I think step 10 overstates what is shown. You write:
“If a homomorphically encrypted mind (with no decryption key) is conscious … it seems it knows things … that cannot be efficiently determined from physics.”
The move from “not P-efficiently determined from physics” to “mind exceeds physics (epistemically)” looks too strong. The same inferential template would force us into contradictions in ordinary physical cases where appearances are available to an observer but not efficiently reconstructible from the microphysical state.
Take a rainbow. Let p be the full microphysical state of the atmosphere and EM field, and let a be the appearance of the rainbow to an observer. The observer trivially “knows” a. Yet from p, even a quantum-bounded “Laplace’s demon” cannot, in general, P-efficiently compute the precise phenomenal structure of that appearance. The appearance does not therefore “exceed physics.”
If we accepted your step 10’s principle “facts accessible to a system but P-intractable to compute from p outrun physics” we would have to say the same about rainbows:
the rainbow’s appearance to an observer “knows something” physics can’t efficiently determine.
That is an implausible conclusion. The physical state fully fixes the appearance; what fails is only efficient external reconstruction, not physical determination.
Homomorphic encryption sharpens the asymmetry between internal access and external decipherability, but it does not introduce a new ontological gap.
So I agree with the earlier steps (digital consciousness, key distance irrelevance) but think the “mind exceeds physics (epistemically)” inference is a category error: it treats P-efficient reconstructability as a criterion for physical determination. If we reject that criterion in the rainbow case, we should reject it in the homomorphic case too.
Take a rainbow. Let p be the full microphysical state of the atmosphere and EM field, and let a be the appearance of the rainbow to an observer. The observer trivially “knows” a. Yet from p, even a quantum-bounded “Laplace’s demon” cannot, in general, P-efficiently compute the precise phenomenal structure of that appearance.
This may be true but it’s really not obvious. The homomorphic encryption example makes one encounter such a case more clearly. If there’s no hard encryption there, why couldn’t Laplace’s demon determine it efficiently?
That is an implausible conclusion. The physical state fully fixes the appearance; what fails is only efficient external reconstruction, not physical determination.
The thing you quoted and said was implausible had “efficiently” in it...
Homomorphic encryption sharpens the asymmetry between internal access and external decipherability, but it does not introduce a new ontological gap.
Yeah it just makes an existing problem more obvious.
At the end of the day the natural supervenience relation of observations on physics should work similarly in the rainbow case and the homomorphic encryption case. The homomorphic encryption case just makes more clear something that might have gotten skipped over in the rainbow case, “the natural supervenience relation need not be efficiently computable from the physical state; the information of the observations doesn’t need to be directly sitting there, the way of picking it out might need to be a complicated function rather than a simple efficient ‘location and extraction of information’ one”
It seems you are biting the bullet and agreeing that the rainbow also has the problem of how a mind can be aware of it when it isn’t (efficiently) reconstructable. But then this seems to generalize to a lot, if not all, phenomena a mind can perceive. Doesn’t this reduce that conception of a mind ad absurdum?
I’m saying efficient reconstructibility is unclear in the rainbow case, but that the same principles have to explain it and non-efficiently-reconstructible cases like homomorphic encryption. I don’t take this as a reducio but as a trilemma, see step 11.
efficient reconstructibility is unclear in the rainbow case,
but whatever the right story is, it must handle both rainbow-like cases and the engineered homomorphic encryption case,
and if some of those cases force non-efficient supervenience, then we face your trilemma.
That part I agree with.
The point I’ve been trying to get at is: Once the same issue arises for ordinary optical appearances, we’ve left behind the special stakes of step 10! Because in the rainbow case, we all seem to accept (but maybe you disagree):
appearance is fully determined by physics,
but the mapping from microphysics to appearance may be extremely messy or intractable for an external observer,
and we don’t treat that as evidence that the visual appearance “exceeds physics.”
Or, if rainbow-style cases also fall under the trilemma, then the conclusion can’t be “mind exceeds physics.” It would have to be the stronger and more surprising “appearances as such exceed physics” or “macrostructure in general exceeds physics.” That’s quite different from your original framing, which presents the homomorphic encryption case as demonstrating a distinctive epistemic excess of mind relative to physics.
and we don’t treat that as evidence that the visual appearance “exceeds physics.”
This is still something I’d disagree with? Like, it still seems notable that visual appearances aren’t determined as an efficient function of physics. It suggests perhaps there is more to reality than physics, otherwise what are you seeing? “Appearances as such exceed physics” is not substantially different from what I mean as “mind exceeds physics”. This seems like a minor semantic issue. Appearances are mental, so if appearances exceed physics than so does mind; I’m not meaning any strong statement like “mind, and only mind, exceeds physics”.
If you generalize to optics, then it seems your condition for “exceeding physics” is “not efficiently readable from the microstate,” i.e.X is not a P-efficient function of the physical state.”But then it seems everything interesting exceeds physics: biological structure, weather, economic patterns, chemical reactions, turbulence, evolutionary dynamics, and all nontrivial macrostructure. I’m sort of fine with calling this “beyond” physics in some intuitive sense, but I don’t think that’s what you mean. What work does this non-efficiency do?
It means reductionism isn’t strictly true as ontology. I suppose it might be more precise to talk about “reductionist physics” than “physics”, although some might consider that redundant.
It isn’t obvious that biological structure isn’t efficiently readable from microstate. It at least doesn’t seem cryptographically hard, so polynomical time in general.
With turbulence you can pretty much read the current macrostate from the current microstate? You just can’t predict the future well.
I’d say homomorphic encryption computation facts, not just mental ones, are beyond physics in this sense. Other macro facts might be but it’s of course less clear.
Again, the same ontological status applies to homomorphic encryption and other entities. However the same epistemic status doesn’t apply. And the “efficiently determinable” criterion is an epistemic one.
A reason to pay attention to mental ones is that they are more salient as “hard to deny the existence of from some perspectives”. Whereas you could say a regular homomorphic encryption fact is “not real” in the sense of “not being there in the state of reality at the current time”.
It means reductionism isn’t strictly true as ontology.
I think you are working from an intuition of reductionism being wrong, but I’m still not clear about the details of your intuition. A defensible position could be that physics does not contain all the explanatorily relevant information or that reality has irreducible multi-level structure. But you seem to be saying that reductionism is false because subjective perspective is a fundamental ingredient, and you want to prove that via the efficiently computable argument. But I still think it doesn’t work. First, it proves too much.
It isn’t obvious that biological structure isn’t efficiently readable from microstate.
Agree that it is not obvious.
Other macro facts might be but it’s of course less clear.
But it seems pretty clear to me that most biological systems actually do involve dynamics that make it computationally infeasible for an external observer to reconstruct the macrostructure from microstructure observations at a given point. And we can’t appeal to ‘complete history’ to avoid the complexity, because with full history you could also recover the key in the HE case; the only difference is that HE compresses its relevant history into a small, opaque region.
What I do agree with you: Physics only tracks microstructure. But phenomenal awareness, meaning, macro-patterns, and information structure are not obviously reducible as descriptions to microstructure. The homomorphic case is a non-refutable illustration of this non-transparency.
But I disagree that this is caused by a failure of efficient computability; instead, we can see it as a failure of microphysical description to exhaust ontology. This matters because inefficiency is an epistemic constraint on observers, while ontology is about what needs to be included in the description of the world.
A defensible position could be that physics does not contain all the explanatorily relevant information or that reality has irreducible multi-level structure.
Close to what I mean. The multi-level structure is irreducible in that (a) it can’t be efficiently computed from microstates (b) it is in some cases observable, indicating it’s real. (Just (a) would be unsurprising, e.g. “the firth nth digits of Chaitin’s omega where n is the number of atoms in a table” is a high-level physical property that is not computable from microstate.)
But you seem to be saying that reductionism is false because subjective perspective is a fundamental ingredient
That’s not the claim. My argument wouldn’t work if in all cases, subjective perceptions could be efficiently computed from microstates. And it is possible for subjective perceptions to be efficiently computed from microstates without subjective perceptions being a “fundamental ingredient”. Rather I am vaguely suggesting something like neutral monism, where there is some fundamental ingredient explaining the physics lens and the mind lens.
But it seems pretty clear to me that most biological systems actually do involve dynamics that make it computationally infeasible for an external observer to reconstruct the macrostructure from microstructure observations at a given point.
It depends what kind of external observer you imagine right? Like if somehow we had a scan of a small animal down to the cellular level, there would be ordinary difficulties in re-constructing the macro-scale features from it, but none of them are clearly computationally hard (super-polynomial time).
But I disagree that this is caused by a failure of efficient computability; instead, we can see it as a failure of microphysical description to exhaust ontology. This matters because inefficiency is an epistemic constraint on observers, while ontology is about what needs to be included in the description of the world.
It seems like I entirely agree, not sure if I understood wrong. That is, I think path (c) is reasonably likely, and what it is saying is that there is more ontology than microphysics. It would be unsurprising for this to be the case, due to the way microphysical ontology, as methodology, is ok with dropping things that can be “in principle reconstrtucted”, hence tending towards the microscopic layer (as everything can be “in principle reconstructed” from there); ignoring computational costs to doing so, hence plausibly dropping things that are actually real from the ontology.
I think step 10 overstates what is shown. You write:
The move from “not P-efficiently determined from physics” to “mind exceeds physics (epistemically)” looks too strong. The same inferential template would force us into contradictions in ordinary physical cases where appearances are available to an observer but not efficiently reconstructible from the microphysical state.
Take a rainbow. Let p be the full microphysical state of the atmosphere and EM field, and let a be the appearance of the rainbow to an observer. The observer trivially “knows” a. Yet from p, even a quantum-bounded “Laplace’s demon” cannot, in general, P-efficiently compute the precise phenomenal structure of that appearance. The appearance does not therefore “exceed physics.”
If we accepted your step 10’s principle “facts accessible to a system but P-intractable to compute from p outrun physics” we would have to say the same about rainbows:
That is an implausible conclusion. The physical state fully fixes the appearance; what fails is only efficient external reconstruction, not physical determination.
Homomorphic encryption sharpens the asymmetry between internal access and external decipherability, but it does not introduce a new ontological gap.
So I agree with the earlier steps (digital consciousness, key distance irrelevance) but think the “mind exceeds physics (epistemically)” inference is a category error: it treats P-efficient reconstructability as a criterion for physical determination. If we reject that criterion in the rainbow case, we should reject it in the homomorphic case too.
This may be true but it’s really not obvious. The homomorphic encryption example makes one encounter such a case more clearly. If there’s no hard encryption there, why couldn’t Laplace’s demon determine it efficiently?
The thing you quoted and said was implausible had “efficiently” in it...
Yeah it just makes an existing problem more obvious.
At the end of the day the natural supervenience relation of observations on physics should work similarly in the rainbow case and the homomorphic encryption case. The homomorphic encryption case just makes more clear something that might have gotten skipped over in the rainbow case, “the natural supervenience relation need not be efficiently computable from the physical state; the information of the observations doesn’t need to be directly sitting there, the way of picking it out might need to be a complicated function rather than a simple efficient ‘location and extraction of information’ one”
It seems you are biting the bullet and agreeing that the rainbow also has the problem of how a mind can be aware of it when it isn’t (efficiently) reconstructable. But then this seems to generalize to a lot, if not all, phenomena a mind can perceive. Doesn’t this reduce that conception of a mind ad absurdum?
I’m saying efficient reconstructibility is unclear in the rainbow case, but that the same principles have to explain it and non-efficiently-reconstructible cases like homomorphic encryption. I don’t take this as a reducio but as a trilemma, see step 11.
I’m worried we talk past each other.
You’re saying:
efficient reconstructibility is unclear in the rainbow case,
but whatever the right story is, it must handle both rainbow-like cases and the engineered homomorphic encryption case,
and if some of those cases force non-efficient supervenience, then we face your trilemma.
That part I agree with.
The point I’ve been trying to get at is: Once the same issue arises for ordinary optical appearances, we’ve left behind the special stakes of step 10! Because in the rainbow case, we all seem to accept (but maybe you disagree):
appearance is fully determined by physics,
but the mapping from microphysics to appearance may be extremely messy or intractable for an external observer,
and we don’t treat that as evidence that the visual appearance “exceeds physics.”
Or, if rainbow-style cases also fall under the trilemma, then the conclusion can’t be “mind exceeds physics.” It would have to be the stronger and more surprising “appearances as such exceed physics” or “macrostructure in general exceeds physics.” That’s quite different from your original framing, which presents the homomorphic encryption case as demonstrating a distinctive epistemic excess of mind relative to physics.
This is still something I’d disagree with? Like, it still seems notable that visual appearances aren’t determined as an efficient function of physics. It suggests perhaps there is more to reality than physics, otherwise what are you seeing? “Appearances as such exceed physics” is not substantially different from what I mean as “mind exceeds physics”. This seems like a minor semantic issue. Appearances are mental, so if appearances exceed physics than so does mind; I’m not meaning any strong statement like “mind, and only mind, exceeds physics”.
If you generalize to optics, then it seems your condition for “exceeding physics” is “not efficiently readable from the microstate,” i.e.X is not a P-efficient function of the physical state.”But then it seems everything interesting exceeds physics: biological structure, weather, economic patterns, chemical reactions, turbulence, evolutionary dynamics, and all nontrivial macrostructure. I’m sort of fine with calling this “beyond” physics in some intuitive sense, but I don’t think that’s what you mean. What work does this non-efficiency do?
It means reductionism isn’t strictly true as ontology. I suppose it might be more precise to talk about “reductionist physics” than “physics”, although some might consider that redundant.
It isn’t obvious that biological structure isn’t efficiently readable from microstate. It at least doesn’t seem cryptographically hard, so polynomical time in general.
With turbulence you can pretty much read the current macrostate from the current microstate? You just can’t predict the future well.
I’d say homomorphic encryption computation facts, not just mental ones, are beyond physics in this sense. Other macro facts might be but it’s of course less clear.
Again, the same ontological status applies to homomorphic encryption and other entities. However the same epistemic status doesn’t apply. And the “efficiently determinable” criterion is an epistemic one.
A reason to pay attention to mental ones is that they are more salient as “hard to deny the existence of from some perspectives”. Whereas you could say a regular homomorphic encryption fact is “not real” in the sense of “not being there in the state of reality at the current time”.
I think you are working from an intuition of reductionism being wrong, but I’m still not clear about the details of your intuition. A defensible position could be that physics does not contain all the explanatorily relevant information or that reality has irreducible multi-level structure. But you seem to be saying that reductionism is false because subjective perspective is a fundamental ingredient, and you want to prove that via the efficiently computable argument. But I still think it doesn’t work. First, it proves too much.
Agree that it is not obvious.
But it seems pretty clear to me that most biological systems actually do involve dynamics that make it computationally infeasible for an external observer to reconstruct the macrostructure from microstructure observations at a given point. And we can’t appeal to ‘complete history’ to avoid the complexity, because with full history you could also recover the key in the HE case; the only difference is that HE compresses its relevant history into a small, opaque region.
What I do agree with you: Physics only tracks microstructure. But phenomenal awareness, meaning, macro-patterns, and information structure are not obviously reducible as descriptions to microstructure. The homomorphic case is a non-refutable illustration of this non-transparency.
But I disagree that this is caused by a failure of efficient computability; instead, we can see it as a failure of microphysical description to exhaust ontology. This matters because inefficiency is an epistemic constraint on observers, while ontology is about what needs to be included in the description of the world.
Close to what I mean. The multi-level structure is irreducible in that (a) it can’t be efficiently computed from microstates (b) it is in some cases observable, indicating it’s real. (Just (a) would be unsurprising, e.g. “the firth nth digits of Chaitin’s omega where n is the number of atoms in a table” is a high-level physical property that is not computable from microstate.)
That’s not the claim. My argument wouldn’t work if in all cases, subjective perceptions could be efficiently computed from microstates. And it is possible for subjective perceptions to be efficiently computed from microstates without subjective perceptions being a “fundamental ingredient”. Rather I am vaguely suggesting something like neutral monism, where there is some fundamental ingredient explaining the physics lens and the mind lens.
It depends what kind of external observer you imagine right? Like if somehow we had a scan of a small animal down to the cellular level, there would be ordinary difficulties in re-constructing the macro-scale features from it, but none of them are clearly computationally hard (super-polynomial time).
It seems like I entirely agree, not sure if I understood wrong. That is, I think path (c) is reasonably likely, and what it is saying is that there is more ontology than microphysics. It would be unsurprising for this to be the case, due to the way microphysical ontology, as methodology, is ok with dropping things that can be “in principle reconstrtucted”, hence tending towards the microscopic layer (as everything can be “in principle reconstructed” from there); ignoring computational costs to doing so, hence plausibly dropping things that are actually real from the ontology.