Notes
Sunday 27 February 2022 - Saturday 5 March 2022
[Notebook: DB 88: Salvation]
[page 11]
Sunday 27 February 2022
The gravitational chapter is getting too long but it is also at the heart of the story.
[page 12]
There is a large field of epistemology which is well settled, particularly about scientific method which is the foudation upon which we are prepared to build technology that involves costs and benefits in the space of life and death.
Transfinite arithmetic:
ta 1: ℵm + 1 ≈ ℵm + ℵm ≈ ℵm
ta 2: ℵm × 2 ≈ ℵm × ℵm ≈ ℵm
ta 3: ℵm + ℵn ≈ ℵn, n > m
ta 4: ℵm × ℵn ≈ ℵn, n > m
ta 5: 2ℵm ≈ ℵmℵm ≈ ℵm +1
ta 6: log2ℵm ≈ logℵmℵm ≈ ℵm - 1
The introduction of the logarithm is problematic, since there exists a smallest transfinite cardinal ℵ0, whose logarithm is undefined. Let us remedy this deficiency by supplying a transfinite null D analogous to 1 and a sequence of cisfinite cardinals ℵ-m defined by the relationships:
ta 7: log (ℵ0 ) ≈ D
ta 8: log (D) ≈ ℵ-0
ta 9: log (ℵ-m ) ≈ ℵ-(m+1)
ta 10: ℵ-m × ℵm ≈ D
and their exponential inverses. We write the extended sequence of transfinite cardinals:
. . . ℵ-n ... ℵ-1, ℵ-0 , D, ℵ0, ℵ1, ... ℵn ...
Monday 28 February 2022
Network connections introduce uncertainty just as we see in the evolving connections between vehicles (understood as well informed [communicating] sources) in city traffic.
The basic strategy is to make every sentence in the narrative justified and sound.
Since Putin invaded Ukraine I have been killing myself a little but with [. . . ], trying to speed up work on my fundamental thesis againat autocrats, and the parallel task of rendering god as identical to the universe. I have to realize that contradictions take time to emerge in our ponderous world and although the inevitable increase in human entropy tends in the direction of cooperative peace and happiness, . . . the system is still vulnerable in zero sum times to [survival oriented] rational actors pursuing pillage and rape. The fundamental role of statespersonship and peacemaking is to prevent us finding ourselves in zero-sum positions. This would seem to be the state of Putin's mind. He is trapped, like the rider of a tiger, in the failing nation that the Stalinist streak in Russian oligarchy has created, and to appease himself he has, like an angry-two-year old, to destroy something., the free democracies that point ot he fundamental shame of auto racy. So I plug on. It took years to work out the first and second world wars but now the answer to the next war is the same as to the answer to covid: every individual must have access to the best available, just like the cells in my body (which have included a few cancerous ones) [hopefully all dead by now]. Vladimir Sorokin (2022): Vladimir Putin sits atop a crumbling pyramid of power
A new week and plenty of ambition, writing out the plot
[page 13]
at length the better to reduce it to a few slogans on a page.
Can we say that quantum mechanics in Hilbert space is neither relativistic or non-relativistic because space does not exist, nor relativity, in the Hilbert realm. Relativistic quantum mechanics only emerged with the origin of Minkowski space and then it is all relativistic [since the metric is always operative]. This is such a breakthrough [insight] that did not cross my mind when I was separating Hilbert from Minkowski space and even when I invented null geodesics to create spacetime. I feel that I have been having a little break[out] from my box every day for the last sixty years and I am still some distance from my goal.
Oliver Passon: 'Feynman diagrams visualize formulae and not physical processes.' Oliver Passon (2019): On the interpretation of Feynman diagrams, or, did the LHC experiments observe H → γγ
Passon page 3; ' The point at issue in this paper is exactly the epistemic function of Feynman diagrams.'
'are virtual particles real?' (is quantum mechanics real?). 'postdoc cascade'.
page 7: ' Most of what we know about elementary particles comes from scattering experiments.'
page 8: Dirac spinor (fermion) polarization vector (photon [boson])
page 9: Feynman diagram as a topological (network) structure .
' Path integral method avoids the formalism of operators in Hilbert space' [apart from coupling pieces of a trajectory together by unitary operators; otherwise it seems to work by superposition alone?].
page 10: The observed interference effects depend upon the superposition of the terms in the perturbativs expression [all the elements of the diagrams must be simultaneously superposed to get the right result].
Tuesday 1 March 2022
We may imagine that QCD applies to particles with moving components inside, like atoms and the universe, and so we might be able to make a connection between gravitation and QCD through the structure of the universe and the fixed points appearing inside the initial singularity through the working of the cognitive version of fixed point theory. [This is] based on logical continuity and the closure and convexity of 'cognitive' sets or groups whose content is restricted, like mathematics, by the exclusion of contradictions, ie p = not-p. Is this too good to be true? Why? Obviously we must encounter a few difficult and amazing points as the universe constructs itself out of [but within] the initial singularity.
[page 14]
The renormalization group is an instance of symmetry with respect to complexity which is the creator and in Cantor's language the permutation group, finite and infinite.
A mathematical theorem is a tautology. The sides of a right angled triangle in Eunclidean space cannot be any other way.
A Habit is an Algorithm: William James. William James (1920): Psychology: The Briefer Course
ℵ0ℵ0 ≡ ℵ1,
ℵ1ℵ1 ≡ ℵ2
Let ℵ0 = 2. Then we have 2 2 = 4, 4 4 = 256, 256 256 = a very big number, and so on.
Whatever we say, we leave a lot unsaid.
Secret police, palace guard, priests: people who have been subverted to support autocratic regimes. This could have been my fate and I would have done it, but fortunately they saw through me.
I am looking to produce a cognitive version of fixed point theory depending on logical rather than topological continuity and the boundaries of the convex set being established as the point at which consistency turns to inconsistency. Are we seeing this in Hilbert of Minkowski space? We must be able to say that there is no way Hilbert space can go wrong because of its all pervading orthogonality. Minkowski space is much more restricted so errors can arise by going beyond the boundaries of consistency, ie 2D Escher type situations that cannot exist in 3D.
Wednesday 2 March 2022
Particles - their skins are visible but their insides are invisible [and we see them only as waves, not sequences of logical operations].
By separating Hilbert and Minkowski space we reduce the cardinal of the vacuum to countable infinity which is quantized and able to be placed into one-to-one correspondence with the set of Turing machines which is the set of all possible computable functions. Can we prove that the are not ℵ1 computable functions, or only an infinitesimal proportion of the mappings
[page 15]
of the natural numbers onto themselves are computable, ie can be represented by a program shorter than themselves [Chaitin]. Gregory J. Chaitin: Randomness and Mathematical Proof
I am feeling a bit like the little dog who ultimately catches a car as my alternative physics seems to be taking on a plausible sense of reality and I may have some real good ideas after a lifetime spent trying to create a synthesis of theology and physics as Aristotle did. Aristotle's approach is stunningly simple and a perfect example of the heuristic of simplicity, making everything out of two models, matter and form and its generalization potential and act , which took him into the region of knowledge which we can now occupy, given that quantum mechanics is a description of computation simplified down to phase. We are now getting comfortable that each quantum of action has, in effect, an embedded computer which makes a particle what it is, ie defined its personality, ie its set of responses to a set of inputs.
What I am (not) looking forward to is the discovery of the implicit contradiction which ruins my moment of euphoria.
Thursday 3 March 2022
Watershed: The Death of Doctor Duncan. Greatly heartened that it took a crew of maybe 10 people two years to get this oratorio together, so I feel that I am going well and will be ready to "come out" by the beginning of March 2024 (a target).
A memory: My father's nail clippers.
Lawyers interpret the law [created by lawmakers] and physicists interpret the physics [created by the universe itself long before physicists came along], but they do it in a narrow frame whose outer boundaries approach quantum computation; but, a broader theological view could see quantum mechanical phenomena as the work of god, not so much a miracle [in answer to prayer] as the usual miraculous everyday process of life that makes us what we are.
[page 16]
physicaltheology.com currently houses the material from anewtheology, [hons] thesis etc.
So we are to convert it to the role of cosmictheology.com CT ⇆ physicaltheology.com [since I think I prefer the term cosmic to physical, and cosmic seems closer to the truth, embracing both matter and spirit]
Cosmic theology page 1: Divine Violence. It has taken 400 years but Russia has finally produced an incarnation of Satan in the body of Vladimir Putin. Putin's Satan is very similar to the Christian God. Our most ancient problem is divine violence, whether wrought by god or satan. Exodus 32: Moses slaughters the worshippers of the Golden Calf, William Niven (2022); Ukraine war: Putin’s ‘denazification’ campaign hits Babyn Yar holocaust memorial to 33,000 murdered Jews
Friday 4 March 2022
From my point of view the application of renormalization is a cure for a self inflicted injury which arises from the fact that we are trying to apply continuous real numbers to an inherently quantized universe. The consequence is to invoke a sort of ultra-violet catastrophe whose most manifest consequence is the cosmic constant problem. Planck avoided a UV catastrophe in classical treatments of the emission of black body radiation by quantizing the interaction between matter and radiation reducing its cardinal from ℵ1 to ℵ0. This approach is considered inadmissable in quantum theory because quantum fluctuations are considered to be inevitable. This idea seems to arise from a false understanding of the transformation in the meaning of the quantum of action from its role in [the creation of] Hilbert space into its role Minkowski space where we find that [instead of a defined logical operator] we have [a transformation with the dimensions of angular momentum] ΔE.Δt ≈ Δp.Δx ≈ h. This arises because the entropy of quantum mechanics [ℵ0] is not sufficient to define an exact point in Minkowski space [which is considered to be real and continuous]. The solution to this problem becomes the subject of cc12_transfinity [where we create and apply transfinite computer networks to model the universe at the Hilbert and Minkowski layers and connect them].
Always looking for a little bit of inspiration to get me moving, what a physicist would call a potential, a store of stationary energy seeking to move. My question now is how does the complex energy that we represent by ∂ ψ / ∂ t in physics become transformed into both a spatial part (potential, memory) and a temporal part (kinetic [dynamic]) as it moves from Hilbert to Minkowski, in other words how does the quantum creation of spacetime also create potential and kinetic energy through a zero-sum bifurcation.
So we ask what is space? in the sense of how does it act. Spatial action is a product of momentum and distance and momentum is the energy stored in a particle due to its inertial motion and due to the bifurcation, the amount of potential energy consumed is precisely equal to the amount of kinetic energy created. The big clue must be that space.momentum and energy.time are duals connected by the velocity of light which we have credited with the emergence of space by its relationship to the Minkowski metric neutralizing space-time separation [by enabling null geodesics] to allow contact causality.
[page 17]
Space is a new symmetry created by breaking some of the symmetry of quantum mechanics. The symmetry in quantum mechanics is energy-time = action. Space is where time stops, made possible by the Minkowski metric and when time stops space becomes the new symmetry, a fixed point in energy-time whose foundation is the null geodesic made possible by the metric of Minkowski space which is flat / inertial / fixed and in a sense embodied in the nullness of the geodesic. In the early days before massive particles all inertial motion occurred at the velocity of light which is a way the velocity of time measured against the metric of space. Looking at this we see that spacetime, gravitation, momentum and potential are all coupled by the orthogonal dimensions created by bifurcations or action.
My dream of theologizing physics has led to to bite off more than I can chew and so introduced some excitement into my mind. For a long time (beginning in 1984-87) I had one idea, to bring about peace through space, which, as Cantor describes it, is the transfinite resource that will never run short. in information science this is true but on the ground, space is very finite and so we fight over it. This idea was too abstract but the design of a physical theology makes it more concrete and introduces the idea of caring for our planet by minimizing our footprint, which links it to the moral world. All these bits and pieces are now here and need to be assembled which is slow work requiring reading which is why E30 is taking months.
A point to remember, or at least to incorporate is the idea that while the cardinal of the Hibert space is ℵ0, that of Minkowski, if it is continuous, is ℵ1, an idea that appers a few paragraphs above to explain the transformation of the quantum of action from a logical point event to a distribution in Minkowski space described by the uncertainty principle. From the transfinite network point of view we see the natural numbers as indices of the element of the set of Turing machines which we associate in turn with the sequence of superpositions generated by the quantum of action as it populates a Hilbert space. By permuting the order of the element of these superpositions as Cantor permutes the order of the set of natural numbers, we can generate a set whose cardinal is ℵ1 and which we might use to explain the continuity of Minkowski space by permutations of the Hilbert space Does this go anywhere? Takes me back to cc16_transfinity. Here we see a connection with the continuity of gravitation.
[page 18]
Saturday 5 March 2022
The relationships between action and energy puzzle me and I wonder of the answer lies in the boundary, ie creative transformation between Hilbert and Minkowski space. In Hilbert space E - hf. In Minkowski space where energy is considered, T + V is a constant, in a zero energy universe which lives in Einstein space V = −T
When we come to the computation of action we say S = ∫ (T - V) dt. Since the total time from t1 to t2 is fixed, we seek to fix the action [by variation] and in Einstein space we are looking for a stationary maximum whereas in Newtonian space we want to get a stationary minimum which means minimizing the [integrated difference] of the functions T(t) and V(t) with the proviso that the [instantaneous] sum of T + V is constrained. So we might say falling things start slowly. This is because potential = mgh or more abstractly, a length. So the loss of potential energy is proportional to distance fallen, h = vt and so the rate of loss of potential is proportional to velocity. On the other hand the kinetic energy is proportional to v2. At any point t within the trajectory we know that the loss of potential is equal to the increase in kinetic [energy]. At the tine t, therefore, taking t1 as zero we find that the rate of transfer of potential into kinetic = potential energy at t / kinetic energy at t. At t the particles has travelled s = ½gt2 and is losing potential at vdt. The growth of kinetic energy is a function of v2dt Minimizing the action between the two times therefore seems to go slowly at the beginning, losing potential at vdt and minimizing the distance we travel at maximum velocity. This seems to make sense in 3-space.
What about gravitation, which we may see in the limit as a space where there is no particular direction for inertial motion? As soon as a field appears, however, inertial motion becomes directed and may become curved so we have the moon floating inertially around the Earth. The idea so far is because gravitation is a fixed point established in a closed compact (logical) 4D spacetime by a version of Noether's theorem which projects the logical boundaries of the universe as a fixed point in its dynamic interior. Because the mathematical connections in this fixing proceed reversibly at constant entropy [ie continuously, where nothing happens] we get a law of conservation of entropy or complexity
[page 19]
without any help from quantum mechanics which exists "inside" the gravitational structure and creates all the detail in the universe which partitions the energy in different ways and gravitation likewise. Here we would like to introduce a quantum big bang which creates potential and kinetic energy while honouring conservation and the zero energy universe. Every time I write out the gravitation is nothing story (told in terms of 'closed' Lie groups, which ultimately we take to be the transfinite hierarchy of permutation [symmetric] groups [it seems a little more plausible by a sort of 'law of sufficient reason']).
Transfinite permutation groups are logical networks which retain [local] quantization despite their complexity [continuity], giving the lie to the nineteenth century definitions of consistency which postulate that we can squash distinct (orthogonal) points together until they become a continuum. An inadmissible contradiction.
It is easy to say 'let the universe be divine' but to get the proof we have to make the pudding and that is what I have been working on since 1965 when I got the idea for the essay How Universal which was the best work of my life because it got me kicked out of the Dominican Order. I left all my 'personal' books behind but I took with me a headful of Aristotle, Aquinas and Lonergan and an incoherent feeling for what might have been had my superiors taken my ideas to the Ecumenical Council and founded scientific theology. I may be deluded, but I think the period 1965-2025 might be enough for me to get the pudding on the way. Jeffrey Nicholls (1967): How universal is the universe?
What makes me write? What makes the quantum world write? A suitable coincidence of situation expressed in the same basis, ie mutually intelligible. BASIS ≡ LANGUAGE. This is so gorgeous, but can I make anything with it?
What makes potential? We are looking for logical drivers for the evolution of the world and my oldest idea is what I have called the Cantor force, the tendency of a system, driven by [consistency and] entropy, to become more and more complex, continuously creating possibilities to move on, and of the transfinite number of possibilities there are some that are computable and reproduce themselves. A long shot as ever, but the only way a system with little control and unbounded activity could be expected to behave, a bit like the Wodehouse's Bertie Wooster. I am always hoping to find a plausible story based on some sort of physical / logical intuition or feeling. How do potential and energy fit together: potential creates energy, the essence of capitalism? In a developed society one modelled the potentials and chooses the best, which may or may not fail, but the effect of a potential in the mind of both a universe [and a person] is to raise
[page 20]
the money (energy) to make the potential real. This I hope is the story that cognitive cosmology will finally tell when it takes the shape in some years time, of a plausible hypothesis that makes a phantastic story into a pudding. On the whole it is no less plausible [than the theory] which claims to make the universe out of the kinetic energy which came into existence by the potential released in the big bang. The links between energy and mind are executed in a network. So back to transfinity again, the original and best idea, the key to the story is that the random fluctuations of the Turing machines are bound in the long run to cut the transfinite permutations down to the computable subgroups of the transfinite symmetrical group.
Logical continuity renders this group continuous [much more effectively than the juxtaposition of isolated points] and we would like to cook up a cognitive version of fixed point theory which leads to the fixed points in any articular transfinite set which would in retrospect identify the network of Turing machines from which our particular set is constructed. In the beginning this is one machine, the quantum of action, and then, like Cantor but beginning from 1, we build up the current universe. In the Cantor world adding 1 is equivalent to generating the set of all possible subsets or permutations of the set in hand. We can imagine a version of Cantor's proof in which the subsets of a set are realised by subnetwork processes which are grouplike and so out of touch with their neighbours, and so random events from each other's point of view. From the beginning we need the existence of replicators, self reproducing entities, the first of which is the divine quantum of action and we can be certain that in the Cantor world a randomly permuted set of self replicators is certain to produce larger sets of self replicators and so we go on from fundamental particles to atoms molecules, cells etc etc. The key must be that this is all a cognitive process that can work past any dead end because built into its history are all the backtracks necessary to back off and take another course.
Permutation groups and critical points. The critial point is when something goes viral like electron orientation at the Curie temperature. This is a network phenomenon motivated [by the fact that] the energy of aligned electrons is lower than misaligned. Also it would seem to be a massive decrease in algorithmic complexity. Domb. Cyril Domb (1996): The Critical point
Can I work any harder? Probably not, I think about my theological project
[page 21]
all the time. Can I think more effectively? That is difficult to judge because most of our insights are random events and the best I can do to encourage them is to read or write all the time, reading guided by the problem in hand, basically statistical mechanics in the context of the transfinite network. From statistics we lean something like Maxwells distribution which is a consequence of random events and Newtonian physics. I am looking for the statistics of creation based on quantum theory and Einstein physics. The advantage of a scientific community it that there are many other minds wandering around in the dark communicating their findings
Quantum physics creates spacetime creates general relativity, all on the basis that the quantum of action is a thing, god, a cut and come again pudding. The Magic Pudding - Wikipedia
