VII Notes
2010
Notes
[Sunday 16 May 2010 - Saturday 22 May 2010]
[Notebook: DB 69 Creation]
[page 10]
Sunday 16 May 2010
We might say that all mathematics is the representation of computations to achieve certain transformations (function or mappings) and a lot of it come down to seeing the common processes underlying various transformations, like the physical growth of an organism.
We take the view of Heisenberg and Wittgenstein that we will model the phenomena without limiting our models by 'extraneous' considerations, like what is an electron really. We just say it is an algorithm that gives certain output if we give it a certain input. Heisenberg Wittgenstein
Monday 17 May 2010
A mathematical theorem is a formal structure which is logically true of its hypotheses are fulfilled. We go on, therefore, using the theories of communication, computation and quantum mechanics to identify the formal elements of the Universe and establish that they fulfill the requirements of the fixed point theorem. We then look for this conclusion in the stationary states of quantum mechanics and in the general observation that all observable messages in the Universe are fixed points, that is can be modelled by eternal forms that remain unchanged between the moment of their creation (this writing) and their annihilation (when these sentences cease to exist in any medium).
Russell: Principles of Mathematics Russell
[page 11]
Fatal error: prove to the pope that monarchy is self contradictory.
Requisite variety: a system of cardinal n cannot control a system of cardinal n+1 because there is a mousehole it cannot watch.
Logic in the physical world. So far we have developed our ideas in the formal Platonic world of mathematics where infinite sets are a reality and we can put them into one-to-one correspondence with one another. The existence of infinite sets requires a Universe of infinite resolution, able to resolve each element of the infinite sets within it.
card(S) = aleph(n)
resolution(S) = 1 / aleph(n)
Now we must move to the real world, slowly resolving itself from the initial singularity, moving through the sequence 1, 2, 3, . . . n . . . ℵ0 . . . aleph(n) . . .
Here our effective starting point is ℵ0 = 2.
If we are divine, there is no reason why we should not understand god, ie ourselves.
The quantization of the Universe explains why we can apply mathematics and logic to it directly in a one to one correspondence, like counting sheep of drafting them into different categories.
Fides quaerens intellectum: I believe that the Universe is Divine and I am searching for an understanding of what this means.
[page 12]
Tuesday 18 May 2010
Russell 2nd ed 1938 Introduction page v: 'The fundamental thesis of the following pages, that mathematics and logic are identical, is one which I have never seen any reason to modify.
What we see depends upon the resolution of our eye. If we are to see n individuals, we need resolution of 1/n, and the same may apply to quantum observables.
Russell page 145: 'An infinite unity will be an infinitely complex proposition: it will not be analyzable in any way into finite number of constituents.'
This is very Platonic: in fact I am an infinite unity and I can usefully be analyzed as head, body, legs, arms, toes, cells etc etc. This is made formally possible by the theory that sets can be partitioned into subsets which can be names ('denoted').
'Indeed it may be said that the logical purpose which is served by the theory of denoting is to enable propositions of finite complexity to deal with infinite classes of terms: this object is effected by all, any, and every, and if it were not effected, every general proposition about an infinite class would have to be infinitely complex.' ie a one-to-one mapping. '. . . It is only by obtaining such propositions about infinite classes that we are enabled to deal with infinity: and it is a remarkable and fortunate fact that this method is successful. Thus the question of whether or not
[page 13]
there are infinite unities must be left unresolved: the only thing we can say on this subject, is that no such entities occur in any department of human knowledge, and therefore none of them are relevant to the foundations of mathematics.' pages 145-146.
Nevertheless mathematics uses the idea of infinity logically to mean 'endless process' like a series converging on a given real number.
'Resolution' gives us an insight into the relativity of transfinity and the process by which rhe initial singulaerity (resolution 1, entropy 0) grows to the present Universe, entropy aleph(n).
We can only talk about infinity in terms of non-halting process (since there is always another digit of precision to compute.)
My 'problem' in the Dominicans was to act out my feelings, so revealing to the management that I did not fit in. Morality, cunning, political nous and other survival strategies suggest that to act on our feelings does not always increase our fitness: it depends on the environment we are in. In the midst of battle, it is advantageous to kill people, but killing has no part in fair trade.
Grey day. I miss the sun. And evil? Not really.
The notion that the tendency for entropy to increase is an 'evil' seems to have precluded much investigation into the source of entropy which we call creation.
[page 14]
CREATION= RESOLUTION (What time do we meet and where?)
'I don't care what any of you thinks. We have got to come to a decision, so vote.'
We define real as 'physically embodied': and the Word became flesh means the word became real. But the existence of discrete physical states as the embodiers of information gives us a degree of freedom in the embodiment represented by the transfinite symmetric network, since each physical embodiment is a process. and we can string them together how we like.
Gödel numbering is a code that generates unique cardinals for every ordinal, the size of the cardinal growing exponentially with the size of the ordinal.
Down this way one catches a glimpse of Riemann's zeta function, since Gödel numbering depends upon the prime numbers. Riemann zeta function - Wikipedia
I have got all the material for a new creation in a file. Now I am looking at it at the lowest level of resolution trying to find one sentence (or so), an abstract that describes exactly what we are trying to do.
We begin with a network of to asynchronous computers, that is (quantum mechanically) with two different energy levels. These are two 'words' in a cosmic language which has yet to evolve as the twosome talk to each other, a feat made possible by the transfer of energy from one to another as a particle which oscillates in a
[page 15]
two state system.
A poll of opinion might reveal that we generally regard entropy as a 'bad thing', to be associated with such horrors as the waste of energy in our car engines and the 'heat death' of the Universe.
We apply the transfinite symmetric network to the real world by mapping it to the set of messages (stationary points) in the Universe. This is necessary for formal reasons, since the transfinite symmetrical network itself is simply a universal formal parent process which may be instantiated at different points in different ways, ie the formal possibilities are made real subject to physical constraints on resolution and complexity.
INFINITE = UNRESOLVED, so creating, making DEFINITE is a process of resolution which fits naturally with the idea of observation.
All the literature is trying to make things definite, to close open questions, either by answering them or by showing that an answer is impossible.
[page 16]
Strength of a case x power of advocacy = 1.
ie heavy advertising ==> dud product.
'Arithmetic has grown to include all that can strictly be called pure in traditional mathematics.' Russell page 158.
page 159: 'A magnitude, then is to be defined as anything which is greater or less than something else.'
page 207: 'What is order?
Russell page 259: '. . . the fundamental problem of mathematical philosophy - I mean the problem of infinity and continuity.'
From an algorithmic information point of view, the problem of indeterminacy, meaninglessness and unresolution.
page 268: formula = computer.
logical continuity is a property of propositional functions.
All the discussion of continuity and limits in terms of measure is quite interesting and demonstrates a large amount of mathematical ingenuity,but we are inclined to think that its practical utility is limited by the fact that the observable Universe is pixellated on the scale of h so that all real events occur in steps if nh, 1 =<n<ℵ0. Limits and
[page 17]
infinities enter the picture when we project the quantum of action onto spacetime, using the uncertainty relations ΔEΔt = h = ΔpΔx etc, where as E, p approach infinity, t, x approach zero.
Russell page 312 '[The transfinite ordinals] do not obey the commutative law.
Planck's constant, h, measures the 'real' atom, the 'message pixel' of the Universe.
Russell page 339: '. . . I hold the paradoxical opinion that what can be mathematically demonstrated is true.' This is so if the proofs are good and their hypotheses are realized. According to R the hypotheses of mathematical proof are either necessarily true of can be proved true from necessary truths., so that all mathematics becomes necessary. But mathematics is too big to exist [simultaneously, ie to be physically embodied simultaneously] , and so must exist serially as Gödel and Turing found, consequences of the formal nature of the Cantor Universe or phase space as a Hilbert space of infinite dimension. The Hilbert Oscillator operates in the transfinite Hilbert space.
Russell page 348: 'Consider a variablex which is capable of all real (or rational) values between two assigned limits, say 0 and 1. The class of its values is an infinite whole whose parts are logically prior to it: for it has parts and it cannot subsist if any of the parts are lacking.'
[page 18]
This is a Platonic view. A more realistic view is that the parts and the whole are dynamically related, coming into relative existence simultaneously (once again quote MTW [page 71] and maybe we can find this in Heraclitus). Misner, Thorne & Wheeler
Russell page 352: 'Every possible value of a variable is a constant.'
The fact that it is so easy to describe the world in terms of complex numbers tells us something, Complex numbers are intermediate stages in calculations, with real inuts and real outputs. The complex numbers are 'forced' on us if we want a complete set of solutions to the eigen-polynomial of a matrix. The world seems to do calculations by splitting the real into two complex numbers, z, z bar, and then at the end reuniting them into a real |z|
On the infinite leap from theism to pantheism it is hard to know how far you have to go after you have taken off.
Transfinite entropy begets transfinite information.
'. . . given any collection, there is a collection of a higher power, to be demonstrated by organizing the original collection in a higher power of different way, ie permutations.
Russell page 382 para 363: 'Projective geometry assumes a class of entities, called points, to which it assigns certain properties.'
The properties are the environment in which the point exists,
[page 19]
just as a whole process defines the precise role of each operation in a large computation which these days may involve many computers in a network and many trillions of atomic operations. The enormous complexity of the internet is based on the simplicity of the [NAND gate].
'Whether the axiom of continuity be true as regards our actual space is a question which I can see no means of deciding. For any such question must be empirical, and it would be quite impossible to distinguish empirically between what might be called a rational space from a continuous space. But in any case there is no reason to think that space has a higher power than the continuum. Russell page 440.
OPERATOR = TURING MACHINE = COMPUTER
Eigenfunctions of operator = algorithms of computer. The complete set of eigenvalues of an operator define a basis, ie a complete set of orthonormal functions or algorithms capable of transforming one whole state vector into another. Sentences like there give me new little glimpses around the corners of my ignorance.
Duchamp: Nude descending a staircase MarcelDuchamp.net
Russell: 'There is no independent system in the actual world
[page 20]
except the whole material Universe; . . . ' page 496.
Russell's 'logical' development of entropy (ie logical creation) 'The existence theorems of mathematics -- ie the proofs that the various classes defined are not null -- are almost all obtained from Arithmetic. . . . The existence of zero is derived from the fact that the null class is a member of it; the existence of 1 from the fact that zero is a unit class (for the null class is its only member). Hence, from the fact that, if n be a finite number, n + 1 is the number of numbers from 0 to n (both inclusive) the existence theorem follows for all finite numbers,. Hence from the class of finite cardinal numbers themselves, follows the existence of a0 [ℵ0], the smallest of the infinite cardinal numbers; and from the series of finite cardinals in order of magnitude follows the existence of ω, the smallest of the infinite ordinals. . . . ' [page 497].
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How is infinity physically realized a la Landauer? We probably do not have an infinite number of distinguishable atoms [except perhaps of the cardinal of all the quanta of action expended in the life of the Universe], so we must settle for reltive infinity, the set of all sets of such atoms as we have is infinite with respect to the set of atoms as the set of all their permutations. From Platonic to concrete.
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ABSTRACTION = ALGORITHM. Although all instances of [the execution of] NAND are in themselves identical as an algorithm, they are all differentiated by the environment in which they occur in a larger process.
Speaking rather logically, we can say that since God is everything and therefore convex and complete, consistency requires fixed points in the life (immanent motion, mapping) of God.
We are not outside an abstract God, but inside a concrete One.
[page 21]
I have to convince myself that writing (as well as digging holes) is real work that can be traded for money. My task is to move from being a legend in my own mind to propagating my legend into other minds in way that will induce them to pay me for a copy of my intellectual property.
The Universe is Divine.: We are shaped by the way we look at things. The search for understanding is the search for a configuration of self that feels at home in its environment. the first step in this search (logically) is to decide who we are and what we are doing here. The problem is that we do not start to ask questions like these until later in life, and by that time we have unconsciously adapted to large portions of the status quo which it is hard to see beyond. DSo with Christianity, the dominant religion in the human Earth.
Contrast 'The Earth is our Mother, we must take care of Her' with the Christian view that the life on Earth, as a result of Original Sin, is a definite mess that will be made over into its original beauty on the last day. In the meantime, since it is already rubbished, we can do what we like with it, clear, mine and poison to our heart's content. Look at Mr Abbott, the outstanding Catholic Among is, from any scientific point of view as mad as a (old time) hatter.
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We understand something when we understand how it grows and we may use this knowledge to nurture it or kill it as may seem best for our current purposes. So we cannot understand the classical God of Christianity. It (He, She, Them) is by definition an impenetrable mystery beyond human ken.
[page 22]
Christian theologians might believe that this is an intellectual stance, but in the context of Churches, it is political. The first rule of monarchy (dictatorship) etc is to keep the masses ignorant of reality and feed them the Party Line. [Animal Farm Orwell] The economic foundation of the Roman Catholic Church (in total an exceedingly wealthy and powerful entity) is its claim to be the sole valid channel of communication with God, our Creator, Lawgiver and Judge.
In the age of PR, no one can have an honest opinion, but is under pressure to fit in. Catholic priests may have doubts about their theology but they'll lose their jobs if they rock the boat.
TURN CONCRETE = TURN POLITICAL
Politics is a form of natural selection, the environment (the collective) developing collective decisions about what to do and enforcing the dominant position on all (you will pay $% in tax).
Christians are poor little rich children encountering reality for the first time. Daddy will save Me. God will save Us and meanwhile we will act with the responsibility of two year olds. Nobody wants to grow up, but peaceful survival requires that at lewast enough of us do to carry the debate toward looking after our Divine life support system. [In natural religion, God is so much closer]
This is my weak spot. I want to go on being an armchair intellectual subsidizing my habit with equal
[page 23]
doses of work and social security. But now I am getting too old to dog (I think I only have about 20 years [of digging] to go) I am going to have to learn to live by preaching, as I rather unconsciously set out to do in the first place. First, however, we need sound doctrine, iescience based; and we need to sloganize it into a simple creed that we can live by and receive increased fitness.
POLITICS ==> CAMPAIGN ==> PLATFORM (THEOLOGY + POLICY)
All politics are underpinned byh theories which try to couple policy to action, so we can work from desired outcome (more tax) to effective legislation (everybody will pay more). So we begin to move from physics to economic and political theory. [Starting always with the isolated case ie Me]
GOD and ASTRONOMY: God made the heavens to God is the Heavens.
Computations are valuable when they correspond to reality, like counting sheep.
Stationary points are created and annihilated as the mapping of the set onto itself changes.[Weinberg on particles ] See this in quantum mechnics where the stationary points are the eigenvalues of an operator. We make this abstract true by choosing a particular operator and computing its eigenfunctions, ie its conjugate basis.
Quantum mechanics: the fundamental stationary state in the Universe exemplified (instantiated) in every physical process in the Universe.
[page 24]
In retraining myself as a natural preacher, I have reached the point where I believe my fundamental doctrine, the Universe is Divine, and I have put quite a lot of thought into how this doctrine differs from the received Christian doctrine and how closely it resembles the scientific doctrine. The feeling of confidence to stand up and speak grows slowly, and the resurgence of the Catholic Abbott gives me a concrete target to try out on, even if my efforts go completely unnoticed. Tony Abbott - Wikipedia
The Universe is a space-time ordered tree of parents and children whose ur=mother (containing alll, ie the lower boundary of all (like a highball glass) [is the initial singularity].
Classical physics produces a sharp hard-edged world, where quantum mechanics is somewhart softer, with a larger set of possible outcomes. As the energy gets lower, things get softer and fluffier, at least from a probabilistic point of view, although all events are ultimately quantum leaps [speed of leap = energy].
Wednesday 19 May 2010
Thursday 20 May 2010
Friday 21 May 2010
Saturday 22 May 2010
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Nin Incest Quantum theoretical observation: '"You understand the You in me".' page 400 - we see ourselves in everything because our observations yield only our own eigenvalues, considering ourselves as embodied eigenfunctions. Nin
