A sentence giving such a property would have to be in the context of a true and complete theory of physics, which I do not possess.
I expect that such a theory will provide a language for describing many such structural properties. I have this expectation because every theory that has been offered in the past, had it been literally true, would have provided such a language. For example, suppose that the universe were in fact a collection of indivisible particles in Euclidean 3-space governed by Newtonian mechanics. Then the distances separating the centers of mass of the various particles would have determinate ratios, triples of particles would determine line segments meeting at determinate angles, etc.
Since Newtonian mechanics isn’t an accurate description of physical reality, the properties that I can describe within the framework of Newtonian mechanics don’t make sense for actual physical systems. A similar problem bedevils any physical theory that is not literally true. Nonetheless, all of the false theories so far describe structural properties for physical systems. I see no reason to expect that the true theory of physics differs from its predecessors in this regard.
suppose that the universe were in fact a collection of indivisible particles in Euclidean 3-space governed by Newtonian mechanics. Then the distances separating the centers of mass of the various particles would have determinate ratios, triples of particles would determine line segments meeting at determinate angles, etc.
Let’s use this as an example (and let’s suppose that the main force in this universe is like Newtonian gravitation). It’s certainly relevant to functionalist theories of consciousness, because it ought to be possible to make universal Turing machines in such a universe. A bit might consist in the presence or absence of a medium-sized mass orbiting a massive body at a standard distance, something which is tested for by the passage of very light probe-bodies and which can be rewritten by the insertion of an object into an unoccupied orbit, or by the perturbation of an object out of an occupied orbit.
I claim that any mapping of these physical states onto computational states is going to be vague at the edges, that it can only be made exact by the delineation of arbitrary exact boundaries in physical state space with no functional consequence, and that this already exemplifies all the problems involved in positing an exact mapping between qualia-states and physics as we know it.
Let’s say that functionally, the difference between whether a given planetary system encodes 0 or 1 is whether the light probe-mass returns to its sender or not. We’re supposing that all the trajectories are synchronized such that, if the orbit is occupied, the probe will swing around the massive body, do a 180-degree turn, and go back from whence it came—that’s a “1”; but otherwise it will just sail straight through.
If we allow ourselves to be concerned with the full continuum of possible physical configurations, we will run into edge cases. If the probe does a 90-degree turn, probably that’s not “return to sender” and so can’t count as a successful “read-out” that the orbit is occupied. What about a 179.999999-degree turn? That’s so close to 180 degrees, that if our orrery-computer has any robustness-against-perturbation in its dynamics, at all, it still ought to get the job done. But somewhere in between that almost-perfect turn and the 90-degree turn, there’s a transition between a functional “1” and a functional “0″.
Now the problem is, if we are trying to say that computational properties are objectively possessed by this physical system, there has to be an exact boundary. (Or else we simply don’t consider a specific range of intermediate states; but then we are saying that the exact boundary does exist, in the form of a discontinuity between one continuum of physically realizable states, and another continuum of physically realizable states.) There is some exact angle-of-return for the probe-particle which marks the objective difference between “this gravitating system is in a 1-state” and “this gravitating system is in a 0-state”.
To specify such an angle is to “delineate an arbitrary exact boundary in physical state space with no functional consequence”. Consider what it means, functionally, for a gravitating system in this toy universe to be in a 1-state. It means that a probe-mass sent into the system at the appropriate time will return to sender, indicating that the orbit is occupied. But since we are talking about a computational mechanism made out of many systems, “return to sender” can’t mean that the returning probe-particle just heads off to infinity in the right direction. The probe must have an appropriate causal impact on some other system, so that the information it conveys enters into the next stage of the computation.
But because we are dealing with a physics in which, by hypothesis, distances and angles vary on a continuum, the configuration of the system to which the probe returns can also be counterfactually varied, and once again there are edge cases. Some specific rearrangement of masses and orbits has to happen in that system for the probe’s return to count as having registered, and whether a specific angle-of-return leads to the required rearrangement depends on the system’s configuration. Some configurations will capture returning probes on a broad range of angles, others will only capture it for a narrow range.
I hope this is beginning to make sense. The ascription of computational states as an objective property of a physical system requires that the mapping from physics to computation must be specific and exact for all possible physical states, even the edge cases, but in a physics based on continua, it’s just not possible to specify an exact mapping in a way that isn’t arbitrary in its details.
A sentence giving such a property would have to be in the context of a true and complete theory of physics, which I do not possess.
I expect that such a theory will provide a language for describing many such structural properties. I have this expectation because every theory that has been offered in the past, had it been literally true, would have provided such a language. For example, suppose that the universe were in fact a collection of indivisible particles in Euclidean 3-space governed by Newtonian mechanics. Then the distances separating the centers of mass of the various particles would have determinate ratios, triples of particles would determine line segments meeting at determinate angles, etc.
Since Newtonian mechanics isn’t an accurate description of physical reality, the properties that I can describe within the framework of Newtonian mechanics don’t make sense for actual physical systems. A similar problem bedevils any physical theory that is not literally true. Nonetheless, all of the false theories so far describe structural properties for physical systems. I see no reason to expect that the true theory of physics differs from its predecessors in this regard.
Let’s use this as an example (and let’s suppose that the main force in this universe is like Newtonian gravitation). It’s certainly relevant to functionalist theories of consciousness, because it ought to be possible to make universal Turing machines in such a universe. A bit might consist in the presence or absence of a medium-sized mass orbiting a massive body at a standard distance, something which is tested for by the passage of very light probe-bodies and which can be rewritten by the insertion of an object into an unoccupied orbit, or by the perturbation of an object out of an occupied orbit.
I claim that any mapping of these physical states onto computational states is going to be vague at the edges, that it can only be made exact by the delineation of arbitrary exact boundaries in physical state space with no functional consequence, and that this already exemplifies all the problems involved in positing an exact mapping between qualia-states and physics as we know it.
Let’s say that functionally, the difference between whether a given planetary system encodes 0 or 1 is whether the light probe-mass returns to its sender or not. We’re supposing that all the trajectories are synchronized such that, if the orbit is occupied, the probe will swing around the massive body, do a 180-degree turn, and go back from whence it came—that’s a “1”; but otherwise it will just sail straight through.
If we allow ourselves to be concerned with the full continuum of possible physical configurations, we will run into edge cases. If the probe does a 90-degree turn, probably that’s not “return to sender” and so can’t count as a successful “read-out” that the orbit is occupied. What about a 179.999999-degree turn? That’s so close to 180 degrees, that if our orrery-computer has any robustness-against-perturbation in its dynamics, at all, it still ought to get the job done. But somewhere in between that almost-perfect turn and the 90-degree turn, there’s a transition between a functional “1” and a functional “0″.
Now the problem is, if we are trying to say that computational properties are objectively possessed by this physical system, there has to be an exact boundary. (Or else we simply don’t consider a specific range of intermediate states; but then we are saying that the exact boundary does exist, in the form of a discontinuity between one continuum of physically realizable states, and another continuum of physically realizable states.) There is some exact angle-of-return for the probe-particle which marks the objective difference between “this gravitating system is in a 1-state” and “this gravitating system is in a 0-state”.
To specify such an angle is to “delineate an arbitrary exact boundary in physical state space with no functional consequence”. Consider what it means, functionally, for a gravitating system in this toy universe to be in a 1-state. It means that a probe-mass sent into the system at the appropriate time will return to sender, indicating that the orbit is occupied. But since we are talking about a computational mechanism made out of many systems, “return to sender” can’t mean that the returning probe-particle just heads off to infinity in the right direction. The probe must have an appropriate causal impact on some other system, so that the information it conveys enters into the next stage of the computation.
But because we are dealing with a physics in which, by hypothesis, distances and angles vary on a continuum, the configuration of the system to which the probe returns can also be counterfactually varied, and once again there are edge cases. Some specific rearrangement of masses and orbits has to happen in that system for the probe’s return to count as having registered, and whether a specific angle-of-return leads to the required rearrangement depends on the system’s configuration. Some configurations will capture returning probes on a broad range of angles, others will only capture it for a narrow range.
I hope this is beginning to make sense. The ascription of computational states as an objective property of a physical system requires that the mapping from physics to computation must be specific and exact for all possible physical states, even the edge cases, but in a physics based on continua, it’s just not possible to specify an exact mapping in a way that isn’t arbitrary in its details.