An aside, concerning what actually requires simulation / arithmetic explanation.


The algorithm of the collapse dynamics itself operates in a domain meta to the physical, and in this regard there is a reversal of causality with respect to the physical and the arithmetic. But I don't think this is what Bruno'spaper The Origin of Physical Laws and Sensations is driving at. The process of the collapse dynamics is deeply interwoven with the physical time evolution of quantum systems in the linear dynamics, and even if we agree that the collapse dynamics is primarily arithmetical, and even prior to the physical, this does not say anything about the nature of the linear dynamics.

As Everett explains, the functional identity of the observer is the record of observations. It is this definition which resolves the fundamental difficulties in the interpretation of quantum theory. It is only this identity to which there is the appearance of collapse. The collapse dynamics is the change to the linear dynamics, and is therefore of different logical type. It is to the linear dynamics as acceleration is to velocity.

As Everett explains, the algorithm of the linear dynamics runs as time passes, and the perceptual point of view / frame of reference passes along the linear time dimension of space-time. That is the algorithm of the body-mind that produces the contents of the sensorium. At the point in time along the linear time dimension of space-time, at which the new observation is formulated in the sensorium, and thus added to the record of observations, the functional identity of the observer, the functional identity of the observer changes. This new version of the observer exists in a different version of the four dimensional space-time universe, defined by a different quantum state.

I would point out that these two different algorithms are being implemented at different levels of logical type, and this too has to be inherent simulation. Time passes as the simulation exercises a specific linear dynamics, a specific time evolution of the position and state of matter and energy in the virtual environment observed by the observer. A new observation is formulated as part of this process. But upon the making of each observation, the algorithm itself changes. This is what experiments show, so this has to be formulated in arithmetic. Thus the arithmetic requires two different levels of logical type, just as a physical reality must if it is to account for the observed phenomena.

All this is what has to be simulated in a simulation, all of which is perfectly feasible. I have written the dual algorithmic form of the computation in C Language which I append here in case anyone is interested.

But just because it can all be simulated, this does not in my view imply 'the reversal between physics and arithmetic'.

But I am entirely open about this.

Andrew


Appendix

Here the logical form of the standard von Neumann-Dirac formulation of quantum mechanics operational for the functional identity of the observer as defined by Everett is presented as pseudocode in C language. If variables ?, observation, and observables[], and function get_sensorium_contents() were instantiated in suitably coherent memory of a quantum computer, such a program would produce the subjective realities of all possible functional identities of an observer, in the form of Everett's branching tree of memory configurations. So the running of this algorithm, and ? the unitary quantum state,is all we have to explain in order to explain our experience of physical reality. As Russell points out in Theory of Nothing page 5 " There is a mathematical equivalence between the Everything, as represented by this collection of all possible descriptions and Nothing, a state of no information.". Since Nothing is equivalent to Everything, ?, which explains the existence of the algorithm, there is nothing to explain except the running of the algorithm!

void transtemporal_reality () {

/* Initialisation */

Boolean new_observation = true;

Observation observation = LIGHT;

Functional_Identity observer = 1;

World world_hologram = NO_OBSERVATIONS;

Correlations_Record observables[];

Quantum_State ?;

Elapsed_Time t = 0;

int c = 0;


while (observer != 0) {

/* Process 1 -- Quantum time -- The exercise of the collapse dynamics - Change of quantum mechanical frame of reference */

if ( new_observation ) {

world_hologram = world_hologram + observation;

display (world_hologram);

observer = observer + observation;

observables[c++] = observation;

? = quantum_state_defined_by (observables)

new_observation = false;

}

/* Process 2 -- Space-time time -- The exercise of the linear dynamics - Change of inertial frame of reference */

else {

t = t + PLANCK_TIME

new_observation = compute_neural_state (?, t);

if ( new_observation)

observation = get_sensorium_contents();

break;

}

}

}






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