(-: ##~~~## A fantasy to be read at leisure time ##~~~## :-)

Written October 7, 1999 to relax from the strains of working on a new interpretation of quantum mechanics – at that time only an actively pursued dream, which took nearly 20 years to fully materialize two weeks ago!

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1. Let us begin with a universal Turing machine (in Penrose’s variant). It consists of a ‘tape’ and a ‘device’. The tape – taken to be infinite in both directions – consists of little squares containing labels 0 or 1. The device is positioned above one of these squares, moving forward or backward on the tape, changing its own state and the tape’s labels – all according to universal rules that depend on the current state and the current label of the position of the device only.

These rules are complex enough so that, provided with a tape that contains the right set of ‘instructions’ prepended to a ‘task’ at hand it will perform this task – any task that is computable in the sense of mathematical logic.

To properly start working, the device must be in a special environment: the tape must have been prepared such that to the left of the device are zeros only, while to the right of the tape may be initially zeros, then the instructions, then the task, then again zeros only. But in fact, it is enough that there are ‘sufficiently many consecutive zeros’ to the left of the device and to the right of the end of the task.

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2. We shall make the device somewhat more flexible by extending its tape space. Instead of letting it move only along a one-dimensional tape we provide a higher-dimensional checkerboard made up of ‘boxes’ in place of the squares – say, for the sake of definiteness, one with 3 dimensions – that extends infinitely in each direction. Instead of moving forward and backward, the device is allowed to move from one box to any neighboring box, again according to prescribed rules. We also allow each box to contain any rational number as a label, not just 0 or 1.

To properly start working, the device must again be in a special environment; we may require for example that the instructions are coded by negative labels, the task by positive labels, and there are enough zero labels surrounding these; the device moves in its initial state in the sea of zeros (without changing anything) and starts working as soon as it hits the boundary of the instructions.

The theory of algorithm tells us that the new machine is not able to perform more tasks than the original Turing machines, but it can do them more efficiently, if the code provided is efficient.

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3. Let us make our device even more comfortable. We remove the borders between the boxes, so that the tape becomes a 3-dimensional continuum, and instead of giving labels to each box, we give labels to each point, allowing these labels to be now real numbers – thus forming a label field. The device is still assumed to be extended, and its rule for moving depends on its state and the values of the label field within its extension. It now moves by changing its shape in an amoeba-like fashion, changing the values of the label field within its extension; again according to fixed rules implemented in the device. Instead of having it move in discrete steps, we have it move (and modify the label field) continuously, with laws described by differential equations.

To properly start working, the device must again be in a special environment; we still require a sufficiently well isolated environment containing instructions and the task, but leave details (that would have to be specified exactly in building such a machine) to our imagination.

At this stage of evolution, the machine (now consisting of the 3D continuum tape with the label field and the amoeba-like device outside the tape) is no longer equivalent to a Turing machine – perhaps it is able to perform tasks that are not feasible for a Turing machine; but perhaps it can again do only the old tasks but more efficiently.

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4. To make the machine even more interesting we assume that the label field changes with time according to rules independent of the device. We also allow several label fields, some of them vector or perhaps tensor valued – a small change compared to what we already did. For the sake of definiteness, let the label fields be the fields familiar from physics, the matter fields, the gravitational field and the electromagnetic field.

The other things don’t change much; but since the gravitational field and the electromagnetic field nowhere strictly vanish we relax the conditions when the device starts working; it suffices to assume that there is a definite rule for recognizing working conditions.

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5. Things get truly interesting if we place additional copies of the device (let us call them ‘souls‘) moving – well separated – in the same 3-dimensional continuum (let us call it ‘universe‘). They err through the universe in an initially inactive state until they reach an environment containing instructions (let us call them ‘genes‘) that they understand.

These instructions, together with the soul’s built-in rules, compel them to localize their activities to the neighborhood of these genes, encouraging them to organize the matter around them into purposeful activities, long enough to perform the tasks they find prepared for them in the environment.

The task is done once the souls reach their final state (let us call the final states ‘heaven‘ and ‘hell‘). Depending on their final state, the souls find joy and peace in eternally satisfying further activities that cannot be expressed in words, or err restlessly through the universe, without ever finding again a task for which they are fit. (Details depend, of course on the programming; this is just a crude scenario that doesn’t claim any connections with reality.)

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6. Remarkable things happen when a soul finds itself given the task of investigating its environment. The latter turns out to be quite predictable in its outlines (one finds ‘physical laws‘) but unpredictable in its details, just as it should be for a task-oriented universal computing machine that the whole system (souls plus universe) represents.

Some of the souls (let us call them ‘reductionists‘) end up priding themselves with the claim to know that everything in the universe is determined by the laws of physics….

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7. Really surprising things happen when one of these inquiring souls (let us call it a ‘philosopher‘ or a ‘physicist‘) observes other souls. While usually, the universe they observe behaves according to standardized rules, certain spots in the universe, let us call them ‘humans‘ (maybe also call some ‘animals’ or even ‘plants’?), seem to be different, purposeful, just like the small immediate environment the soul is able to control (let us call it the soul’s ‘body‘). And within some of these souls (let us call them ‘dualists‘) the suspicion – no, the compelling belief – arises that these moving spots in the universe are occupied by souls more or less like themselves.

Closer examination shows that it is possible to communicate with these spots in a way in which is impossible to communicate with the remaining matter in the universe. Moreover, this communication turns out to be meaningful, as if the other spots were indeed other souls, with access not only to the physical fields (including the physical extension of the souls’ working space, their bodies) but also to the internal state processor (let us call it ‘consciousness‘) that governs their activities.

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8. Unfortunately, physical laws forbid the too detailed look at what happens within a body without destroying the environment necessary for a soul to carry out its task. Thus the poor dualist soul is never able to prove its belief to nonbelievers. The dualist souls remain the focus of mockery of those reductionist souls who claim that there is nothing else than fields; that souls – the very devices that make the whole machine interesting – are only figments of the imagination, epiphenomena of the local irregularities of the label fields….

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