Notes
[Notebook: DB 59 Draughts]
[Sunday 17 September 2006 - Saturday 23 September 2006]
[page 169]
Sunday 17 September 2006
Control: The whole point of a game like tennis is to
[page 170]
have sufficient control of the ball to place it outside the other player's action cone so that they lose control and the point.
Go to bed desperate: I have lost control of the writing; wake up happy - I am back on track, a hundred good words written (in the computer) and it is not even 0800 yet.
Quantization is introduced by boundaries, ie by communications with other particles. When a particle is 'free' it is not quantized.
A computation is a communication
The ur-conspiracy theory is about a god behind the scenes that controls every element of the Universe at every moment.
Why is space 3-D? [Maybe] We don't have to look for some esoteric explanation. It is the minimum size in which every point can communicate with every other without our wires getting crossed. We can extrapolate this idea across all peer levels.
Natural selection arises because there are always more possibilities than can be realized -- infinitely more.
Monday 18 September 2006
Countably infinite = observed to be discrete = observed simpliciter.
Second quantization was concerned no so much with measuring and observing stationary states (ie eternity) but with the creation and annihilation of particles. The Hilbert oscillator comes back into the picture after a long holiday. It oscillates in the spectrum of quantizations, first, second . . . , and we model each level of quantization by a group of certain transfinite cardinality.
Tomonaga: Tomonaga
The symmetric network is a computational manifold, that is a formal structure capable of being placed into one to one correspondence with every possible communication and computation. The idea is the same as the use of a differentiable manifold as the language to represent the general theory of relativity.
The theorem uniting gravitation and quantum mechanics in the computational manifold (Shannon-Turing manifold) seems quite simple. The computation manifold is the union of all consistent sets of operations. In the computational manifold, by analogy with the Riemann manifold, every point of reality is occupied by a Turing machine. These Turing machines are individually deterministic, but binding them into a network, we make possible non-deterministic strings of functions.
[page 171]
GRAVITATION = COMMUNICATION THEORY
QUANTUM MECHANICS = FUNCTION THEORY = COMPUTABLE FUNCTION THEORY.
Observable = computable function. [function = joint, union, connection, mapping etc] [logical = function]
The hardest thing is to proceed 'without loss of generality'. Particulars are safe harbours, where we can settle down, but the general is hard to stay with. So Einstein had a long struggle to transform coordinates out of the picture and to get down to the real system in which points interacted directly, rather than by referring themselves to some frame of reference, ie the world acts by one-to-one correspondence.
A particular Turing machine is defined by an algorithm and a set of initial conditions. It uses that algorithm to transform the initial conditions to a final condition. The same algorithm can deal with a countable infinity of inputs, and there are a countable infinity of algorithms. So we expect . . . . The result (given the foibles of transfinite arithmetic) is ℵ0 different outputs (= ℵ0 inputs x (ℵ0 algorithms) [ie at least from a cardinal point of view, the thing can be a group, ie it is (cardinally) reversible. Prove reversibility in the ordinals?]
Only functions with algorithm can be Turing machines. But what if the algorithm is just a lookup table?
Schrödinger 's equation is a representation of the state vector of a mechanical system.
[page 173]
COMPUTABLE MANIFOLD
Now we can interpret the symmetric Universe as a phase space for the computable manifold. Every point in this manifold is a Turing Machine that is an algorithmic representation of a computable function operating with certain initial conditions, ie at a certain point in its domain. This manifold describes the linear deterministic features of the Universe.
Tuesday 19 September 2006
'On a computable manifold with an application to the P-NP problem'
We come to the question of why quantum mechanics resides in a complex space. The answer seems to be that complex exponential functions are periodic and the symmetries of the symmetric Universe, acting as constraints on recursive functions means that the less complex the function, the more frequently it is executes. The whole Universe, ie god, is only executed once (though we cannot talk about it in detail). The structure of the symmetric Universe, to avoid degeneration, requires two way communication. If a message goes from 321 to 123, ie in permutation language we write 321/123 and then describe the permutation as 13 then the 321 rearranging itself to 123 prompts the 123 to change itself to 321, so that there are still 1 123 and 1 321 in the Universe, though they have exchanged
[page 174]
places (or have they?) After all the name of the place is the string that resides there. 123, 321 are atoms, 31, 13 and 'virtual' photons going in opposite directions which interfere with one another to give a standing wave, a real photon ((? whose amplitude is some product of the 'virtual photons'. Things remain virtual until they are complete, and can then be observed.
An unstarted engine is a virtual (potential) power source. Once it is started we can call it real and see what it does.
Virtual: amplitude without probability ie an unfulfilled desire (potential) to communicate which can only be completed by a reply from somewhere. So, in a full Universe (like a full bed) if someone wants to move at least one other has to move.
The operating system of a computer is there to manage the memory and communications so that the processor can communicate with its environment.
..
A symmetric group is a complete orthogonal system which may be built up from a pair of orthogonal systems to any dimensionality by tensor production.
Physics remains rather obscure but the creative power of god's body is slowly emerging from the mist. We ask the physical world why it is driven
[page 175]
to create.
The most basic regimes operate by the algorithm of farmers and gardeners. Encourage the ones you want. Kill the rest. Such an algorithm is a bit too basic in the human world, where we all have an equal right to life. The 'justitial entropy' of a society is reduced if its distribution of opportunity is anything other than flat.
Physics operates between the cardinal ℵ0 (quantum and ℵ1 (continuum) Our hypothesis is that similar structures are induced by the interaction of neighbouring cardinals at all levels of cardinality. Every transition from moment to moment can be modeled by a 'transfinite transition', in other words the symmetrization of the set of symbols so that they are used equiprobably, that is with maximum entropy and therefore maximum stability.
To make a living one must expose oneself in public or at least play a convincing role )I'm a brain surgeon . . . )
Integration hides a lot of detail. It has a smoothing effect, whereas differentiation emphasizes differences.
Creation involves using memory and time division multiplexing to create a new path from some starting point in the symmetric network to some end point.
One can choose to move in space, but not in time. he cock ticks inexorably on as I sit here nearly motionless enjoying beer, chocolate, etc.
[page 176]
Was ancient Greek civilization a product of alcohol? dope? Simply a fertile period in recorded intellectual history?
Exclusion principle: every [electron] state can be occupied by 0 or 1 electron.
All real (?) operations cover a distance in a time. This distance may be in 3-space or space-time or in some more abstract space, like Hilbert space, banking space, market space, etc. Computation space, viewed as a manifold, is the biggest possible observable space, allowing ℵ0 different messages to be transmitted any number of times. We consider each message to be a link, proof or computation which connects . . .
A place in this world. A person in this world? The divine persons are defined by relationships and operations. We can expand this to all personalities ( = sources ==> sinks).
Security comes from testing. If it is not strong enough, do not climb on it.
When time is of the essence one must accept a certain amount of uncertainty, since getting more precise results would take a longer calculation, like long term observation of an electron in a trap.
Agatha: two sides of the question - different angles of vision - which was the true angle . . . the true angle . . . Crooked Christie page 227.
[page 177]
In quantum mechanics every angle between the observed and the observing frame is possible, and all changes of angle are parts of a group of rotations.
So what am I doing here? Trying to find out what I am doing here will [involve] consuming and helping others to consume quite a lot of physical resources.
The covariance in the symmetric group arises because we can take any permutation as the base state or set of states and express all the others in terms of it.
Quantum mechanics introduces plumbing into the computable manifold, helping us to visualize hat is going on in the world. By plumbing I mean a system of pipes with no leaks, in or out. If a practically incompressible fluid, flows through such a system, we know that the flow is conserved. If one flow split into two equal flows, we know that each of these carries half as much flow as the original, and conversely when two equal flows join. Now we can imagine a flow that endlessly branches and combines, but we can still cut slices of it and measure the flow in all the tubes crossing out slice and find that flow is conserved over parallel infinite slices. In quantum mechanics what flows is probability amplitude and what is conserved is the sum of all the probabilities of the outcome of an event, that is observation.
Conservation of flow in the quantum network means that the probability of al actual elements adds up to ℵ0 at any one slice through the system. Probability current is incompressible.
[page 178]
Same as a current of electrons. They may take all sorts of different routs, but the number crossing a given cut through the circuit is always constant unless there are reactive elements in the circuit.
The integrated action passing through an observable slice of spacetime is constant, equal in quanta to ℵ0. if the slice cuts the Universe into past and present, the ever advancing spacelike surface whose position is clearly known by every agent in the Universe. I can know my past. I cannot know my future. This boundary on knowledge is also a boundary on action, fitness, survival etc.
CONSERVATION OF PROBABILITY = ACTUS PURUS
Probability is conserved in the quantum world because amplitudes add linearly and operators are unitary, ie the 'length' of a vector, its dot product with itself, ie |v|2 = 1, even though the vector may be spinning wildly in place at omega = E/h, . . . . Or we can impose these conditions. Either way rate of action (energy) = probability. How many actions are probable in the Universe in a second (or any other unit of time)? Aleph(0). If the time unit is 1/ℵ0 the probability of any event is 1.
[page 179]
Strength of coupling = rate of communication = bits per second = bandwidth.
Is the Papacy the last monarchy to claim divine right?
Quantum overlap = overlap of network elements involved in processing the overlapping state vectors.
Locally everyday experience is a paradigm for all process in the Universe. All are subject to fluctuations arising rum their interactions with their environment. The biggest fluctuation in the life of each event are its birth and death which may define a range of intervals from h/(mass of Universe x c x c) to its inverse. So we say ℵ0 cycles with a period of 1/ℵ0 = 1.
Catholicism and similar religions split the pantheon by dividing it into good guys and bad guys. This is an unnatural dichotomy. All we can legitimately dichotomize are acts, which are different from people. Nevertheless, by correlating acts with identified people, we produce 'tomographies' of personalities which enable us to predict their likely responses to future stimuli.
The symmetries of the Universe, like chemistry, are outside us, common to all atoms, and inside is, special to the vast complex of interacting molecules which is me.
PROBABILITY SPACE is CARDINAL (MEASURE SPACE)
SYMMETRIC SPACE is ORDINAL (COMMUNICATION SPACE)
[page 180]
[Although] the divine Universe seems a bit far out, we very soon find that we do not have to change the language too much. jesus was divine. So are we all!. God is everywhere? Obviously!
To get somewhere in any community one has to speak the language so fluently that it is no longer a barrier to communication.
LOCAL INFINITY ==> MACHINE INFINITY
DISTANCE = 1/NYQUIST, is distance is inversely proportional to frequency of communication. Since we measure frequency of communication by bandwidth - 4-momentum, we see that distances get shorter as the local concentration of energy goes up, as genera relativity suggests. Opposing this 'bosonlike' tendency for everything to gather into clumps with unlimited quanta (events) in the same state, is he 'fermionlike' rule that possible states can contain at most one particle, ie send just one message, whereas bosons can be 'broadcast'. Broadcasting corresponds to symmetry which makes all the listeners the same. Fermionlike behaviour is one to one, every particles living in its personal state.
FERMION = GENERAL COVARIANCE
BOSON = RIGID SPACE ? EUCLID/LORENTZ/MINKOWSKI
The corporatization of murder: I can kill you because we work for different state armies. What we are witnessing in our time is a gradual phase change from
[page 181]
monarchy to democracy. Monarchy (particularly when it sees itself by 'divine right' or 'born to rule') claims absolute power of life and death over its subjects. You do not have to look too far to see frequent instances of this sort of thing. Democracy, on the other hand, is based on the symmetries of equality, freedom and the right to life. An idealist might like to see these ideas implemented perfectly (perhaps by taking the monarchical option of killing everybody who knew too much or otherwise did not fit in) but in practice the degree to which something can be achieved is determined by the productivity of the algorithm and the noise (ie non-algorithmic activity) in its implementation.
Here we think of STATE in a quantum mechanical sense. A monarchy resembles a boson state, where there is a strong tendency to toe the line. Democracy, on the other hand, is fermionic, ie free, equal and respecting one another's personal space. How do we map this idea from personal to particle space. Quantum field theory a a socio/politico/religion model.
The symmetric network is populated with a vast number of symmetries, but looking from any point, the asymmetric (ie incomputable) zone is always bigger.
SYMMETRY = COMPUTABILITY
Orthogonality reduces the need fro computing power, as when we lay out a house. Almost any three strings would do, but horizontal and vertical give a much more convenient description give a much more convenient description of [a normal house].
