vol VII: Notes
2018
Notes
Sunday 14 January 2018 - Saturday 20 January 2018
[Notebook: DB 82: Life and Death]
Sunday 14 January 2018
[page 108]
Monday 15 January
The big worry of course is that all my theological speculation is the same sort of castle in the air as I accuse Catholicism of being. I do not doubt the fundamental proposition, that the Universe is divine, and I am pretty happy with the identification of the classical God with the initial singularity and the quantum vacuum. The next step, the application of fixed point theory to the emergence of the observed Universe from the initial singularity also looks good and we can be pretty sure that it happened from our cosmological observations. Other parts of the story seem more speculative but nevertheless worth a look, in particular the substitution of logical continuity for physical continuity as the the principal explanatory paradigm and the associated model of the world as a computer network. So where is my source of insecurity? Principally the loneliness of not seeing anyone else in the theology industry following this trail. This is the principal motivation for going to university, since it will have the effect of bringing my ideas to the attention of my teachers and so be much more effective than my internet efforts. Probably the only reason to abandon the university plan is a massive increase in the internet traffic that would make me think someone is listening. This can happen whether or not I go to university.
Fire and Fury: how to make an issue out of scientific theology. I think I have enough to go political but I wish I could take the scientific route, producing a more of less irrefutable case for the existence of
[page 109]
certain facts: ie q) who is God? a) Us. God is what you make it. Wolff: Fire and Fury: Inside the Trump White House
I am so happy to have written something after a cold opening to the day reflecting on the difficulties of existence. Existence is dynamic, it is a full time job.
As gods we have split personalities like the rest of the Universe part deterministic, part random. The fact of evolution shows us the power of determinism to control randomness, in other words creation makes chaos work for us [like a Carnot machine].
God is us comes with the responsibility for what we do.
P vs NP, ie polynomial versus exponential which means in the Cantor world deterministic vs random, selected to survive vs selected to fail [since computing permutations is exponential (?)]. We use the transfinite hierarchy to digitize relative computability. An organism can survive if it can respond to all its inputs in time. If it cannot execute a necessary process in the time available it will die. For security, one would like to have time in hand, like more than a night's supply of firewood on hand.
What I am trying to explain is how the world can create a glorious creature like you so that we can apply the same methodology to creating a truly glorious and graceful society of glorious and graceful creatures. To be stable, however, this society must be able to handle freeloaders and wreckers (who are a species of freeloader, executing their anger at the cost of others, a la Trump)
We opt for P ≠ NP [but it would be interesting to discover the opposite].
[page 110]
Quantum vacuum represents the random realm of the incomputable. Although it follows the Cantor Universe in to the transfinite, it nevertheless obeys the conservation of energy in its dynamics, so that the rate of processing is fixed in the vacuum but some processes are meaningful, deterministic and closed while others lead nowhere [in other words the vacuum is an ergodic process eventually exploring all the permutations of the natural numbers, the permutations of permutations and so on without end. The observable world is selected out of this].
Tuesday 16 January 2018
We can imagine all logical operations as manipulations of strings, and we can find any manipulation of a string S of length n in the n! permutations of S [as long as this process is executed at constant length = constant entropy = reversibly, as in the permutation group].
The permutation of S are strings of unique symbols, in other words the position of any si ∈ S gives it a unique identity of meaning derived from its context in the string [ie the role of the string in some process]. We can therefore construct strings using a set of symbols of smaller cardinal than the cardinal of the string itself [eg the binary symbols o, 1, each of whose meanings depends on its ordinal position in the string].
One would like to produce a proof that by producing a mathematical description of the evolutionary Universe which shows that P ≠ NP is true in reality [and makes evolution possible by introducing relative incomputability = uncertainty = variation]. This is to be the method of e21 An attack on the P vs NP problem deriving from e20 On leading theology into Cantor's paradise
A computer that never halts never produces an output and so remains invisible.
Chaitin Scientific American (1975) reprinted in (1987) pp 47-52: Some random numbers are by chance computable, eg 01010101 . . .. Chaitin: Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory
[page 111]
We are guessing that the solution to the P v NP problem requires us to go beyond merely considering strings of symbols to looking a the meanings of the symbols, which takes us into the transfinite realm [via order].
Wednesday 17 January 2018
This statement is unprovable leads to the creation of space so that inconsistencies an exist, like the card with the sentence on each side that says the statement on the other side is false. Space enables the existence of both p and not-p, so we can say that the real distinctions between the persons of the Trinity formally create space in God. Chaitin in Information, Randomness and Incompleteness
In trying to solve the P v NP we need to go back to the existence of computers as formal elements of space-time with a time based processor and a space of memory. Turing established the dichotomy computable / incomputable. Computational complexity theory is concerned with the spectrum of computability on the computable side of the dichotomy. This spectrum is created by the constraints of physical reality, and so we must take formal notice of physical reality in seeking to prove P ≠ NP or vice versa.
In fact we might find that the limitations on physics might be the same as the limitations on formal systems. I love the way my mind notes connections overnight, since I had worked my way through the essay on Cantor's paradise to the section entitle 'the Gödel Turing bound' and now I am in effect writing the introduction to this section. The psychology of the Universe, based on logical continuity
[page 112]
gives us a foundation for interpreting physics in terms of the limits to formal systems.
One of the features of computers is that they can only exist in 4D spacetime, but [a] Turing machine can exist on a plane [line?]. Its memory can, but the processor must be orthogonal to the tape.
P ? NP is a question for algorithmic complexity.
Containerization is compression in an information theoretical sense that the data needed to address a container full of elements is much less than the data required to address each individual element [in the container]. The container, like a set, is in effect a symmetry. So we can write human = {x | x conforms to the universal declaration of human rights}.
Chaitin page 23: 'One says that one string defines another when the first string gives instructions or constructing the second string.'
The tacit dimension is the capitalized information that gives meaning to a statement, ie the context of a statement. This context is a symmetry of the genre in which the string is emitted and the structure of the process by which the string is constructed. Looking at me as an algorithm I am instantiated by everything I say. Symmetry comes from lower layers and is effectively incomputable because invisible to a higher layer, but can be instantiated. With some curation, this may become meaningful, ie when I get the frame right. The whole shebang is here to give meaning to one statement: the Universe
[page 113]
is divine.
Thursday 18 January 2018
An oracle is equivalent to capital, something already done which serves to speed up a current task, like factory to mass produce products. In the first instance, the factory has to be made 'by hand', but now it puts out products with minimum effort. I am in effect an oracle, a huge aggregation of evolutionary capital which serves to carry the world along in some way like writing these words.
A newborn is a universal computer, abstracting language from the world and then processing it.
Every event in the world is a consequence of a theorem, ie the output of a logical computation process modelled by quantum mechanics.
One again we see how the ingestion of a simple chemical lights up the sluggish morning mind. Engineering solution vs mathematical solution. Which does the Universe use? Maybe mathematical at the root and engineering once it is complex enough for Gödel and Turing to become operative, ie arithmetic evolves out of logic. Whitehead & Russell: Principia Mathematica (Cambridge Mathematical Library)
Many things happen in an evolving world which are unfair, ie out of the range of established justice.
We say that measure zero of the strings generated by the Cantor universe are computable so the system is essentially
[page 114]
random and ergodic and provides a model for a vacuum in which energy is conserved, ie potential + kinetic = 0.
Much of the computational complexity discussion appears to ignore meaning, ie the correspondences between symbols established by communication. This writing would be meaningless if it did not honour the properties of the English language, lexicon, grammar, syntax etc [and draw on a huge volume of established literature, its tacit foundation].
Mathematical incomputability exists in infinite time, but in the finite time of the real world all those functions are [effectively] incomputable that cannot be done in time. If [incomputability] was not the case there might be no uncertainty, no variation and so no evolution.
So we set out to explain the evolution of the world by producing the logical analogy of the Carnot machine which we have toyed with under the title Hilbert Oscillator. An essay on value
Computing permutations is exponential, ie NP (?). Heap's algorithm - Wikipedia
Chaitin page 55: Gödel's theorem and information: ' Gödel's theorem may be demonstrated using arguments having an information theoretic flavour. In such an approach, it is possible to argue that if a theorem contains more information that a given set of axioms then it is impossible for the theorem to be derived from the axioms.'
Algebraic information theory a la Chaitin and things
[page 115]
like the P v NP problem seem very one dimensional compared to the layered transfinite network and the Hilbert oscillator that describes the dynamics which give us a hierarchy of complexity that leads from hydrogen atoms to ourselves and beyond, but I am still not clear about the detailed application of these ideas. Meaning, symmetry, instantiation and all these things are beginning to make sense as bits and pieces, but still not clear.
One of my oldest ideas is symmetry with respect to complexity and I feel that we can use this to work our way from quantum mechanics to the whole Universe by making the transfinite hierarchy out of a layered system of Hilbert spaces. We start with a Hilbert space of countable dimensions each an eigenfunction corresponding to a Turing machine. Where do we go from here? We permute the dimensions of the Turing space — how do we explain the assemblage of fundamental particles — by networking, following the idea that quantum mechanics describes a network. We want to get from Hilbert space to transfinite computer network. Have got a lot of the pieces, now we just have to put the together in the right way.
Insight is a logical jump, not a continuum and what I am waiting for now is the insight which will couple the transfinite network to quantum mechanics. Something to think about on the way to Adelaide.
The Einstein approach is to work from local to general. In this case the local item is the quantum event and we assemble the divine and universal computer network out of coupled local events.
Friday 19 January 2018
Saturday 20 January 2018
Zurek: Communication brings two
[page 116]
systems into the same state, a shared basis. Wojciech Hubert Zurek: Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
Symmetry exists when something changes but everything looks the same. So the symmetry of equality before the law means that even though the defendant changes the judicial process remains the same.
We do not need to understand the ideas of bit-string physics to appreciate the enormous value of the methodology which upgrades our understanding of the Universe from a networkof continuous but conserved flows to a logical network. This is the transition from physical to psychological which lies at the root of both our understanding of the Universe and of the actual functioning of the Universe where the only permanent features are subject to endless variation. So a computation is a flow of energy but it is highly modulated to convey logically bound meaning which is implemented with computers. Noyes & Van Den Berg: Bit-String Physics: A Finite and Discrete Approach to Natural Philosophy
The layered entropy count S1, S2, S3 . . .
