Notes
[Sunday 23 August 2009 - Saturday 29 August 2009]
[Notebook: DB 67: jciii]
[page 130]
Sunday 23 August 2009
Gauge invariance and the single qubit. Gauge theory - Wikipedia
'Prove' that the Universe is divine, or die trying. Do this by showing that the Universe is not not-divine. . . .
Fides quaerens intellectum Anselm of Canterbury - Wikipedia Proslogion - Wikipedia A scientist as scientist, obeying the scientific epistemological ethic considers an hypothesis simply as a possibility with no intrinsic 'weight' to be tested against the data. At the
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opposite pole, [people may] build their whole operational life around their faith and as part of this commitment seek to understand the faith in a way that makes it consistent with reality. As in the Roman Catholic Church, this attitude generally forces the introduction of invisible or fictitious forces to account for any lacunae or apparent contradictions in the formal content of the faith. From the scientific point of view the faith approach is unsafe. The 'isolated quantum system' is the quantum mechanical deus ex machina and can describe any system, which emits 'waves'. So we could use it to study a car engine using only an instrument that measures waves, ie amplitude, frequency and phase. By spectrally analyzing this data, ie superposing it on a known set of waves, we can isolate the frequencies associated with the crankshaft and camshaft rotation, valve opening and closing and so on, and also the spectrum of the 'noise' vibrations induced in the static components of the engine (its potentials) by the moving parts. This approach is isomorphic to the quantum mechanical approach to the Universe.
EIGENVECTORS = FREQUENCIES = ENERGIES EIGENVALUES
AMPLITUDES = RATE OF OCCUPATION
The relationship between ordinal and cardinal in quantum mechanics is represented by the relationship between eigenfunction and eigenvalues. This relation is dictated by the structure of linear algebra, and so we may think of linear algebra as the potential (the fixed point) in the dynamics of quantum mechanics.
We take quantum mechanics 'on faith' because it works and the majority of its practitioners don't question it because there is no point until they find something that contradicts it. It seems to be perfect, but it still seems oputside the intuitive pale, which in the
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end, I am trying to bring it inside so I can form a consistent picture in my mind.
The opposite of isolated is perturbed.
The relationship between eigenfunctions and eigenvalues is the relationship between the content of a message (ie a message represented by an ordered set) and the frequency of its transmission. The world is so simple at this level that the message itself is simply a frequency, and the frequency of the message is measured by us as the line weight of some energy / frequency / momentum that we can measure.
The criterion for a stationary state is closure.
COMMUNICATION = REFLECTION.
. . .
I am a private network to some extent under my own control, a fact assumed by the makers of commandments and laws designed to constrain my behaviour through my voluntary assent to the law. Laws can also be enforced by violence, killing the deviants.
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Those of my features which are outside my control serve as input data for my life like all the other inputs coming from my environment. On this definition, my own body is part of the environment of my conscious (and somewhat controllable) mind. My mind, insofar as it can operate independently of my environment, is analogous to an isolated quantum system, under self-control, just like God. [I am also subject to insights, which like quantum jumps disturb the continuity of resting consciousness]
The core of Christian doctrine is that since the Fall we have not been capable of effective self control without special grace from God. Fall of Man - Wikipedia Divine grace - WikipediaHere we are concerned with control, obedience, law, grace, etc from a cybernetic point of view.
A good computer program can repeat the same algorithm again and again provided that it does not get stuck on an error and become unresponsive to its input. The same for a car engine, which continues to cycle until its parts become so worn (erroneous) that it cannot go on (provided it has sufficient fuel and lubricant).
On the one hand, every sentence here seemed important enough to write down, a step forward, and on the other, I often momentarily despair of ever reaching my 'goal', which I hope I will know when I see it.
We begin with one item in one pigeonhole. We turn to two items and two pigeonholes, and find that there are two ways to arrange them [as long as the items and pigeonholes are distinguishable]. Then we go to three items and three pigeonholes, finding that there are six arrangements all available by sequences of swaps. In fact it is time to stop being lazy and work out the transfinite symmetric network in as much detail as Turing worked out his machine. Group theory and Quantum Mechanics - Weyl. Weyl
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Personal immortality is not on the cards for a while yet, but it might be possible for the species to live until the sun dies.
The Universe is quantized because it is the unique event.
Monday 24 August 2009
Wiki dictum: 'In nature everything is continuous'. Continuous function - Wikipedia The arrival of quantum physics showed this needed modification, but it was generally held that the discrete events of the Universe emerged from the continuous evolution of isolated quantum systems. Zurek showed that quantum jumps are necessary for the transmission of information during observation, but left unanswered the question of why the wavefunction collapses.
In a sense, the discreteness and continuity of Hilbert spaces are artefacts of the view that a function comprises a mapping between a domain of points and a range of values. We allow the relationship between domain and range to be expressed by real of complex numbers, and we assign one dimension of the function space to each point in the domain. When we come to discussing the action of operators on function spaces, we show that these operators have as many eigenfunctions and eigenvalues as the dimensionality of the space, something not surprising, because we put it in 'by hand'. In a way it is simply a consequence of the mathematical notion that a continuum is made by crowding enough discrete points together.
Perspective: On energy and entropy
PHYSICAL = OBSERVED
Tuesday 25 August 2009
The Father's observation of Himself is the Word, ie an image of himself which is not Himself, ie orthogonal to Him. So we see Thomas' model of the Trinity as isomorphic to quantum theory (which we take to include quantum mechanics and its applications, including quantum field theory).
Quantum field theory is concerned with the creation and annihilation of particles, that is the writing and erasure of memory states in the Universe. The existence of memory, we feel, requires the existence of space.
Is the 3D-ness of spin a cause or a consequence of the 3D-ness of space?
It is easy to get bogged down in details, as I do with physics.
No state in the current Universe is isolated as we see from Feynman diagrams which couple a state of interest, eg the electronic energies of a hydrogen atom) to all the events that influence it. Feynman diagram - Wikipedia
Although theology has become largely discredited as a science over the last few centuries [this] does not necessarily mean that it is dead yet.
DYNAMIC (SYMMETRY) = OPERATION, eg not-p corresponds (among thousands of other things) to spin flip.
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Wednesday 26 August 2009
Why am I tense? To me tenseness is closely related to anxiety about performance, ie can I execute this task without without error, error counting all possible failure modes (like falling off the ladder, or a screw missing its desired substrate). And landing a plane (which I do not do) one is probably always conscious of the possibility of error, which is reduced by training and experience.
Error avoidance, clearest in good software, means searching the space of possibilities for paths to failure and avoiding their beginnings, as when approaching a corner one slows down sufficiently to bring the probability of success into an acceptable range. Then there is safety and little tension, whereas if one is racing for some reason, one may corner more riskily. What we are seeking is the window into a secure future on the planet, ie a sustainable system. An important aspect of sustainability is to improve the timing of our responses to changing phenomena, that is to increase our knowledge of the world and its possibilities by employing more scientists to delineate the way things are and more technologists (artists) to explore the implications of the way things are. We might take a note from our own physical makeup in which nearly half our processing (measured by energy consumption) is devoted to information processing.
In fact most of my tension when I think about it arises from self imposed (in return for a payment) obligations to other people, ie work. Luckily I am approaching retirement age.
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Good software, like quantum mechanics, is linear, meaning that all interactions are local and complete, concerning only the agents involved and having no effects on the non-involved agents (innocent bystanders). [This is 'object oriented' programming and this might explain why the Universe also is object oriented, ie particulate]
Such activities can also be called private, and so we think that private memory (ie private property) is the key to linearity.
Linearity increases with entropy (?) since there are more independent degrees of freedom = independent memory locations.
NONLINEARITY = gossip behind one's back, ie private matters being dealt with in public, ie interaction / communication which if itself is non-linear and non-reversible.
From experience I think gossip can be fun and even valuable, as long as no one acts upon it. One's relationship with every person must be based on direct communication with that person. Of these things about which we cannot speak, we must remain silent.
Good laws attract their own enforcement. If you don't speak the language you don't couple and you are invisible. This is my problem and I am trying to develop a model spectacular enough to attract attention to myself, and trade.
The special thing about quantum mechanics are its new ways of computing probabilities with little arrows, as Feynman explains in QED. Feynman
Thursday 27 August 2009
ORTHOGONAL = INDEPENDENT PHASE
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The simplest Turing machine: read p, go into state not-q; write not-p, go into state q; write p, etc. No need for stepping L and R since tape has only one square, so that only one state can be written on the tape at a time.
Then to a machine that adds a square to its tape and then steps back and forward between the two squares in a way which correlates with the states, given four possible states, but maybe, some connection between them so that p(00), P(01), p(10) and p(11) have different probabilities which nevertheless add up to 1.
The dynamic element of the Turing machine has no memory, it is all on the tape (making the dynamics potentially universal).
When we Fourier analyze a car engine, we get a set of frequencies and phases, like an atom. Can we look at the Turing machine dynamic as the Fourier transform of the Turing tape. Further, following Landauer, we see Fourier transformations as embodied in the physical world.
The Fast Fourier transform Fast Fourier transform - Wikipedia
Here we are taking off on another flight of fancy, seeing where it leads. This flight, like all the others in this notebook, is tracked to some extent by these words. So we see a particle as the transform of a field and ask which is more real, the particle or the field. We answer with Aristotle that they are principles of reality and are always concretely united
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in the real like forms and energy (erstwhile matter and form - in modern physics, matter = energy matter - form -act == matter -, ... ,). So we can understand particles as form (static messages) and field as energy, the superpositions of possible acts. We overcome the zero point energy problem by the conservation of energy: everything is not excited at once (ie every particle is not in existence at once [every message is not sent at once]), but excitation is passed on from one form to the next, and conserved, so we see time, action and energy all flowing along together. Every action, pure act in itself, receives an identity from its input and output, so we may see a photon as pure act (with polarization?).
Act defined by before and after. He killed her means before his act she was alive, after it she was dead, acyclic.
Fourier transform tells us the amplitudes of different frequencies in a signal.
Signal = physically embodied (form and act)
Symbol = abstract (form alone)
CONTINUUM == NO (resolvable) DATA
We build the Turing Universe in the same way as Turing built his machine, from binary to transfinite.
Although the symmetric univere is transfinite, we understand it best in finite digital (preferably binary) form. We build a Universe using two components, form and action. An action transforms one form into another. The nature of the action is defined by this transformation, however achieved.
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Initial singularity, one form, one action, essence == existence.
It is an historical question whether form:action:: essence:existence.
We build a model Universe with a binary tree, since the best entropy/energy ratio is binary signals (?) Gatlin
We can accept what Thomas says as being about the world because his only mistake was to think God was not the world, because all his proofs for the existence of God are wrong. He assumed that act was superior to potency (power) but that is not the case: act and form both contribute to what happens: the world is concrete; we merely abstract from it to describe it in words, in a formal way, but we know that behind every macroscopic act there is a countable infinity of microscopic acts.
Mathematics is the study of mapping, ie transformation. Maps may be at constant entropy (1-1) or be compressed (abstracted) or expanded (interpolated).
The most general transformations at constant entropy are permutations, which may then be restricted by constraints like 'continuity', in which the permutation retains the order of its domain and merely moves everything along one, bringing the last back to the first.
Friday 28 August 2009
Dawkins: God Delusion DawkinsSEXUAL SELECTION / RELIGIOUS SELECTION
Dear Doctor (Professor, TV star) Dawkins . . .
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REAL RELATIONSHIPS can be mapped to symbolic logic.
Dawkins page 19: 'I prefer not to call myself religious because it is misleading. It is destructively misleading, for the vast majority of people "religion" implies supernatural.'
Gutless! Religion is always with us and must be reformed, not denied. 'Science and reason' must reclaim the term.
Natural selection works at every level, above and below us. Since its power is unlimited in terms of the number of variables that may be selected for. Every space begets transformations of equivalent complexity (entropy). So a specific network (organism, country) is selected in competition with all other peer networks.
A RIGHT is a domain of NON-COMPETITION
Once established, a right should not need fighting for, but social momentum, which keeps the old alive [means that it takes time for a right to become 'fixed' in the social constitution].
John Howard's belief that a Bill of Rights would take away our rights is unfounded. The Bill of Rights is a law like any other to be interpreted by judges and changed by the legislature or the people if they see that the wording is not leading the judges toward a collectively decided goal.
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Attack the old God, or build a new God? Dawkins likes attacking but his simple mechanistic mind seems inclined to throw the baby out with the bathwater (and how much more valuable is a baby than a tubful of used water?).
A partisan in his own mind in a good cause. But it is a mistake to destroy an old service [before] the new one is ready, because then you are without service.
Dawkins page 31: 'I shall define the God Hypothesis more defensively: there exists a superhuman, supernatural intelligence who deliberately designed and created the Universe and everything in it, including us. This book will advance an alternative view: any creative intelligence of sufficient complexity to design anything, comes into existence only as the end product of an extended process of gradual evolution.
So saying that evolution is not intelligent, that intelligence does not work by trial and error.
Dawkins page 36: 'I am attacking God, all gods, anything and everything supernatural, wherever and wherever they have been or will be invented.'
Very model dependent? What do we mean by God? He is merely attacking a certain set of hypotheses about God and showing that they are paper tigers, which does not get us far. What we want is a legup to a model of God which is consistent with the world.
Huxley: 'Agnosticism is not a creed, but a method, . . .
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Conjecture and refutation, with minimum momentum, tracking reality with maximum fidelity. Popper
Dawkins page 53: 'If he existed and chose to reveal it, God himself could clinch the argument, noisily and unequivocally, in his favour.
He does, but it is not easy to see through the fog of the past, any more than quantum mechanics was easy to see from the classical standpoint.
REPRODUCTION is the execution of an ALGORITHM
Dawkins page 51: '. . . it is a common error . . . to leap from the premise that the question of God's existence is in principle unanswerable to the conclusion that his existence and his non-existence are equiprobable.'
There is no reason why this should not be so in the minds of theologians (who deal in both the existence and non-existence of God) as it is in quantum mechanics - no reason to be in one state or another, so be in a superposition.
Gould: Non overlapping magisteria Rock of Ages Gould
Instead of being a scientists and accepting religion as a fact of life to be studied, Dawkins the Dictator simply wants to stamp it out. eg page 56: 'I am tempted to go further and wonder in what possible sense theologians can be said to have a province.'
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Dawkins page 61: Gradual evolution = intelligent design [as any intelligent designer who has gradually improved a product over decades knows]. The question is who designs the intelligent designer, and the answer it designs itself by a process of evolution, trying and selecting different designs. So the Universe bootstraps itself into existence by recursive creation.
No matter how gradual creation is it is still quantized so that from one point of view the leap of creation is always the same from not-p to p, where p is any proposition = ordered set = Turing machine.
Saturday 29 August 2009
Why do I wish to make the Universe digital? Because it greatly increases the variety of functions available to model the Universe vis a vis continuous functions whose variety is restricted to the variety of the algorithm that generates them. A continuum is in a sense simply the repetitious execution of some bit of code, eg p = not-p [ie replace p with not-p] (a 'wave function').
The elimination of evil (= error) requires the evolution of a mutually consistent set of algorithms. As TV shows, we like to watch people go to extremes, kill each other, take off all their clothes or (like Dawkins) take an extreme position and live on the resulting controversy. This is part of the creative tendency manifested by Cantor's theorem: every box will be broken and people will think outside it, but the boxes themselves are good because they are simple, closed algorithms which can be successfully completed ad infinitum (like hammering a nail) in a manner which increases the fitness of users. [these 'boxes' are the stuff of work]
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Climbing Mount Improbable = CREATION ALGORITHM Dawkins
Dawkin's model of God is a caricature of the Standard (Theological) Model. Thomas Aquinas
Dawkins page 109: '"Who made God?" . . . A designer God cannot be used to explain organized complexity because any God capable of designing everything would have to be complex enough to demand the same kind of explanation in his own right. God presents us with an infinite regress which he cannot help us escape.'
So traditional theology (which occupied many more minds rather more subtle in their distinction of babies and bathwater) picks an arbitrary initial point and call it God, a point which is in its own space omnino simplex, ie needing no explanation but serving nevertheless (in a way to be elucidated) [to explain] everything else. Some of the attributes of God established by the theologians are self contradictory in a complex system but not in a zero entropy system.
Our fundamental potential (drive) is to order the world for our own benefit, and God is the box that induces that ordering, a la quantum mechanics where box = potential well ==> discrete (energy, momentum) states. Discrete angular momentum (action) states are the foundation of all this.
My practical grandparental drive tells me that instead of wasting time reading about God I should be painting my daughter's house in preparation for the coming child. But it is Saturday so I can climb out of that box and get on with the problems of the overall organization of a living planet as it affects us humans. Dawkins in a reductionist, which is good for breaking old moulds ('pi' the type), but gives little guidance to the new.
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About 40 years ago, as a result of my own conversion (metanoia) I became interested in the dynamics rather than the statics of belief, moving from what one believes to how one changes a belief, and very quickly saw that the method was the scientific method, and for theology to be refounded as science we would have to begin with the hypothesis that the observable Universe is divine. Metanoia - Wikipedia By divine we mean the self contained explanation of its own existence. Why does the initial singularity complexify: Cantor's theorem. How does it complexify? Quantum mechanics. Our guide to the application of quantum mechanics is the proposition (hypothesis) that human insight is (iso-, homo- crypto-?) morphic to the collapse of the wave function. Both find a frame of reference in which an otherwise confusing jumble of experiences fall into a simple order like the theory of evolution or the eigenvalues of an operator [or the heliocentric model the solar system]. Insight = diagonalization.
Quantum computation = quantum diagonalization, finding a simple basis of operations for a complex operation, just like finding a way to build something given a set of operations {cut, measure, plaster, paint, . . . }.
Dawkins page 114: '. . . Darwinian natural selection is the only known solution to the otherwise unanswerable riddle of where information comes from.'
Information = point (path through) possibility space whose value is equal to the entropy of the space.
The ancients were prepared to admit that God was a mystery. Darwin shone a bright light on that mystery by moving the creation of the World (or God) from one sudden event to a huge
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tree of communicating events designed by constraint (selection) on the outcome of a given set of initial conditions (a genotype or ordered set).
DESIGN:CHANCE::INFORMATION:ENTROPY
. . .
Consciousness raising = exploring new possibilities.
The starting point of all religion is the initial singularity = God
Dawkins page 118: '. . . Darwinian evolution, specifically natural selection . . . shatters the illusion of design within the domain of biology and teaches us to be suspicious of any kind of design hypothesis in physics and cosmology as well.'
More paper tiger: randomization and selection is design, as any designer knows. Thinking outside squares is essential to the trade. Conjecture. And then selection (Refutation). Dawkins' fundamental misconception is that the Universe is not intelligent like we are or vice versa, both of us proceeding by trial and error, guided by the memory of past experience.
Mount improbable: replacing a sudden jump with a continuous path. This works right down to quantum mechanics, where we find only a mathematically postulated continuum between the sudden jumps.
Natural selection does not explain the increase in entropy upon which it works. This is a combinatorial thing whose origin lies in bonding. These words are bonded by the paper, but at the origin of the Universe orthogonal dimensions are
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bonded by parenthood = entanglement.
God, as a point in a space comprising one point, has an entropy of zero. But God as a point in a space of two points carries one bit of information corresponding to the one bit of entropy of the space it occupies. And so on. God remaining a simple point reflecting all the complexity of the space in which it lies.
How many electrons are there? The same as the number of times the subroutine electron is called vs the number of times it is terminated.
Dawkins page 153: simplicity, information and entropy.
No mention is made of cybernetics, requisite variety etc, all elements of control theory that implements dynamic designs.
GOD =NOTHING (FORMALLY)
GOD = EVERYTHING (DYNAMICALLY) The living God has a transfinitely complex structure of stationary points which are windows into the divinity surrounding us, ie messages, ie Turing machines.
The selfish gene is a static entity which Dawkins seems to give more explanatory power than the dynamic phenotype that decodes the DNA into a life and passes on some of its text to the next generation.
Dawkins page 158: 'If the argument of the chapter is accepted, [true?] the factual premise of religion - the God Hypothesis, is untenable.'
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Depends of course on the model of god used by the religion in question. Natural Religion - God = Universe.
MAXIMUM ENTROPY = POTENTIAL FREE (all elementary events equiprobable).
Dawkins' preoccupation with text and formal arguments is a repetition of the fundamental error of all 'religions of the book', that they are not well equipped to deal with dynamics. Newton's introduction of calculus showed us how to deal with continuous dynamics. Theology must learn to take on the much more complex dynamics of digital networks (where by digit we mean some discrete symbol, orthogonal to its peers.)
HUMAN RIGHTS = ORTHOGONALITY
Dawkins page 164 quoting Richard Lewontin: '. . . one point which I think all evolutionists agree upon, that it is virtually impossible to do a better job than an organism is doing in its own environment.'
This goes for Theologians, of course!
The by-product theory of religion, Dawkins page 172 sqq.
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