Notes
[Sunday 13 September 2009 - Saturday 19 September 2009]
[Notebook: DB 67: jciii]
[page 185]
Sunday 13 September 2009
Our connection is not with a mysterious absolute as many monks, mystics, eremites, popes and even scientists would have us believe, but with one another. We are all one species, can all love one another and cooperate with one another to create sustainable wealth and security.
How can we make meaningful conversation about a meaningless world? It has been a foundational hypothesis of almost all thinkers that human thought and communication processes somehow contained a clue to the nature of the world. Augustine went so far as to use human psychology and human relationships to explain the Trinity of Persons in God. Lonergan tries to use it to prove the existence of God. This is true to the extent that there is no need to prove the existence of God once we understand it correctly. God, like his alter ego, the Universe, obviously is.
Monday 14 September 2009
The quantum computation people assume an infinitely accurate transfinite process accessible to us through the continuous function theory of Hilbert space, which seems to me unlikely. Nevertheless, this transfinite power is available to us in the classical domain through permutations of discrete symbols as Cantor saw. This works through meaning. My name, for instance, may be the value of a variable in a computation,
[page 186]
and since I am a transfinite reality, this computation is manipulating a transfinite set as a unit. The physical meaning of a set is available at each transfinite level, so people are perfectly defined units, defined dynamically to be the individual life, ie individual process, ie a set is a pure act.*
The transfinite symbolic process model opens physics to theology and gives us the key to a proper theory of everything.
*Our personal identity is absolute even though we are continuously exchanging matter, energy and information with our environment. As human personality is blind to the underlying physical process, so physical processes are blind to the meanings (roles) attributed to them by living personalities.
The ratio of continuous functions to all possible functions of a set onto itself (permutations) is easily computed. The total number of permutations of a set of n objects is n!. Of these, only n are continuous in the sense that the order of the elements is unchanged, they are all just moved one place to the left or right to realize the cyclic subgroup of the group of permutations. The ratio of continuous functions to all possible functions is n/n!, which in the limit of transfinite n becomes aleph(n) / aleph (n+1). Transfinite arithmetic.
Communication theory tells us that error free correspondences can only be established by discrete entitites.
[page 187]
Tuesday 15 September 2009
We see the Turing machines as logical continua. All have an initial point. Some end (halt) and some don't (non-halt). We may also think of physically embodied Turing machines as engines which perform some task as long as they are supplied with action (energy) and the cycle of operations is unbroken (ie the ignition is left on). Life, on this picture, is an engine.
All continuous mathematics, as applied to physical systems, is a statistical abstraction from discrete events. Quantum mechanics serves to predict the traffic on particular channels as represented by a density matrix. A diagonal matrix represents the frequency of transmission of messages from a state to itself, ie the frequency that we will observe the state (?).
All work is writing, ie arranging elements of the world (words, musical notes, bricks) in a way meaningful to the writer and quite possibly to other readers. This document is primarily written to myself to capture fragments of an overall picture of my role in the Universe which I hope one day to assemble into a product that can be traded for income = fitness for myself, my family and community.
Algorithmic computation proceeds stepwise and requires memory.
The primary fixed point in the Universe is represented by the Schrödinger (energy) equation. A measurement (message) is the output of an operation.
The pattern of dirt on my electric jug is a record of the rate at
[page 188]
which I touch it in various places with my dirty hands when I come in for a cuppa.
What is the meaning of quantum mechanics? Some have said that it has no meaning and is merely an axiomatic foundation for algorithms to compute the probable outcomes of various events. Here I think it means that the Universe is a communication network whose lowest physical layer is described by quantum mechanics.
The explanation of everything is the unity of the world: it is one logically continuous process that has spawned a huge number of children (in the object oriented programming sense) which include us. Child process - Wikipedia
Sciama quoted in Deutsch page 335: 'When it comes to the interpretation of quantum mechanics, the standard of argument suddenly drops to zero.' This seems true of Deutsch's book which totally ignores the problems raised for a multiverse by conservation and symmetry. He says all the elements of a symmetry exist at once, as though the ball was to be found in every number of the roulette wheel, overlooking the law of conservation of the roulette ball, etc etc. Roulette - Wikipedia The point about symmetry is that individual outcomes are equiprobable.
Quantum mechanics has no memory. When we introduce memory, we come to quantum field theory. The definition of velocity requires memory, since we must compare two measurements taken as different times and places, so the earlier one must be recorded (stored) for later comparison, just as scientists do with their data, collecting large amounts of it then taking it home to mull over it.
[page 189]
Is a network more than a computer? By network we mean asynchronous processes that require buffering (ie memory) to communicate with one another, whereas in a single computer everything marches to the same clock, so all communications can be realized in one step, ie synchronously, rather like the cyclic subgroup of the permutation group.
The asynchronicity of a network of independent computers enables a network to explore a much greater space (a superposition) that a deterministic computer can do. The storing of superpositions in quantum mechanics is dealt with by ignoring it. In the network view, each element of the superposition is a node (transformation) in the network. This is my feeling, paralleled by communities of people whose influence on one another leads them to places they might never visit alone.
Only an infinitesimal fraction of all possible functions are continuous.
Deutsch's multiverse is just like God in that most of the explanation of events in this Universe comes from other inaccessible Universes so it is no explanation at all. It is so because it is God's will.
Many Worlds: God knows simultaneously all possible futures. [this is as formally impossible as the set which is a member of itself].
The whole content of quantum mechanics is the constraint of continuity, that is no memory [instantaneity] This constraint is broken when memory, ie fixed points, enter the picture, ie the dynamics becomes complex enough [and delay enters].
Lo, Popescu and Spiller: characteristic features of quantum mechanics, complex interference, superposition, entanglement, uncertainty, collapse of the wave function, [no cloning, reversible unitary evolution, irreversibility, measurement and decoherence] Lo, Popescu & Spiller
[page 190]
Formalism cannot explain action. Like the Zen and everybody else, we just accept that life is pure action.
Deutsch is making the case for the omnipotent, omniscient and invisible pure deterministic God, because although he speaks at length about explanation he has nothing to say about meaning.
Wednesday 16 September 2009
We achieve complex outcomes (like driving from a to b) by an ordered set of actions. A decision realizes one element of a symmetry (set of possibilities) to the exclusion of others, so that energy goes to it and not the others [this is now a source defines its output from a symmetrical set of letters].
What is the ultimate size of the Universe? The Cantor Universe.
How big is the Universe? Depends on the measure: physical, in terms of mass, length and time, ie the cardinal of the set of actions: metaphysical, in terms of the ordinal of the set of actions, the set of all possible permutations of all the [atomic] actions of the world [ie permutation of the set of Turing machines], from which conservation of energy forces us to select a subset.
Lying in bed in the morning is decision time. What will I do today? Having decided on the overall tasks, we get down to details, exploring the possible moves to minimize the route to completion. This profess is valuable because it eliminates false moves and wasted action, so contributing to my fitness. Thinking (modelling) time is rarely wasted.
CONSERVATION OF ENERGY == CONSERVATION OF PROBABILITY
[page 191]
So now I am down to which sheet of fibro I will install next, and thinking about how to manage the electrical connections that have to be made through it.
Do cells think like this as they go through their day? Atoms? Here, in a way, enters the question of consciousness, ie self awareness. We generally reserve consciousness exclusively to ourselves, but if we look at it from a cybernetic point of view, we may be able to extend it to other entities. Consciousness is self-awareness for purposes of self guidance, so it is part of our feedback mechanisms for navigating through the often confusing sea of life.
At first glance we might think that there is more information in the continuum 0 .. 1 that there is in the binary digits, 0, 1. Quantum mechanics tells is that this is not so -- reading a qubit yields at most one bit of information. The hope of quantum computation rests on exploitation of the mechanism lying behind quantum events, which is expressed as linear algebra in Hilbert Space.
Praying, saying the same thing to yourself over and over again is an aid to memory and execution like practising the piano or pole vaulting [or learning a trade, like surgery].
Thursday 17 September 2009
What are the points of FXQi? fqxi.org
1. logical continuity
2. quantum mechanics describes a network -- quantization
3. creates by development of discrete messages.
At the fundamental level the bonding determines the particle and
[page 192]
the particle determines the bonding, in other words the two must arrive at a contract for staying together that allows each to retain its individual nature to the extent that the bond can be broken and everything goes back to the way it was.
BONDING = MEMORY = CORRESPONDENCE
A computer can only work if every value has a definite address that can be accessed by the processor as required at a specific point in the execution of a program
The relationship of motion to stillness is one of the oldest problems in [reasoned investigations of the world]. Two thousand five hundred years ago Parmenides and Zeno held that motion was an illusion and only stillness was real. He appears to have reached this conclusion from the observation that we cannot have permanently true knowledge of a changing reality, so if our knowledge is true in this sense, motion is illusory.
We have retreated from that extreme position by taking a kinematic view of motion and taking this to a continuous limit [hoping to avoid Zeno's paradoxes] using the methods of calculus. Although the world is not still, it has still points which can be represented by differential equations like Einstein's equation which describes gravitation.
Science is in general more concerned to unearth eternal (or at least long lived) truths, leaving the ephemeral workings of the world to tradesmen, gossip magazines and all the other human dialogue concerned with the moment to moment working out of life.
A state is a formal representation of a real situation.
[page 193]
One can be binded to a state in the sense that the formal description of bonding is based on a formal description of states, and the rule that particles will bond if the act of binding releases energy, so that the bound state has lower energy than the unbound states. In other words, the bound state requires less work to maintain (ie actions per time) than the two unbound states.
So my state will bind to your state of the 'two of us can live as cheaply as one' and other requirements of compatibility are met.
Describe local behaviour with a differential equation and integrate to get the global picture. Such integration is really a fancy addition of identical units without meaning. At the other end of the spectrum we have systems integration where every move is unique and its effect may range from simply being an additive unit to being a flag whose value indicates a branch in the process ie bit is set, launch all, massive attack.
Newton's first law defines memory : a state that only changes when it is changed Memory locations are states, each with a unique identity that may or may not be occupied in various ways which convey information.
The Cantor Universe gives us an absolute scale of entropy.
Information theory is based on an ergodic source, that is a source whose randomness explores all possibilities. This is the appropriate statistical model for meaningful communications because Shannon shows that an optimal encoding is indistinguishable from noise, so the most meaningful source appears the
[page 194]
closes to noise. The difference between noise and meaning is the decoding system.
The mathematics of quantum mechanics tells is with beautiful precision what outcomes we can expect from certain inputs when we question the world, sending messages to it and recording the replies. But the mathematics does not explain it. This must be done in the discrete domain of meaningful text.
Formally an action is the execution of a computation so there are as many different atomic actions in the world as there are Turing machines, a countable infinity, ℵ0.
Energy is measured in atomic actions per unit of time, expressed in a fundamental equation of physics, E = h bar.omega where h bar measures the quantum of action and omega is frequency in radians per unit of time. More usefully, E / omega = h bar, the ratio of energy to frequency is a constant.
We rate logical processes by a product of word length and frequency, and note that the general tendency in the Universe is for long words (like galaxies) to have a relatively low frequency while short words, like the communications of an atom, to be more frequent. In a nutshell, high energy - fast processing.
Quantum mechanics is concerned with words of length 1, ie empty sets.
A gas is an unbound system, 'binding' and so correlating only by direct communication (collision). Liquid, volumetrically bound (an incompressible fluid - perhaps the ideal
[page 195]
phase to model physical humanity; gas = free humanity communicating only by personal contact and not constrained by some greater structure.
E - h bar.omega, d psi / dt = omega = e / h bar (Schrödinger's equation)
The future of physics will rely on a paradigm motivated by the relationship pointed out by Feynman between computing and physical events. The root of this change is the substitution of logical for geometric continuity.
Geometric continuity = boson
logical continuity = fermion
