Notes
[Sunday 27 April 2008 - Saturday 3 May 2008]
[Notebook: DB 63 aTheology]
[page 148]
Sunday 27 April 2008
A quantum oscillator is a cycle of creation and annihilation,
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which may occur in layers to give us the transfinite oscillator. Begin with differential equation - Hamiltonian - ammonia maser - creation and annihilation of photons and states - black body radiation - stationary states. And then we turn to quantum field theory.
The conventional explanation of quantum field theory revolves around the uncertainty principle and vacuum fluctuations. The creation and annihilation of particles from the vacuum relies on the Einstein formula E = mc2, which follows from special relativity. This I need to understand better.
The key to general relativity: Tensor equations that hold in the rest frame hold in all frames? A black hole looks scary to us because the transformation to and from it quite extreme, making time into space and space into time. [Locals do not notice this and see us as the scary ones]
Every movement is a transformation. The aim of physics is to represent these transformations.
To be written something must be invariant because writing is invariant. Every paradigm change is epistemological. The paradigm change that grew in the 12th century arose from the European assimilation of Aristotle, who sounds like a relentless collector of data, and who interpreted it according to a creative rearrangement (transformation) of the ideas available to him in his times, Plato's forms and his own preoccupation with real material things. Between them, Aristotle and Plato laid the foundations of dynamics, that is transformation. He established the 'causes' of transformation, that is four invariants that could be used to explain transformation,
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matter, form, agent and purpose. We understand spacetime transformations intuitively and appreciate them in all the moving systems around is, flowing water and air, plants, animals, minds and so on.
Aristotle interpreted transformation as causal, meaning that some things story the same, the invariants. And here is our epistemological principle: to be truly written (ie represented in memory) something must be invariant because writing is invariant and truth is invariant.
One would estimate the recurrence period of approximately 1000 years [for scientific paradigm changes]. Our forebears discovered monotheism in about 1000 BC, made God human in 0 AD, realized that creation itself was also a path to God around 1000 AD and now? This paper is intended to hint at a new direction in theology.
I must admit that in my heart I am at war with the Roman Catholic Church. I have experienced it as a bad thing, although I accept that it was this personal evil that prompted the search for an alternative. I cannot really go to war until winning is certain, that is my weapons (models) are more powerful than anything they have got. This is purely a battle for hearts and minds, however, without having any military battlefield action, so we must supply all carrot and no stick. Although there is stick in showing that certain ideas are false, and that one must therefore abandon them or be seen as an old foggly. Sudden urges to action like engaging the Pope on his visit to Australia need to be controlled by
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the need to state the ideas clearly enough to gather a community that will gradually grow and propagate the new view. Such evolutions are possibllt slowed down if force is brought to bear, although the spread of all the major religions seems to have caused conflict.
The big thing for me is that my theology seems satisfactory to me, at least as satisfactory [as that I learnt from the Church].
Now. I identify the world and God, Monotheism in the hands of Platonizing philosophers led to an exceedingly abstract model of God (actus purus) which set God ad the world apart as far as logically possible: one is not the other. We now come to heal that rift and interpret the whole process in quantum mechanical terms which express the invariant features of all transformations, all changes. This transformation (a computable transformation) becomes our equivalent to Aquinas actus purus.
War is a business proposition, and extension to the extreme of work, that is all activity devoted to security, growth and reproduction. There comes a time when it may be effective (if unpleasant) to kill the competition rather than die of starvation.
As a responsible citizen, an organization dealing in religious software should be a taxpayer and therefore run for profit accruing from the services it renders. On the other hand, free is a good marketing tool. So we offer free knowledge but may charge for applications and embodiments of that knowledge. Money begins to flow as we move from knowledge to knowhow.
On the nature of God.
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The Catholic Church has the gift of absolute truth. John Paul II But the world changes, so the Catholic Church must change. They would say the details change but there model of god and the world remains the same, an invariant truth.
Tensors on different manifolds tell us how transformations remain invariant through changing coordinates. The fixed point is the metric tensor. What is the metric tensor of literary space?
Theology is a branch of dynamics. The aim of dynamics is to predict from conditions at to what is going to happen at to . Often we need to know what happened at to t-1 etc to make a good prediction. So some theologies would say 'do this now and you will go to Hell later', or sticking to the present life, all actions can be partitioned into good and bad and indifferent according to certain criteria.
There can be no causality (and so no meaning) on a spacelike slice because no two points can communicate with one another [? without delay],
In a relativistic space-time diagram the spatial dimension looks like the time dimension reflected in the null vector. My 4-velocity = u.u = (do / d tau ) 2 = c 2 = 1.
We all move through proper time at the speed of light.
Lorentz transformations transform process into memory and
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vice versa, that is kinetic energy into potential energy.
. . .
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. . .
Aristotle and Aquinas both made the transition from the material physical world to the spiritual metaphysical world via the potency / act symmetry. We might think of this symmetry as the Lagrangian of the transformation from matter to spirit, rather like Dirac's Lagrangian of the transformation from classical to quantum mechanics.
In network terms contact = ability to decode, ie sharing a language, binding together in molecular biology network terms.
Monday 28 April 2008
Clear, cool and windy; autumn at last.
Where are we now? Still exploring the route from physics to theology analogous to the path taken by Aristotle and Tom. Aquinas' God was both eternal and living. To cover this apparent contradiction, he divided motion into immanent and transeunt, the former having the character of a permutation, moving from actuality to actuality rather than from potentiality to actuality. What this implies is that each potentiality is an activity, just a different one. So in modern physics potential energy is just as actual as kinetic energy and plays an equivalent role [in making things happen]. The difference lies in a point of view. One does not feel the potential from an inertial frame but gains energy relative to a frame not falling in the potential. All this sort of metaphysics thus applies to gravitation.
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The article on God can be written as a commentary on the Prima Pars of the Summa pointing out (projecting) where we agree and where we differ,
God is in a sense in orbit around us. In the distant past we can imagine that there was no concept of God and no distinction between God and the world, the perigee. God reached its apogee in the Dark Ages when it became the unapproachable mystery conflated from Plato's One and Aristotle's First Mover. Unmoved mover - Wikipedia The return trip began with medieval theology and we are now ready for a new perigee, or should we say peritheon. Following Lonergan, we see the common thread as insight. Lonergan
A theological quest: to get God and the World back together again after the Roman Catholic Church took him away.,
Commentary on Aquinas: the thousand year cycle.
In a stable world it takes action (= force) to move things. Force = gradient of a potential, where gradient is usually taken as a gradient with respect to space (del ). Action, on the other hand, is a gradient with respect to time, dS / dt = energy = L. S = integral L dt.
More energy = steeper with respect to time = faster = higher frequency.
. . .
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Quantum mechanics is not dissipative. Rigol et al N 452:854 Rigol
Medieval natural theology: Ball N 452:816 Ball
Nature Essay: The Theological Cycle
Energy is the time gradient of action. It is conserved, and proper time is always positive and increasing, so we allow the action gradient to be both positive and negative representing a space where uphill + downhill = 0, ie downhill = - uphill (as you might expect).
So we think of the Universe falling downhill through time driven by 'pure act', the reversible physical foundation which flowers into the irreversible (eternal) metaphysics (string the words together and perhaps a meaning will come, what we might call 'theoretical writing' by analogy with theoretical physics). Fiction seeking understanding which, if it comes, gives meaning to the fiction.
[diagram] ONE GOD - COMPLETE SET OF BASIS STATES - ONE GOD
Information theory tells is we cannot approach deterministic (reversible) transmission of messages without quantization. We can understand why gravitation is not quantized when we understand why quantization exists. Deterministic transmission requires non-interference - non collision = non-intersecting paths between all points in a convex set
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==> 3D. Parallel lines = non-intersecting lines. Only in 3D space can all the lines joining pairs of points be parallel. Also, because quantum mechanics is reversible <a | b > = < b | a >* and the probability of a complete message (a halted communication, round trip) is <a | b >2 = <a | b > < b | a >*.
The message is a vector, ie it has two independent (orthogonal) components,
The algorithm relating political unrest to food prices is no doubt transfinitely complex since it depends on a complex network of individual choices in an economic network embedded in a wider society. Nevertheless we can to some extent observe and parametrize these things in order to derive a differential operator something like d unrest / d foodprice = f ( ).
A group of transformations, ie transformations which meet the axioms of a group.
Re Ball: We would like to take the origins of science back to the big bang by proposing that the Universe creates itself by scientific method, that is by evolution, selecting from the variations proposed by imagination those that faithfully model the world of experience.
Tuesday 29 April 2008
. . .
It is well known that all the dynamics of a real world computer network can be expressed in terms of the Sheffer stroke or NAND
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operator. Sheffer stroke - Wikipedia
Quantum mechanical fields are an attempt to understand the network that produces the particle we [observe].
It seems a common belief that energy quantization if represented by the expression E = hf, but this is not true because although the action represented by h is quantized, f and therefore E may be real numbers.
Wednesday 30 April 2008
In order to communicate, two spacelike separated points on a spacelike surface (ie two memory locations) must last longer than the space-time interval between them.
MASSIVE = having internal process that therefore some memory within. This holds for the Universe as a whole, but initially (ie the photon age = layer) there are no distinct massive particles within it.
The purpose of this work is to point out the tip of a new iceberg in the sea of knowledge. At this point, the density of this iceberg is only infinitesimally greater than that of the sea, so it is beneath the surface almost everywhere and the size of the top gives no indication of the size of the iceberg.
One beauty of the transfinite cardinals is that they have no intrinsic size or measure, as suggested by the equivalent 2 ℵ0 = ℵ0 ℵ0 = = ℵ1, ℵ0 + ℵ0 = ℵ0, a bit like c + c = c.
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c + c = c is true because the only velocity of light anyone can ever observe is c and c + c has no observable meaning, but does put a formal constraint on the transformation that adds velocities. The equation aleph(n) + aleph(n) = aleph(n) may induce a similar sort of transformation which we would like to see as a feature of the transfinite oscillator. Would also like to link this in some way to the fact that quantum mechanics is cardinally invariant and [to] the uncertainty principle which links to periodic functions and recursive function theory. The point is that without interrupting it, we cannot find out how long it will be until a given Turing machine halts at a stationary answer.
Symmetry can only be broken when the same transformation of the symmetry can lead to two different systems one of which is not the other but both of which are descended from the same original symmetry by the same transformation. This is made possible by the principle of requisite variety, where we learn that one can at most partially constrain two.
On Gravitation shows us the role of the continuum in physics and geometry. The continuum is by definition unconscious because it is not differentiated enough to look at itself. It exists in the initial singularity and continues to exist throughout the Universe whenever the resolution of the observer us less than the variety of the observed, so the observer cannot see al the details and assumes continuity. Fractal. Mandelbrot
Kauffman. The Search for the Laws of Self-Organization and Complexity, 1996. Kauffman
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The Universe has laws and explanations because it is all derived by computable transformations from an initial singularity. Should we say 'reversible computable'? Probably not, because that would make complexification impossible. Instead let come computations be reversible and some not. The reversible ones form a group (the group of unitary transformations). So we can find a backbone of transfinite groups leading us to the initial singularity, and this backbone is surrounded by a cloud of unique structures that cannot be mathematically compressed, ie they have no symmetry from the point of view of their leaves. So we have a tree of bifurcations created by non-deterministic transforms.
The network idea combines determinism (Turing machines) and indeterminism (non-correlated interrupts)
The fixed points of the Universe have a logical structure isomorphic to a computer network.
UNCERTAINTY = MEASURE OF LEAST SIGNIFICANT DIGIT.
In big numbers, the least significant digits are the most 'random'.
Kauffman. Complex systems cannot exist without order. This is Cantor's theorem and it explains the world (in a formal sense). We make it dynamic by building network connections between all the points in the Cantor Universe.
Kauffman page 22: 'The algorithm itself is its own shortest
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description.'
The Universe is its own shortest description, ie in the limit there is no empirical residue.
Kauffman page 23: 'A theory of emergence would account for the creation of the stunning order outside our windows as a natural expression of some underlying laws. It should tells us if we are at home in the Universe [personalities of God], expected in it, rather than just present despite overwhelming odds.
Submitted: On the (non-) quantization of gravitation.
This first thing I have ever managed to write (I think) that does not mention theology, . . . by sticking very close to physics and writing bout the initial singularity.
The Universe as a whole has a probability of 1. Let us say that the number of events in the Universe is ℵ0, where (depending on local complexity) ℵ0 may take any of the values 2 .. ℵ0.
. . .
So we have a hundred events making up the Universe, and might assign a probability of 0.01 to each of them at maximum entropy = stability = stationarity = speakability.
Bell: Speakable and unspeakable in quantum mechanics. Bell Energy and action as such are unspeakable because there is nothing to say, and so for all structures, part speakable, part
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unspeakable (gravitation).
Time, like energy is meaningless, not relying on meaning for its existence so open to the full power of transfinite covariance. But as we work our way up through the layers, reference frames (addressing) becomes important, so as to allow 'deterministic' random addressing in a random access (naked) memory. This can only exist in 3D [or bigger].
3D is necessary and sufficient for random access memory
Fingers crossed (also only possible in 3D if they are to retain their integrity.
Evolution = teaching energy to execute algorithms, where we have phases of complexification and then bottom up rewrites to simplify the thing without losing functionality.
Revenge: It is about 40 years now since the Pope let me go, and I have come to feel that the world is not big enough for both of us. Has anyone ever been privileges to see such things. Each insight is a blessing, but to see that deterministic computation is continuous as meaningless shows how we reconcile this seething world with divine simplicity.
THEOLOGY - PORNOGRAPHY. They are using God to bolster their own power. I want to give God back to the people. Not like Jesus, who might have mistaken himself for God, but cosmologically, a la Kauffman, making ourselves at home in the Universe rather than thinking of ourselves as exiles longing for home, as the Roman Catholic Church would have us do.
Kauffman page 28: 'Wisdom, not power' ? Maybe wisely used power is closes to the mark.
What we are doing is retracing Aristotle's steps from earth to heaven, armed wit recursive function theory rather than just matter and form / potency and act,
Stem cells = (computational tree) roots. Energy (action) is totipotent or as Thos would say actus purus = omnipotens.
Thursday 1 May 2008
Did Newton's theology give him the faith in the concrete Universe to head off into the extreme abstraction of mass points and absolute space and time. He did not need to ask how the system worked ('hypotheses non fingo') because the Being looked after it:
Newton Book III General Scholium; 'This most beautiful system of the sun, planets and comets could only proceed from the counsel and domination of an intelligent and all powerful being.'
Newton needed the vacuum to enable his particles to follow there inertial courses without perturbation. Now energy is the vacuum. Since it carries no structure it communicates no information to the particles with which it interacts (via gravitation) so allowing them to follow their geodesics. We need structure other than this vacuum to perturb us from our geodesics so we feel this vacuum. Casimir effect - Wikipedia
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NEWTON'S FIRST (GALILEO's) LAW ==> VACUUM for its realization.
'It is the dominion of a spiritual being which constitutes a God: a true, supreme or imaginary dominion makes a true, supreme or imaginary God. And from his true dominion it follows that the true God is a living, intelligent and powerful Being; and from his other perfections, hat he is supreme or most perfect. He is eternal and infinite, omnipotent and omniscient; that his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things and knows all things that are or can be done.' (U of Cal edition, pp 544-545. Newton
The basic idea of God in the network picture starts locally: I am my own God, and my experience is part of the wider experience of the layers of divinity that encapsulate and support me, both more or less complex than myself.
Kauffman: Systems are constrained by their dynamics, ie by the pattern of communication between their elements.
Kauffman page 71: 'Order for free'
We cannot have creation without the infinite. This idea has been lurking for a long time and is implicit in Gödel's theorem, the principle of requisite variety, Turing's theorem and the general notion that an alphabet cannot completely define its own arrangement, so even proteins need chaperones. My permutations are infinite with respect to me, and so open my future to a set of possibilities exponentially larger
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than my cardinal number. Just have to learn to count this.
Kauffman page 74: Is there a way that an autocatalytic set can evolve without all the complications of a genome?' [evolution requires memory]
Order is a dynamic concept. Chaitin shows that there is no distinction at the symbolic level between a random number and a densely coded message, and yet one is ordered (in Kauffman's sense) because it is part of a network process, subject to encoding and decoding, whereas the other may be just noise, making sense to no extant system or receiver.
page 78: 'If a system falls into a small state cycle, it will behave in an orderly manner. But if the state cycle is too vast the system will behave in a manner which is essentially unpredictable'. [that's me]
What if it just gores through its states in numerical order, like a train along a line.
The only way to measure a cycle is when it comes back to some previous condition. Such a measurement requires memory and the longer the state cycle and so the more complex, the more memory in both location count and durability is needed.
On the (non) quantization of gravitation: I do not quite understand what I have done, but it feels good, ie it does not seem to involve any contradiction either with itself or with anything else I understand about the world.
Physics is founded on the vacuum.
[page 166] N K net has N nodes each with K inputs.
What do we call [K]? A coupling constant? A density of connection constant. In a real network all the error free connections are time division multiplexed into peers, since there must be two way traffic to defeat all error, and the signal has to pass error free through the channel twice (there and back) so that one node can compare to test for error. A coupling constant is the proportion of messages that are error free [and so exert a force].
Friday 2 May 2008
A typical bit of human behaviour is to decide to do something (like give up smoking) and then change the decision when it reveals an element of hardship or hardness.
Schwinger in Schwinger page 342: 'The requirement of invariance under time reflection imposes a restriction on the operator properties of fields which is simply the connection between spin and statistics of particles.'
We imagine a layer of the Universe so simple that it embodies quantum mechanics without any of the boundary conditions that bind it to specific implementations in the more complex world.
Energy is totipotent; the past is fully determined, ie decided, which is not to say that it is not open to the future in the moving present which was, is now
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and always will be the initial singularity of 'actus purus'.
So we layer the Universe. The past is act, completed., which we might think of as potential, ie static formalism in transit from past to future. This formalism is completer and determinate in itself and so via Turing and Gödel points to the future possibilities that remain open in the past. Will get it clear one day. What we want to say is that the action of the initial singularity (ie god) present in the present links past creatively to future. Maybe we can say the future is a consequence of the incompleteness theorem and Turing machines are the incomplete machines that get us there, but we cannot (maybe) do anything incomputable.; yet with perfect computation, Gödel still holds (otherwise his proof would be invalid through incomputability.
Khinchin: Mathematical foundation of quantum statistics.
page 1: 'In quantum mechanics, the state of a system defines the physical quantities only as random variables, ie it determines the laws of distribution obeyed by the physical quantities and not their values. This essentially statistical feature of quantum mechanics is independent of and distinct from the statistical aspects of the special methods of statistical physics. In statistical physics the mean value of a physical quantity is found by averaging the quantity over different states of the system. In quantum mechanics, however, we speak of the mean value of a quantity in a certain definite fixed state.'
So Classical: many distinct states, one real average
Quantum: one fixed state, many possible outcomes each a distinct
state
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(eigenstate)
Khinchin page 2: 'It is very important to distinguish carefully between the concepts and computational methods of quantum mechanics on the one hand and those of statistical physics on the other. We introduce a special terminology and system of notation for each of them, and we rigorously avoid confusing the two sets of ideas since they effectively have nothing in common, except that both are statistical in nature.'
Which seems quite a lot. Both are rooted in the theory of probability and measure, the difference being that amplitudes are vectors and real probabilities are scalars and interact as scalars (measurable quantities). A vector, on the other hand is a set of measures that obey certain rules and lets us define different ways of linear combination, addition of vectors and multiplication by a scalar.
