Notes
Sunday 13 February 2022 - Saturday 19 February 2022
[Notebook: DB 87: Cognitive Cosmology]
[page 194]
Sunday 13 February 2022
Lust for life - the love of god π god is love, joie de vivre
Wilson: The remormalization group is a continuous group in contrast to the digital logical view that network layers are symmetric with respect to complexity because the operation of an algorithm is independent of how fast it is executed [but this is irrelevant here because we are dealing with spatial rather than temporal complexity?]. Kenneth G Wilson (1982): Nobel Lecture: The Renormalisation Group and Critical Phenomena
Wilson page 102: 'II There are a number of problems in science which have a common characteristic, that complex microscopic behaviour underlies macroscopic effects.'
'Unfortunately there is a much more difficult class of problems where fluctuation persist out to macroscopic wavelengths and fluctuations on all intermediate wavelengths are important too.'
'In quantum field theory, "elementary" particles like electrons, photons, protons and neutrons turn out to have composite internal structure on all size scales down to 0. At least this is the prediction of quantum field theory.
page 103: 'At the critical point a pressure of 218 atmospheres and temperature of 374 Celsius the distinction between water and steam disappears and the whole boiling phenomenon vanishes. . . . At the critical point one finds bubbles of steam and drops of water intermixed at all size scales from macroscopic visible sizes down to atomic scales,' . . . "critical opalescence". Critical opalescence - Wikipedia
'Theorists have trouble wth these phenomena because they have many coupled degrees of freedom. . . . Some extremely clever transformations have enabled special cases of these problems to be solved analytically. . . . many problems of critical phenomena and virtually all examples of strongly coupled quantum fields have defeated analytic techniques until now.'
[page 195]
Wilson page 104: 'The "renormalization group" approach is a strategy for dealing with problems on many length scales. The strategy is to tackle the phenomenon in steps, one step for each length scale.
Monday 14 February 2022
Wilson page 104: Ising modelpage 106: Is 'loss of analycity' a problem for a computational model which is digital from the beginning?
In a world of greater than 4 dimensions the Landau picture is correct. . . . below 4 dimensions, fluctuations at all scales up to the correlation length are important and the Landau theory breaks down.' This assumes Minkowski space is continuous?
Fluctuations correspond to different branches in the network?
page 111: 'The remormalization group approach, . . . As the fluctuations at each length scale are integrated out a new free energy functional FL + δL is generated from the previous functional FL. This process is repeated many times. If FL and FL + δL are expressed in dimensionless form then one finds that the transformation leading from FL to FL + δL is repeated in identical form many times (the transformation group thus generated is called the "renormalization group"). As L becomes large the free energy FL approaches a fixed point of the transformation and thus becomes independent of details of the system at the atomic level.'
page 113: 'Unfortunately it was found in the 1930s that the higher order correlation in the series for e and m are all infinite due to integrations over momentum that diverge in the large momentum (or small distance) limit [maybe an artefact of the fact that the relevant distance is not the distance in Minkowski space but the "distance" in Hilbert space where the action is].
page 113: '(. . . the natural scale of QED is the Compton wavelength
[page 196]
of the electron, 10-11 [or zero if we accept the idea (page 113) that the energy of an electron is infinite, part of the overall problem arising from using the real numbers to describe the quantized world].
Wilson (1979) page 158: 'For example the critical behaviour of fluids, ferromagnets, liquid mixtures and alloys can all be described by a single theory. Kenneth G. Wilson (1979): Problems in Physics with many Scales of Length
'The remormalization group is not a descriptive theory of nature, but a general method of constructing theories.'
eThe most convenient context in which to discuss the operation of the renormalization group is a ferromagnet or permanent magnet. . . . For iron the Curie temperature is 1044 degrees K. At higher temperatures iron has no spontaneous magnetization. As the iron is cooled the magnetization remains zero until the Curie temperature is reached and then the iron abruptly becomes magnetized. If the temperature is reduced further the strength of the magnetization increases smoothly. Curie temperature - Wikipedia
page 160: 'The total energy of two adjacent spins is smaller when they are parallel that when they are antiparallel.
page 164: 'What does it mean to solve or understand a model of a physical system?'
page 178: ' The renormalization theory of elecrodynamics does not abolish infinity; on the contrary the electron is defined as a point particle whose "bare" charge is infinite. In quantum electrodynamics the bare charge has the effect of inducing a charge of opposite polarity in the surrounding vacuum that cancels most of the infinity, leaving only the small net charge that is observed in ordinary experiments [with, eg, pith balls] . . . '
'The renormalization procedure provides a means for subtracting
[page 197]
the infinite shielding charge from the infinite bare charge so a finite difference results [you all wish, although of course infinity minus infinity is undefined].
Wilson page 179: Colour charge of quark diminishes as you approach it [just as plausible as above electron story]
Kondo effect - WikipediaKondo effect: superfluid helium Kondo effect - Wikipedia, Superfluidity - Wikipedia
Length scale vs complexity scale. Transfinite network is universal enough to deal with critical phenomena.
Quantum transformations are deterministic and do not change outcomes but observations do by introducing new operators from the classical particle world so we have a continual interplay between quantum and classical which is not deterministic even though processes in the Hilbert and classical Minkowski world can be deterministic [with Shannon type quantization].
Tuesday 15 February 2022
Energy is the charge to which gravitation responds [maybe a sort of null charge]. We have created spacetime through the velocity of light and the null geodesic.
Now we introduce 3D via communication and fermions given that in the simple system superpositions are either positive (giving bosons) and negative (giving fermions) and fermions have to keep away from one another making 3D space necessary for universal communication.
Now we need massive particles, potential energy and electric charge. We make charge [and magnetic moment] out of photons and mass out of energy trapped by null geodesics which are the insides of massive particles and are in effect Lie groups formed as fixed points in the initial singularity [assuming that the initial singularity is the archetypical particle].
How do we make electric charge and magnetic moment out of photons and the electromagnetic properties of spacetime via sepcial relativity?
[page 198]
Spacetime is curved because it is closed by consistency. How do we explain this? QED might be the next section.
QCD is based on the notion that protons are eternal and neutral particles are combined particles and antiparticles. In the end all this is no weirder than 'standard' physics.
How do we get the conservation of energy out of endlessly creative actions? Because there are only ℵ0 Turing machines created as dimensions of the primordial Hilbert space and we demand that the universe be computable.
Wednesday 16 February 2022
Like the skaters, skiers, snowboarders etc I am trying to pull something off that is beyond me: sixty years later, have I got anything to offer? I keep taking little step that will fit together to make the complete essay to get cognitive cosmology on my map.
Thursday 17 February 2022
Woke in fright. My perennial fear is that I am going nowhere though my cause is just and it is in the nature of time that I cannot turn back, and the journey is too exciting to miss. Both theology and physics [as we have them] are hyptheses. Our ony guide is experience, personal experience and the carefully curated and measured experiences of scientists. Einstein and others have shown that genius can go astray and ' There are more thingsin heaven and earth, Horatio, than are dreamt of in your philosophy. So anther morning of self-checking to see if my project has legs, a question I will ask every morning until I achieve a coherent closure of my trip around the world of pain and wonder. The uncertainty is exciting and given requisite variety andf the simple beginning, an inherent feature of the universe. The fundamental idea of my whole project is
[page 199]
that an initial singularity of pure action tries everything and these trials that involve contradiction are selected out to give us the universe we know. The evil we experience as a consequence of the process of "selecting out", not the work of evil spirits.
The principal caveat in all my work is that given the fundamental principle above, all that follows is my speculation about how this led to the current universe, building on the idea that our intelligence is an image of the intelligence of the divine universe, which shines throughout with the creative light of Aristotle's 'active intellect'.
A principle: causality requires contact, but we have two approaches. In Hilbert space where there is no distance and entanglement enables instant correlation but no transmission of information, (perhaps because information is physical and complex Hilbert space is only "half physical"). In real physical space we have communication possible because photons have both frequency and phase and we are in the physical realm of space and time and momentum and energy which transform identically under the Lorentz transformation. How do we get from photon momentum and energy to massive particles energy = mc2 and momentum = mv. How do we get a grip on all these features, momentum, mass, curvature, gravitation. The problem is to order the emergence of these features in terms of a series of zero sum bifurcations Here in the universe we see the roots of intelligence and emotion.
What we are thinking is that every additional quantum of action adds a dimension, that is an oriented complex plane, to the Hilbert space and we would like to correlate these with Turing machines of increasing complexity through superpositions which are feeding into more and more complex features in Minkowski space.
[page 200]
The speed of light couples time and space and null geodesics decouple [from] spacetime [into] the quantum world where spacetime does not exist but photons of ℵ0 different frequencies in one-to-one correlation with Turing machines do. Do we need the transfinite network, like the Trinity, to carry us from the initial singularity to the universe? All these sentences are in effect geodesics through [cognitive] spacetime similar to inertial computations where curvature is absent. Can this mean anything, a potpourri of words just like those created by the uncontrolled singularity. I am trying to select a coherent picture of the creation of the universe out of the millions of words in these notes: 87 volumes × 200+ pages × 300 words = 5 000 000+.
Friday 18 February 2022
From a [ferromagnetic] point of view every sentence is a 'spin' and as we approach the critical point, more and more sentences (Turing machines) become correlated until at the critical point the whole essay becomes a fully coupled network, every source within which adds meaning to every other.
The mass of a particle is a measure of the rate of action = energy within that particle.
Lets assume that the only 'dimensions' [represented in] Hilbert space are energy and time [phase] which correspond to action. The emergence of length comes with the velocity of light which makes spacetime possible and the emergence of the boson/fermion duality which comes with the two initial possibilities of superposition [additive and subtractive]. Then mass and and potential arise with photons being trapped in particles giving a rate of action = energy / mass and electric charge / magnetic moment, another zero sum duality.
So we are looking for a logical sequence of zero-sum bifurcations: [forming a tree]
[page 201]
0. action-energy (phase, superposition)
1. Fermion / boson - photon, no fermion without space [and mass]
2. space-time, null geodesics - contact. Minkowski / curvature / gravitation
3. massive particles / fermions / fixed points / Lie groups / Turing machines
4. Potential / kinetic [mass is potential] - zero-energy universe
5.
Creationsaves.com. The allegedly violent Saul of Tarsus aka Paul of the Epistles introduced a totally unscientific definition of faith into the Christian canon, unfortunately endorsed by the founder of modern Catholic Theology, Thomas of Aquino [who appears to have fully believed the Catholic story and added greatly to it]: "Faith is the substance of things hoped for the evidence of things that appear not (Hebrews, 11:1). It is no better than hypothesis and the faith base of most religions is clearly false [from a fact based scientific point of view]. But Aquinas was sucked in. He looked forward to a post mortem vision of God and explained that this is the purpose for which we were created.
We already enjoy the vision of god in our divine universe, but the religions hooked on the false heaven have devoted their immense powers of persuasion towards convincing billions of people that we are damaged beings in a damaged world, making us slaves to the biggest lie ever told. Salvation does not come from an imaginary God but from the Universe that created itself and us. Instead of hating our lives and looking forward to a false hope, destroying our beautiful world as we go, we need to stop, take a deep breath and face reality.
Saturday 19 February 2022
Work on creation saves using E16 green theology (2016). Jeffrey Nicholls (2016): Essay 16: Green theology: a path to heaven
Perhaps I have seen the point at last. Einstein put general covariance on the map and showed us the universe, but he fell down on quantum theory. The point of general covariance is that gravitation is nothing because everything can couple to everything through a codeless code. Quantum mechanics is the exact opposite.
[page 202]
There is no invariance in quantum mechanics: every event is unique, dispersed through the space[time] of consistency by an analogue of the Cantor universe which is complex enough to give a unique but private address to every possible quantum event. We match the set of elementary events to the set of Turing machines connected seamlessly in some order, that is one of a set of permutations of the natural numbers of which there are ℵ1. And since there is no logical limit on the number of orthogonal points in a set, we can then permute the set of ℵ1 elements to create a set of ℵ2 elements and so on without end. Each of these permutations is a processing pipeline, a string of Turing machines [coupled by sharing memory locations]. Differing orderings give differing results, laying a foundation for a network formed by a superposition of a set of ℵn strings which is capable of connecting any two points (sources) in the relevant transfinite set. This system is maximally concrete rather than abstract because it suggests that every pair of points is connected by a unique process comprising a unique permutation of a string of processors.
From a medieval philosophical point of view this structure is one point in the spectrum of universals and the Cantor world is fully structured and every interaction is unique. This structure may also serve as a model of God which reconciles the ancient contrast between the absolute simplicity and complete complexity which carries a representation of every possibility, but these representations exist in the quantum domain where we cannot see them. Here we see a form of two factor authentication. We do not get a connection until certain conditions are met which means that a suitable meeting of quantum states [a contact], a measurement operator and an unknown vector with nevertheless has a probability of interaction (measured by the Born Rule) depending on the distance between states in Hilbert space, and since every state is a superposition or other states, we can expect a spectrum of eigenvalues corresponding to
[page 203]
a spectrum of eigenfunctions. . . .
. . . another glimpse into the foundations of reality. We like Hilbert space because it treats music (and any other string of data) geometrically. The fundamental point is that what are called orthogonal rays in quantum mechanics are in fact orthogonal complex planes. We see a state as a line on such a plane and a point or particle in Minkowski space created which such planes meet so that their lines cross to define a point. the arrangement of systems to get these hypothetical lines to cross is called quantum mechanics which we conceive mathematically as a measurement operator meeting an unknown state yielding a reading which tells us something (but not everything) about the meeting planes. We see only the eigenvectors of the measurement operator each with a certain probability depending on how close states of the measured system are to the orthogonal basis states defined by the measurement operator.
Simply, in quantum space, ie complex Hilbert, each complex plane is half a real particle, and it turns out that the complex vectors and rays do very well describing the physics that tells us that the mathematical symbol i maps onto a feature of reality that we will call spirit (ie theological aether) which is an invisible complex, but real, ie concrete.
Mathematicians glory in their abstract pictures but their abstracts only make sense if they are logically continuous implying no contradictions which we imagine are what cause structures to fail [decay], a bit like Escher pictures.
Particles have Hilbert space inside, like the initial singularity, that is the universe and these Hilbert spaces hold the Turing machines that give the particles (taken as black boxes) . . . their characteristic behaviour in response to stimulation.
[page 204]
Cantor showed that there is no limit to the internal complexity of a set and yet it can be treated as a named point ("the universe", "me") and sets can interact through one to one correspondences of their element (ie me and X producing a child), manipulated by mathematicians or by the natural processes that are modelled by sets.
