Notes
[Notebook: DB 58 Bringing god home]
[Sunday 30 April 2006 - Saturday 6 May 2006]
[page 106]
Sunday 30 April 2006
The network model gives a way to deal with the problem of superpositions. It is assumed by quantum computation theory that superposition is real and gives great power to quantum computation because it allows a large or even infinite number of processes to be executed in parallel. Lo, Nielsen On the other hand, we wish to abide by Landauer's hypothesis that all information is represented physically, that is to say, observably. Landauer
. . .
[page 107]
. . .
The general theory extrapolates form the local structures observed in inertial systems to the whole Universe. In other words it gives us an overall picture of the consequences of communication delay in a structure formed by communication.
LETTER : WORD PART : WHOLE
My purpose is to present a revised standard model to the theological community which will be acceptable to the scientific community, thereby unifying the two after x hundred years of rift. Built from the same ingredients that Thomas used: observed phenomena; a tested explanation of the phenomena; a symbolic system in which to represent both phenomenon and explanation.
All the features of special relativity arise from the finite velocity of light. As c approaches infinity, we approach Newton. All the structure of general relativity follows from special relativity and the equivalence principle.
LIGHTCONE <--> PHONECONE <--> MAILCONE, SHIPCONE, etc
Every observation is an exchange of messages. So we find in quantum field theories that particles in relative motion see the same Lorentz changes in one another as human observers do, and react in an appropriate manner.
Invisible alternatives interfere.
The distance between quantum theory and theology is short. [[quote (Hilbert? 'that's not mathematics, that's theology. In both we have a visible
[page 108]
process believed unable to account for itself, driven by an invisible process that gives meaning to all the observed events.
The Catholic church rules by fear of losing a vast [fictitious] reward, one which will cost the Church nothing while giving it means to harvest a magnificent income and live a magnificent way of life.
Monday 1 May 2006
SYMMETRY = PROTOCOL
A set is defined by its elements and the elements of sets may be sets. From an abstract mathematical point of view, we consider sets in two ways. First as a collection of amorphous entities which can be placed into correspondence with the natural numbers and so counted. Each set can then be assigned a cardinal number, the count of its elements. At the beginning of the numerical hierarchy is the empty set, the set with no elements. The existence of the empty set suggests that even though a set is defined by its elements, it is nevertheless a conceptually distinct entity. The empty set is a unit which can be an element of another set whose cardinal is [1]. There is only one empty set, so we cannot construct a set of cardinal 2 by putting to of them together. Instead we use Peano's idea of adding one. In set theory we get a set of cardinal n + 1 by enclosing the set cardinal n and all its elements in another set whose cardinal number thereby turns out to be n + 1. In this way we create a formal method for creating any given natural number simply by applying the method the right number of times. All this palaver we abbreviate into the set N of natural numbers, N = {0, 1, 2, 3, . . . } the dots representing repetitions of the method of creating new sets (and new cardinals). The set of natural numbers contains all the formal entities that can be created by the method (or algorithm) stated.
[page 109]
Physics and mathematics enjoy an intimate relationship that goes back many thousands of years. It most probably arose with counting physical objects like beans and sheep and developed as measurements of the environment became more complex. We can see an early high point in the understanding of perspective and the creation of anamorphic paintings. Geometry remains our preferred way of modelling and understanding the physical world, giving us a visual represent[ation].
We have two apparently incompatible areas of mathematical physics gravitation and quantum mechanics. Will the network concept unify them?
MTW page 191: The problem is to fit together local flat spacetime descriptions of physics into an overall view of the Universe. Misner, Thorne and Wheeler
curvature - parallel transport - geodesic (inertial path)
M T W page 197: Elie Cartan : Newtonian and Einsteinian theories can be described in terms of curvature without using a metric.
Tuesday 2 May 2006
Calculus of variation (de Maupertuis, Lagrange, ) = mathematics of evolution.
We may model the world as a set of series converging to moving targets. Homeostasis --> tracking.
Tracking = move - observe (warmer or cooler) - move (in the desired direction, ie toward the warm = vicinity of target.
Aristotle says a little error at the beginning . . . . This is the deterministic process. The scientific
[page 110]
does not care how wrong it is in the beginning because it has ways of detecting and correcting errors in its model by comparing them to well tested observations of reality. This gives science a wonderful sense of security arising from its basic article of faith - the consistency of the world. If our observations do not fit our model, we know that it is the model that has to change. Authoritarian enterprises are built on the opposite idea, that reality must be made to conform to the model.
One by-product of bringing this project to a satisfactory conclusion will be to feel unified again. The transition from one state (Catholic) to another (natural) has occupied about forty years, during which time it was often hard to know what to believe in; an inconsistent model can lead to behavioural difficulties as in the extreme when a system destroys itself (effective suicide). Things have never been this bad, but the numinous power of my Catholic upbringing often led me to hide from the things I was finding. It is a mental transition akin to the transition between classical and quantum.
This is not just my problem. We are all parts of a vast system with deep authoritarian roots which must become scientific if we are to survive. In other words we must tailor ourselves to the world in which we find ourselves if we want to live in harmony with the Universe, ie in harmony with god. Getting to this point may take a little pain, a prerequisite of every religion (who said this?)
[page 111]
Classical: The complexity/cardinality of the mathematics is equal to the complexity (cardinality) of the world.
Quantum: the cardinal of the observable world is infinitesimal compared to the cardinality of the process behind it.
The perennial philosophy, as anthologized by Huxley, sees a divine controller behind our experiences of the world. Huxley Most of these authors considered the divinity as completely beyond human ken. Here we suggest that our physical models of the world already give us powerful glimpses of the divinity, and there seems to be no limit to how far we can move along this line of development. It appears to be infinite in the same way that the natural numbers are infinite. We can always take one more step, whether it is adding one or creating a new alphabet for permutation, ie a new set of building materials.
Horse racing is a scientific exercise. The punters and bookmakers between them construct a model designed to predict the order of the horses at the finish. The actual outcome of the race (recorded on film) tests the model (or in fact set of models, one per punter, integrated by the bookies). And depending on the governance of the races, the actual ability of the horse and jockey may have more or less influence on the outcome.
NETWORK == SUPERPOSITION ie 'simultaneous' (complete) access to all the elements of a set of states.
STATE == FILE == ORDERED SET
The boundaries of order (correlation, meaning) are the limits to communication, which limits the size of superpositions (and or creates a hierarchy of distances between elements of a superposition?)
[page 112]
Any node in a 'complete peer network' is a state which can 'download' any other state on the network while simultaneously uploading itself [or parts thereof]. So each node may be considered to be an observer which can 'se' the states of the other nodes. It does not have the entropy (cardinality) to see them all in complete detail, but must be content with a somewhat blurred look whose information content is equal to the entropy (bandwidth) of the observer.
I observe my friends n conversing with them. A conversation is a series which may diverge or remain within certain bounds, or converge to a fixed point. A conversation is an harmonic (anharmonic) oscillation.
PEER == ELEMENT OF A SUPERPOSITION (All peers of a given set have the same cardinal). With an alphabet of length n one can establish n! peers. Electrons are peers, as are all other particles? Hydrogen atoms (eg). peerage == possible bondage: peers may bind. And no n-peers? They just don't speak the same language.
Communication is limited by computability. Mathematically Turing machine gives absolute bounds, but available resources define practical bounds, which we are always pushing.
The probability of observing a particular element of a superposition is a measure of its distance from the observer, measured by the 'overlap integral' how much of one state is contained in the other as measured by the inner product which is a sort of correlation function. Dimensions where both the multiplied vectors have large components have extra wright in this product. How does this work computer wise? Let us think of computers in the same inertial frame vs those in different frames (moving at different velocities). The two way travel time limits the bandwidth of [causal, meaningful] conversation.
[page 113]
At a certain level of abstraction, solving all problems is a search through state space. An heuristic principle s something we use to constrain (and speed up) this search.
The state space we search is represented by the transfinite network. We permute our alphabet by reciprocally transmitting elements of an alphabet. This reciprocal transmission (permutation) both establishes a correspondence between the two elements concerned, but swaps them.
This could go on ad infinitum and at random, except that communication is a constraint on possibility so possibilities compete for existence, those surviving which communicate most efficiently with the new environment (the 'fit').
Gravitation is a phenomenon which arises solely from conservation of energy and delay in communication, so it applies to all particles and all fields and does not require a particle of its own. Every particle is a graviton in its own way ????
If you alter my state, I'll alter yours. True of electrons and photons etc, but what about people? Hitler altered a lot of people's states but did this change him? Not a fraction as much as it changed them. We must explain phase changes, ie catastrophic events where a small change in a parameter like temperature causes a discrete change of state (liquid-gas etc).
A relayed message from particle to particle, once the first few atoms have begun to form a crystal, or the termites have managed to stack up the first few bits of mud toward a nest. Cellular (= alphabetical) automatonism.
The Lagrangian of the Universe can be written out in about twenty paves (Veltman) which is a bit long winded for a theory of something which started off as an unstructured point, ie an
[page 114]
not-ordered set (ie a system of indistinguishable (but countable) elements, ie identical elements. Veltman Quantum mechanics deals with identity in a beautiful way (Feynman). Feynman
The 'local' theory of the transfinite numbers can only deal deterministically with cardinals less than the 'machine infinity'. Anything bigger must be dealt with by 'defocussing' down to less than local infinity. For human 'counting at a glance' infinity is generally less than 10, probably about 5.
A wiki-seed.
Wednesday 3 May 2006
To explain something = to discover a Turing [machine] that models x = to discover the network protocols used by x.
In my history there was a fairly long period of bitterness running from say 1964 to Palm Sunday 1985. Since then the alternative has been with me and my life has been a slow exploration with enough new visions to keep me at it as intensely as time and other commitments have permitted.
The breakout of an idea is the first operationally clear and distinct (= algorithmic) expression of the idea.
The way ahead is not very clear to me, as this book illustrates. Each snippet displays an interaction between two or a few elements in my explanatory vocabulary (alphabet), and one hopes that these little connections will eventually lead to a network structure that has a place for each one of them and each one in its place. The principal task of natural theology is to explain its own genesis, a task which Lonergan worked on with some success. Lonergan
Lonergan's schemes of recurrent rely on error free propagation to be perfectly periodic. At any level of 'error'
[page 115]
evolution may take place, producing new schemes of recurrence that outcompete the old in the search for resources, so that the overall evolutionary process is 'quasiperiodic', which may be imagined as helical.
Thursday 4 May 2006
One of the greatest selling points of natural religion is its relationship to education. I and many of my peers were taught our religion. This was necessary because the religion is largely bullshit, which is why it has to be enforced by human institutional authority. The natural divinity, on the other hand, has been part of our evolutionary history since the beginning, so it comes naturally to us. Education simply needs to adapt to the nature of the world (including the human world) and needs no other guide. On our assumptions, this guide is fitly called divine, since we are guided by the whole (infinitely complex) structure of the world.
Formalism. The root of formalism is the ordered se, that is a collection of elements with a certain set of relationships between them. Our paradigmatic ordered set is the natural numbers in their natural order, beginning with 1 and adding one to generate each successive number. We can see no formal limit to this generative process, even though a classical physical representation of even a fraction of these numbers might use all the matter in the Universe. The equivalent of 0 is the complement of the set f natural numbers?
As Cantor noted, the idea of ordered set can embrace everything thinkable, that is anything representable (in, for instance, the states of neurons in a human brain, or the sort of highly encoded message we are using here which our heuristic model suggests is generated using states of neurons in sensory and motor circuits
[page 116]
transduced to states of muscle cells, so that I sit here writing.
Friday 5 May 2006
My own history is my most certain evidence for the consistency of the model I wish to present. The first 25 years of my life becoming more and more deeply entangled in the contradictions between the doctrine of my religion and the world as I found it. By entering a religious order, I not only undertook an extreme form of exertion ('supererogation')in order to gain a place for myself despite my apparent failings.
This contrasted with the evolutionary viewpoint which seemed to give a reasonable explanation of my deviant tendencies, including a tendency to search the space of alternative religions to see whether it is possible to find one consistent with nature, as revealed by science.
A model based on the theory of transfinite set devised by Cantor and his successors. Set theory is itself an application of the predicate calculus, which also defines the space in which Turing machines, Gödel statements, probability theory, quantum mechanics and relativity theory all take place. We start with set theory because it is a graphic representation of arithmetic which helps us to see the structures that can be encoded in numbers, that s cardinal and ordinal views of sets.
The view of the gulf between Church and world came clearly into focus when I read Lonergan's Insight. In my interpretation, Lonergan was using a theory of knowledge to constrain the ontological variety of the world. The world he claimed, contains an unintelligible element and cannot therefore be god, whom common sense and traditional doctrine demand to be completely intelligible. The unintelligibility he calls empirical residue, messages from the from the environment which are observable but meaningless.
[page 117]
Quantum mechanics, on the other hand, is sufficient to provide a symbolic element to map onto every allowable state of the world.
Each new child builds its operational repertoire by imitation and 'education', guided (forced) imitation.
Randomness does not necessarily equate to meaninglessness. (Chaitin). Chaitin
Personal experience is a source of theological and religious data because theology and religion are specifically concerned with human feeling, fitness and survival techniques.
Schneidman et at: 'Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440:1007.
'Here we show, in the vertebrate retina, that weak correlation between pairs of neurons coexists with strongly collective behaviour in the responses of ten or more neurons.' Schneidman
