VII Notes
2010
Notes
[Sunday 2 May 2010 - Saturday 8 May 2010]
[Notebook: DB 68: Salalah]
[page 353
Sunday 2 May 2010
Feynman 17: Feynman
[page 353]
The rules of quantum mechanics give us the traffic in various channels.
Creation: The purpose of this article is to display the isomorphism between the classical Christian model of God and quantum mechanics. Following the time honoured method of the physical sciences, we first look for a mathematically defined space that defines a large set of possibilities and then seek functions on thart space that mimic the observed probabilities of various events. We assume that God comprises everything that exists, that is everything that can be observed and decoded from these observations. Quantum mechanics is, we shall say, the alphabet of physics. It defines the broadest set of rules which constrain the observed Universe within the Universe of possibilities, which is, for quantum mechanics, Hilbert space.
We might trace the origin of the classical model of God to Parmenides, whose vision convinced him that motion was rather illusory and real reality was eternal, outside time, what we here call formal. Plato introduced the set of unchanging forms that defined corresponding realities here below. Aristotle, Aquinas, Thomas, Lonergan, Jeffrey.
Our fundamental insight is that dynamic systems have stationary points, conserved features which are nevertheless are subject to a higher dynamics, recursivity. (The couplings are extremely light.. The atoms with me probably cannot tell that they are part of a living system rather than a 'dead' solid, their spectra are the same.) This enables us to see our Universe at once as divine pure act and practical formal complexity realized as the algorithms that are realized by the Universe.
[page 354]
We observe that all messages are digital, compounded of strings of symbols like this sentence. You might object that the speedo in your car is an analogue instrument, and that there are many analogue channels of communication in our world, like the old vinyl records. All of these can be approximated digital;ly, and since the turn of the last century quantum mechanics and physical theory all confirm that all the fundamental messages in the Universe are quantized like clicks of a Geiger counter or ticks of a clock.
Shannon's model, and Zurek's translation into quantum mechanics.
Quantum mechanics fundamental linear law:
|ψ> = ∑i Ci |i>.
the |i> are vectors representing a certain event. the Ci are the amplitudes for that event on the distribution |ψ>.
An application to human sexuality. Aristotle and his followers distinguished layers in the human form, attributing to us a vegetative soul which controlled those functions of growth which we share with plants, an animal soul which we share with animals and a special human spiritual soul which makes us specifically what we are. From the modern perspective, we are an animal which has come to be after billions of years of evolution which began with the first self-replicating forms. Our animal features evolve relatively slowly, and we might expect ten thousand
[page 355]
years to be the period required to make notable changes in the phenotype of a human or other animal population. Of course intensive breeding can yield higher rates of change than natural selection except perhaps under extreme natural conditions. Social systems, at least in recent times, evolve at a rate whose time constant is roughly a generation, and the education of each new generation is substantially different: curriculum reform.
Quantum mechanics: stationary states and fixed points. A differential equation is a fixed point, as is every complete sentence of the form ab. Physics is an interplay of cardinal and ordinal arithmetic, the ordinals being hypothesized to give meaning to the observed distribution of cardinals (measurements, eigenvalues).
|Φ> =Â|Ψ>,
|Ψ> and |Φ> are input and output; Â is a [network of] Turing machine[s] (computer[s]).
Monday 3 May 2010
Unobserved quantum systems are not quantized because there is no communication.
Chemical nomenclature and ordered sets. IUPAC nomenclature - Wikipedia
Feynman I-9: '. . . there is nothing that living things can do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics.' Feynman
CONTINUITY - SYMMETRY
'collapse of the wave function' = symmetry breaking.
[page 356]
'We speak of probability only for observations that we contemplate being made in the future.'
Pure actuality is the foundation of symmetry because all processes are on an equal foting, unlike the potency / act theory where the potencies require actualities to activate them. What quantum mechanics tells us [is] that there is a conserved volume of actuality which moves around in the symmetric Universe.
Going all the way to the proposition God is isomorphic to quantum mechanics (via initial singularity). Does this make sense - new interpretations of old ideas.
Quantum mechanics tells us the statistical behaviour of imperfectly resolved systems at the edge of reality, the edge of resolution. Insofar as God is omnino simplex it is completely unresolved. The interaction of two unresolved systems can give us a message, it is a message.
An act is an undifferentiated event, even though in the concrete world every act is part of a logically continuous process stretching back to infinity.
Deterministic logical continuity (broken symmetry)
Random logical consistency (symmetry).
We might guess that quantum mechanics is linear because it is simply cardinal arithmetic and the units we are counting are quanta of action.
[page 357]
Tuesday 4 May 2010
Having argued that the isolated quantum system is isomorphic to the classical god, we now turn to 'broken isolation', the emanation of structure within God, the doctrines of the Trinity and quantum measurement.
Here we have a blank page and no ideas. Now for the first cigarette of thje morning!
Quantum mechanics = God I: Both are the source of all structure in the Universe. The initial singularity is subject to logical confinement.
We might say that ih dψ/dt = Hψ is a fundamental equation of mathematical theology.
The large scale structure of the Universe represented by Einstein's equation G = T is the simplest structure consistent with a network of inertial frames each of which is isomorphic to a computer and in some way bale top break its inertiality by communication with other frames through the structure of spacetime we call gravitation.
We do not have the emanation of structure from a source (as imagined in the Tantra?) but the immanation of structure within a dynamic system. We creates structure by bifurcation, a process that requires second order differential equations ('consciousness of one's own process'). The first bifurcation we imagine is that of energy into potential and kinetic energy.
Isolated systems: god, initial singularity, inertial frame, isolated quantum system. What is common to these four candidates?
[page 358]
Bifurcation into space and time,energy and momentum.
Through second order differential equations, one has two degrees of freedom, eg position and velocity. We can change position with velocity and velocity with acceleration.The principle of inertia suggests to us that velocity is 'nothing' (isolated, inertial) and the fun starts with acceleration, a result of communication between isolated systems.
Isolated systems are linear, meaning that everything is deterministically connected to the values of one variable (scalar, cardinal). We lump variables into packages like vectors or myself, a very large system of variables that follow one another around as me.
. . .
Casti: How can a fixed point theorem go wrong. Ie what are the necessary conditions for it to be true, so if condition is not true, theorem is not true? Casti
POTENTIAL = MEMORY = ENVIRONMENTAL SETTING
Point = any closed set (in a space of isolated sets) or an open set (in a space of coupled points).
Casti page 51: Euclidean geometry preserves line length under translations, rotations and reflections. Kelin: each geometry is defined by its group of transformations and the invariants of these transformations. Erlangen program - Wikipedia
Casti page 54: 'homeomorphisms' Homeomorphism - Wikipedia
What is a point: something that acts as a unit.
Casti page 55: equivalence class - canonical representative: species -= holotype. Topological equivalence = the same network with all the same connections but different levels of traffic along the edges.
The entropy of the Universe is bounded below but not above, like the transfinite numbers, each of which is the least upper bound of its predecessors.
Motion: homeomorphic (constant entropy) transformation.
page 63: Determining fixed points is the same as solving equations.
n! ordinals correspond to each cardinal n
How do the concepts 'compact' and 'convex' apply to the transfinite symmetric network? Compact space - Wikipedia Convex set - Wikipedia
Compact: contains its boundary
Convex: line joining any two points is wholly within the set.
Automatically true for a network in which we consider either the nodes of the edges to be points in our set.
What is the power of proof? Does Brouwer's fixed
[page 360]
point theorem bind god? It does insofar as its opposite is inconsistent and we hold that god is internally consistent.
Wednesday 5 May 2010
Creation: increasing the number of fixed points. Mathematics is the study of fixed points = fixed relationships.
REGULATION (of anything) = CYBERNETICS
Thursday 6 May 2010
Zurek 2003: 'How can one then establish correspondence between the quantum and the familiar classical reality? Zurek
Quantum/classical border: classical = error free = quantized (Shannon)
Reduced density matrix: Nielsen and Chuang page 107. Nielsen & Chuang
It seems that the classical view that continuous functions are deterministic is an error, since one cannot be certain of the location of a point in a true continuum. Only quantized systems can be deterministic a la Turing machine.
The structure we envisage is bounded below (by God, the initial singularity, or just a mathematical point) and it is this bound that gives the Universe the structure we observe. It is not bounded above and we take the Cantor Universe as a stating model for this evolution, since it begins in the zone of discrete countable entities (that can be labelled with
[page 361]
the natural numbers) and grows from these without bound.
Data
The empirical basis for this article is my fortunate life. Not all the fortunes were good, and none of them were predictable at my birth, I grew up in a small Australian country town as far as you can imagine from the European culture tjat peppered the town with churches and clergy. I was brought up Catholic, and at the age of 18, entered the Order of Preachers, the Dominicans . . . blah blah.
The theory we have developed enables us to give some formal foundation to the terms open mind and closed mid. While the closed mind attends to the alphabet of human life, the open mind explores what can be done with this alphabet, ie if closed mind is equivalent to layer n, open mind is equivalent to layer n + 1. Open mindedness is the source of dynamics - things can change including minds and mental images. The fundamentalist would bind us to ancient beliefs.
[OPEN MIND = SYMMETRY]
Marriage in the traditional sense is the highest impact form of fundamentalism because the establishment of an indissoluble bond between two people at the most total level is not something that can be legislated if a system is to be stable and not fail through its own internal tensions. [from a formal point of view, the function of motion is the relief of stress.]
The management would say that rigid control of sexuality is necessary for social integrity, While the Church is preaching control of sex it is sheltering its own agents who have totally inappropriate sexual relations with children, perhaps driven by the vow of chastity they are
[page 362]
required to take to enter the higher grades of priesthood.
The school was not so bad [as the Order turned out to be], probably because it has to compete for students in a marketplace dominated by government funded and managed schools via the education department [which had some respect for children's rights].
We create transfinite numbers in the same way that we create sentences out of words and words out of letters and letters out of ink [the continuous, undifferentiated substrate].
Friday 7 May 2010
von Campenhausen Father of the Greek Church von Campenhausen
page 1: 'The "Fathers of the Church" is the term used to describe the orthodox writerts of the early Church.'
'In fact the term "Father of the Church" itself stems from the sphere of dogma and originates in the needs of Catholic apologetics. Patristics originated in the urge to assemble witnesses to the "authentic" orthodox tradition, that it might add the weight of its authority to valid or disputed doctrines.'
page 3: 'The present book is confined to the Church Fathers who wrote in Greek. The Christian literature available to us begins in the Greek world, and Greek theology occupies the leading place in the first four centuries of the Church's history.
page 5: '. . . the acceptance of the Greek legacy was spiritually inescapable and a vital factor in what we now call theology.'
[page 363]
Justin: 'Justin's Christianity is marked by an urge to give practical expression to his faith and by the absolute certainty of his ultimate convictions. Christians possess the truth on which to base their lives; this is proved by the high moral standard of their conduct. The sources from which they derive their knowledge of God as furthermore, undoubtedly reliable. To what extent their teaching fulfils the real mission of philosophy, which, according to Justin, is above all the explore the Divine. [von Campenhausen page 7]
The writers of the Old testament and the Greek philosophers all places the Divinity outside the World. Christianity made a step in the right direcion by making one human Divine. Here we wish to complete the task by makinbg all of us and our world divine, so highly expanding the notion of Divinity.
van C page 10: 'It is clear that [Justin] regards the validity of the Bible as absolute.'
'[Justin] appeared in public in his own name and no longer worked, like the early Christian teachers, within the religious community, but within the new sociological framework of a private philosophical 'school'.' ,p. page 11: 'Like the first Christian teachers, he proclaims that he has received the "gift of grace" for [his] task from God him,self.'
[We can go along with that]
page 38: 'Origen was probably the first Christian writer of whom we know for certain that he came from a Christian home and was given a Christian education.'
page 39: 'Behind the gigantic work of scholarship which [Origen] was to achieve was there from the very beginning an austere
[page 364]
and ascetic earnestness and the iron resolution of a man who never lost sight of the possibility of martyrdom. It may be that in his youth his enthusiastic radicalism bordered on the heretical.'
von C page 40: 'Origen was the first Christian to join the intellectual elite of his age, drawing attention to the teaching of Christianity in a way that forced even his enemies to take notice.
page 42: 'The new element which Origen gave to the Church was primarily the great systematic summary. He was responsible for the change from occasional and superficial interest in philosophy to the methodical study of intellectual problems, from the aphorism of educated discussion to the responsible construction of a well-established theological system.
'None of the later Greek Fathers achieved this integration to the same degree. Origen is the only one to present the whole of Christianity in the form of a workable philosophical system.'
A theory of Peace II [A Theory of Peace (1987)
PERSONAL = FREE (ISOLATED?) Perhaps I am coming to the end of my intellectually isolated phase.
von C page 43 '. . . the sin of departing from God.' Which is what we are doing by treating the world as a happy hunting ground and cesspool.
'. . . fallen Creation.'
The evil we have been doing to the world is only now becoming
[page 365]
clear to us.
von C page 44: 'Origen does not acknowledge the existence of 'absolute evil' or the possibility of eternal separation and damnation. The heretical nature of this idealistic conception is increased by the fact that for him the final restoration of the Kingdom of God can hardly consistently form a final and absolute end. It follows from the nature of spiritual freedom and from the character of divine education (which leads but never forces) that new darknesses and new eras of redemption may be unleashed in the infinite distances of time . . . To him time is not an ultimate, seen from God's point of view. The true life lies beyond time, in eternity. In our earthly state, however, we are not in a position adequately to grasp this eternal being.'
Much of the current conflict in the world appears to have religious roots. A look through history suggests that this has always been the case We can see this in the persistent initiation of males into warriorhood. The complementary passage of females into motherhood it attended by its own baptism of pain and needs no elder applied torture.
GOD - FUNDAMENTAL FIXED POINT.
Equating God and the Universe is the equivalent of injecting time into God and recognizing the invariants of the Universe.
Jesus is a cult of personality. We need to ditch this one person rule and make a cult of (if anything) [the] dynamics of living personalities with one another. While our source is a fixed point (our environment) our behaviour within the confines of the environment is free.
[page 366]
Where our capitalist personality sees tonnes of coal as dollars to be burned, the person awake to the nature of the Universe sees the rather sacred buried remains of ancient life.
Energetic obesity: We consume 100x our basic metabolic rate.
Fundamentaliusm values ideas over reality. Science values reality over ideas.
Fundamentalism: closed mind, a remnant of our two year old intellectual phase imagines ourselves to be at the centre of the Universe summed up in the phrase 'just for us'. (to pollute and trash as we wish).
The whole of Christianity revolve around the existence of an omniscient, omnipotent judge who sees us as we are and judges us accordingly. So it may be, but by what criteria? Something dreamt up by a ruling class justifying and increasing their wealth and power?
. . .
Origin, Hexpla von Campenhausen page 46: Hexapla - Wikipedia
von C page 51: 'The "case of Origien" is the first celebrated example of rivalry and conflict between the free unofficial power of an independent 'teacher' and the authority of his ecclesiastical superiors.
page 53: 'In [Origen's] opinion, the thing that matters in the long run, the living knowledge of the truth, cannot be transmitted and controlled by officials.'
[page 367]
Hypatia Hypatia - Wikipedia
Synesius of Cyrene Synesius - Wikipedia
von C page 140: 'Greek Christianity knew no conflict between Church and State in the medieval sense. There were struggles for power, but they were always concerned with power inside the Church itself. Even the greatest bishops never demanded to be heard on political questions or to make political decisions. On the contrary it was the Emperor, as the Christian holder of supreme earthly power, who ordered and supervised the affairs of the Church. Limits were set to his action only in the innermost spiritual and sacerdotal spheres.'
The worst problem in my childhood was control of what the Church (via the nuns, brothers and priests) held to be mortally sinful dirty thoughts. On modern parlance dirty thought = game over for you.
von C page 141: 'Chrysostom settled in the neighbourhood of Antioch as an ascetic and devoted himself to spiritual exercises and serious theological work.'
Echoes of the weird and ancient connection between the search for knowledge and ascesis, although in fact (?) the mind works at the same speed (near maximum) in all circumstances. Fore 'learning' rather than insight, time on the job is important, but mentally we are always on the job, surviving from moment to moment, some more error prone than others.
'Monasticism was already widespread in and around Antioch at this period.' Why? 'The monks were the saints of the people who went on pilgrimage to their caves and cells, and they included distinguished theologians in their ranks. They quite
[page 368]
often supplied the Church with its leading clergy and bishops.
Chrysostom John Chrysostom - Wikipedia
Saturday 8 May 2010
Clancy Trauma Clancy
Layered networks are ubiquitous, and networks may be networks of networks. Dynamically, a network may be analyzed as a set of computers, inputs and outputs. Statically, a network is a set of memories (ie addressed locations where information may be stored through time) and messages which are stored and forwarded in the memories. From a physical point of view, memory is spacelike, ie a filing system for events (messages). We can represent the dynamics of a network by considering a (time) ordered set of such spacelike slices. This approach is very close to that taken in relativity in which we set out to picture a set of spacelike slices corresponding to an event like the formation of a black hole. In classical General relativity, our spacelike slice contracts to a single point, a singularity. This singularity is considered to be separate from the surrounding spacetime,since it has no structure and cannot communicate because it is spacetime for itself. A structureless entity can be nothing other than a perfect copy of itself, as has been explored carefully for more than a thousand years by those seeking to model the Trinity (Augustine, Thomas Augustine Aquinas).
The study of child sexual abuse and its consequences gives us a model of now networks may be damaged by
[page 369]
inappropriate communication (cross talk, corruption).
Performing a dangerous task requires a careful consideration of the possible outcomes so as to avoid the (traumatic) errors, and with luck bring off a perfect operation in which there has been no need to correct minor errprs of procedure (eg bending a nail).
Splinter under the fingernail: a large amount of pain for a tiny injury and then we must face the probkem of getting it out without more pain.
Quantum computation is analogue and error prone. Classical computation is digital and error free. We can imagine the transition along the lines of Dawkins Climbing Mount Improbable, one small and selected step at a time. Dawkins This we call creation, ie the generation of time invsriant spaces and structures.
Binning and counting = selecting eigenfunctions and counting their rate of repetition. The Large Hadron Collider is fllled with physically realized observables (the detectors) which perform this task which was once done by physicists looking at photographs of cloud and bubble chambers, emulsions and so on. CERN, Bubble chamber - Wikipedia
Collapse of wave function = act of creation = emission (and reception) of a particle = message. Quantum mechanics works in the time domain and somehow generates structures in the space domain. We understand the space domain (con-constructively) as stationary points in the time domain, ie regions where time stops, ie there is no energy attributable to the state, ie stationary = zero energy.
[page 370]
Competition brings the best out in me so I motivate myself to battle on with the equation God = Universe (God - dynamic = Universe (set of static)) by mentally challenging the Congregation for the Doctrine of the Faith. Holy See
From dynamics to statics via calculus. Calculus is in a sense recursive because its differential equations are themselves static, but then we can make differential equations of differential equations so describing a higher (deeper?) layer of stasis and the dynamics of which this stasis (differential equation) is a fixed point. So we are entering Hofstadter's world of symbols talking about themselves whose dynamics define the limits of representability represented by the transfinite computer network and quantum theory.
How does the network take us from unobservable quantum machanics to observable quantum field theory. The particles are the messages, the invariants, the symmetries of the otherwise invisible dynamic process. The simlpe fact is we cannot observe an isolated system because to observe it is to break its isolation.
I offer my enterprise, the Theology Company P/L as a consultant to revise the theoretical foundations of the Congregation for the Doctrine of the Faith.A 20 year plan, constructed in the open community.
TTC's first client is the RCC.
Zurek 2007 meets Shannon 1949 through the requirement of orthogonality for communication. Zurek Shannon
[page 371]
The transition from unitary to observed is unspeakable? It is also based on the symmetry (lack of order) of the basis states.
Quantum jump = jump into an orthogonal basis, We write it out in symbols. To understand the meaning of these symbols one needs the sort of minimal grounding in the application of linear algebra to function spaces to be found in books like Feynman or Nieldsen & Chuang. Otherwise interpreting the symbolic argument as a series of replacements of one symbol by another, the symbolic transformation represented by the = sign and implemented by computation.
Orthogonality meets Shannon's criterion for indistinguishability.
The basis vectors of a Hilbert space are orthonormal but have no order among themselves. When we iuse the inner product to compute the length of a vector there is a natural pairing. When we use it to compute the angle between two diferent vectors se can pursue a similar ordering or we can permute one of the orderings with respect to the other to get an inner product that represents what? aleph(n)!!
Now somebody's theorem: if |v> and |w> are individually normalized, all dot products of the permutation of their bases remains normalized.
The superposition/selection model applies to all scales, so a first a system acquiring new data (ie being observed by a new operator) is confuded and then it slowly recurses itself to a stationary solution.
[page 372]
Confusion = continuum = superposition of all permutations.
We can best understand ancient theological models if we release them from the institutional forces that try to constrain the meaning of these structure, by, for instance,limiting the recursive creation of divine persons to 3 rather than let it grow to a transfinite numbner
Similarly we are all divine and not just Jesus.
Similarly all particles can be created and annihilated, just like us.
Recursive procession of the word and Heracleitus. Panta rhei except there are stationary points. Daniel W Graham
