometric series of the form f(x) = ½a0 + ∑ (an sin nx) + (bn cos nx) if the series is subject to the condition of being uniformly convergent in general. The series represents the function in general from −π to π
page 34: Cantor's uniquenes theorem: difference of two representations = 0.
page 37: '. . . Cantor set himself the task of developing a satisfactory theory of the irrationals which in no way presupposed their existence . . . How might he disentangle the various levels of singularities condensed one atop another. . . .. This in turn raised the dificulty of relating the arithmetic continuum of real numbers with the geometric continuum of points on a line.'
[page 67]
Dauben page 38: The infinite sequence a1, a2, . . . , a2 is said to be a fundamental sequence if there exists an integer N such that for any positive rational value of ε |an + m −an| < ε for any m for all n > N means that an has a limit b. First he called b a symbol.
page 39: Cantor regarded [the elements b of B] as meaningless in themselves: '. . . their objectivity was of a very different kind from that enjoyed by rational numbers.'
Question: is ε ultimately too small to be called rational, ie 1 / ∞. The generation of the transfinite numbers is done by cooking up smaller and smaller εs. See axiom on page 40 copied on page 61 above, Friday 26/5.
limits points = first derived set.
