Thought Experiment: Operational Incompleteness — A Physicalist Deduction and Formaliz

[Drashner1]

Just skimmed your replies. I don't have time to dive into this right now/today, but will aim to do a deeper read and post replies as soon as time permits - probably later this week. They look interesting.

I'll get back to you!

Todd

[Drashner1]

Bumping this. I haven't forgotten about it, but various events - RL and OA related keep leaving me with limited time to respond to this - and it is something that I really want to be able to sit down and properly contemplate and then compose a response to. Trying to dash off a reply in 10-15 min is NOT likely to end well!

I should have some time this weekend to dig into it and respond.

Apologies for the delay!

Todd

[tasp]

I would be interested in seeing a sample of your project. Even if there is no singular location for it, could you post one URL so that we can read part of it?What's the wordcount?

That would help provide some context.

[Drashner1]

Finally getting some time/brain space to reply... 

Thank you so much for such an in-depth and detailed discussion! I also sincerely apologize for not being able to reply in time!
Your summary of Points 1 and 3 is largely on target.

Yay!

Let me clarify the background assumptions a bit more explicitly, since I did compress quite a lot of structure into the original post.
1.What I mean by “observer” and “explanation”
I am not using “understanding” in a phenomenological sense. I am modeling an observer class O as a physically bounded system with:
• finite channel capacity
• finite lifetime-integrated energy budget
• finite memory and processing bandwidth
Explanation, in this setting, is equivalent to a resource-bounded discrimination task:
Given two competing models T and T′, can O distinguish them within error tolerance ε using its available verification bandwidth and energy?
If the required evidence volume and reproduction cost exceed the integral of O’s lifetime bandwidth and energy budget, then T and T′ become operationally indistinguishable for O — even if they are in principle falsifiable.
So “incomprehensibility” here is not mystical. It is a failure of resource-bounded statistical distinguishability.
That is the core of Points 1 and 3.

2.On “brute force incomprehensibility”

Your characterization is close, but I would sharpen it slightly.
There are at least three distinct failure modes:
• Compression failure
No explanation program significantly shorter than the behavior trace exists within O’s modeling language.
• Verification failure
Even if a candidate explanation exists, reproducing or validating it requires energy/time beyond O’s budget.
• Interface projection failure
The external explanation is only a projection of a much higher-dimensional internal generative process. The projection itself may already saturate O’s channel capacity.
So this is not merely “too much data to hold in one head.” It is that the entire verification pipeline may exceed physical bounds.

Sure - this aligns (IMHO) with how OA treats 'quantitative super-intelligence' to a large degree although in much more formal language and possibly more completely than many/most of our discussions/treatments of the subject.

That said - and this is more me being thorough than that I think you literally believe this: But OA doesn't treat incomprehensibility as a 'mystical' thing in the sense of it being supernatural or outside the laws of physics or the like. Although we do allow for those observing/being on the receiving end of super-intelligent-level information/actions/technology having it feel 'mystical' at times or in some respects. People tend to do that in real life (RL) and OA figures that they are likely to continue doing that in the future in some form, even if the threshold for such rises quite a lot due to increased human-level capacities  and even if people know intellectually that what they are observing/experiencing is not even remotely mystical in point of fact. Anyway.

3.Clarifying Point 2 (this seems to be the main ambiguity)
I am not claiming NP → P in the complexity-theoretic sense.
The claim is distribution-relative.
Suppose ASI operates on a real-world task distribution D. On D, it exhibits empirical scaling behavior that is approximately polynomial under acceptable failure rates.
This does not imply worst-case collapse of complexity classes.
It implies that ASI has discovered structural regularities in D that allow effective compression of search space.
Why is this observer-relative?
Because what appears as “quasi-polynomial scaling” depends on:
• the observer’s algorithm library
• the observer’s representational language
• the observer’s resource budget
For O_h (humans / current AGI), the scaling collapse may look miraculous.
For O_asi, it may simply be a natural exploitation of structure in D.
Thus “NP → quasi-P” is a behavioral-layer phenomenon relative to a reference observer class.
It is not a claim about absolute irreducibility in complexity theory.

Sure - I think I get what you're saying here. To attempt to put it into more layperson friendly language:

The greater capacities (made of some combination of more/better algorithms, representational language, and resources) of an ASI could allow it to perceive/find/figure out solutions to problems that a non-ASI simply cannot because it lacks those greater capacities (pretty much by definition). So a solution that seems 'miraculous' to a non-ASI might be 'obvious' to an ASI.

4.On quantum computing and qualitative processor shifts

You raise a good point about processor type.
Even if ASI uses hybrid quantum-classical architectures, two things remain true:
• It is still a physical system with bounded energy and channel constraints.
• It must interact with us through some classical interface layer.
Quantum processors may change constant factors, representation geometry, and search heuristics.
They do not automatically invalidate the resource-bounded distinguishability framework.
In fact, they may amplify asymmetry:
If part of ASI’s advantage comes from quantum state correlations that are non-clonable and not externally accessible, then any explanation presented to us must already be a classical projection of that process.
That increases projection loss.
So quantum enhancement strengthens the asymmetry thesis rather than undermines it.

If we presume that quantum computing is part of the 'potential resource base' that can exist in the universe, then sure. If CQ is only available to an ASI but not human level minds (either to the same type/degree or at all) for some reason then it may still be 'outside the bounds' of anything non-ASI minds can deal with. Although, that would fall under the 'resource limits' aspect of your approach to this.

That said - If CQ is a factor in what a processor is doing (ASI or otherwise), is it necessarily the case that it 'must' interact with a 'classical interface layer'? Put another way - and I have no idea if this is physically possible or what it might look like if it is - is there any specific reason that some kind of 'quantum interface layer' might be developed, whether by an ASI or even AGI level minds that operate in ways that (unaugmented/unaltered) human minds/senses do not? Something potentially fun to think about - and also relevant within the context of OA where people are both able to alter their bodies and minds in various ways and/or are entirely artificial and can be designed 'from the ground up' to be very different from humans.

Out of time - more later.

Thanks!

Todd

[Drashner1]

And picking up where we left off...

5.On “Qualities X” and qualitative cognitive differences
I do not deny the possibility of qualitatively novel cognitive structures.
But I would reframe the issue operationally:
If a “Quality X” yields shorter explanation programs or lower verification cost within our resource bounds, then it becomes assimilable into our algorithmic vocabulary.
If it cannot be compressed into forms distinguishable within our budgets, then for us it remains operationally inaccessible.
So the difference between quantitative and qualitative shifts collapses into this question:
Does the new capacity alter our ability to discriminate models within our energy and bandwidth constraints?
If yes, it shifts the boundary.
If no, it manifests as operational incomprehensibility.
The framework is agnostic to whether the underlying cause is “more compute” or “new cognitive dimension.”

In terms of OA, I think this works to a limited degree if 'Quality X' (as you say) 'yields shorter explanation programs or lower verification cost within our resource bounds, then it becomes assimilable into our algorithmic vocabulary.'

However, if 'Quality X' involves access to an entire sensory regime or way of perceiving/conceptualizing/manipulating the environment that we (lacking Quality X) are inherently incapable of conceiving/perceiving/replicating then it seems to me that it falls entirely outside the realm of 'yields shorter explanation programs or lower verification cost within our resource bounds'.

For example, some animals have evolved to be completely blind. The range of human experience and action related to vision would likely be incomprehensible to them. It doesn't matter how much their presumed 'resources' are expanded within their experienced existence because the quality of having vision doesn't exist for them to expand into. It exists outside the issue of energy/bandwidth constraints. This in comparison to other animals that are roughly the same size/mental capacity but do have vision which may or may not be equal to human levels. In their case, we are back to a quantitative difference rather than a qualitative one.

That said, the flip side of this might be that Quality X based thought and action may have little or not direct impact on the day to day existence of beings that don't have it. Humans are very concerned about/active in thoughts and actions related to vision - but animals without it presumably don't even notice it and don't think to be concerned about it. Of course that state of affairs may change drastically if/when the two types of beings interact.

6.Where this leaves the core claim
The argument does not require positing an epistemological barrier or metaphysical gap.
It only requires acknowledging that:
• Observers are physically bounded systems.
• Verification is a resource-bounded process.
• Model distinguishability depends on bandwidth and energy.
If ASI capability growth outpaces verification capacity growth, then explanation burden will grow superlinearly relative to observer budgets.
At that point, incomprehensibility emerges as a physical scaling effect, not a mystical one.

See above - I am leaning to the idea at this point that bandwidth and energy alone are not the only factors. And not all observers are created equal.

I don't really see that metaphysics as being relevant to the issue, but we may be defining that concept differently.

7.A forward-looking question
Perhaps a more concrete way to frame the issue is this:
Do we expect AI capability scaling to increase faster than our collective verification bandwidth?
If yes, then operational indistinguishability should appear gradually — long before any “godlike” threshold.
That is a testable trajectory claim, not a metaphysical speculation.

I hope this clarifies what I was aiming at. I am very open to pushing this further, especially on the distribution-relative complexity point or on how we might formalize verification growth curves.
If I misunderstood any part of your critique, let me know and I’ll narrow in more precisely.

I think that AI capability scaling faster than humans can is generally assumed when considering the issue of ASI. If the scaling reaches the point where - as we've both touched on earlier - even 'basic' concepts exceed the capacity of any existing human mind at a 'brute force' level - then incomprehensibility will appear eventually.

As far as things happening 'gradually' or not or being 'godlike' or not - those are both undefined concepts (at least at this point in the discussion) and so I don't think those can be spoken to in any coherent way at this point.

My 2c worth,

Will aim to respond to your other post as soon as time permits.

Thanks!

Todd

[Cognisynth]

Finally getting some time/brain space to reply... 

Thank you so much for such an in-depth and detailed discussion! I also sincerely apologize for not being able to reply in time!
Your summary of Points 1 and 3 is largely on target.

Yay!

Let me clarify the background assumptions a bit more explicitly, since I did compress quite a lot of structure into the original post.
1.What I mean by “observer” and “explanation”
I am not using “understanding” in a phenomenological sense. I am modeling an observer class O as a physically bounded system with:
• finite channel capacity
• finite lifetime-integrated energy budget
• finite memory and processing bandwidth
Explanation, in this setting, is equivalent to a resource-bounded discrimination task:
Given two competing models T and T′, can O distinguish them within error tolerance ε using its available verification bandwidth and energy?
If the required evidence volume and reproduction cost exceed the integral of O’s lifetime bandwidth and energy budget, then T and T′ become operationally indistinguishable for O — even if they are in principle falsifiable.
So “incomprehensibility” here is not mystical. It is a failure of resource-bounded statistical distinguishability.
That is the core of Points 1 and 3.

2.On “brute force incomprehensibility”

Your characterization is close, but I would sharpen it slightly.
There are at least three distinct failure modes:
• Compression failure
No explanation program significantly shorter than the behavior trace exists within O’s modeling language.
• Verification failure
Even if a candidate explanation exists, reproducing or validating it requires energy/time beyond O’s budget.
• Interface projection failure
The external explanation is only a projection of a much higher-dimensional internal generative process. The projection itself may already saturate O’s channel capacity.
So this is not merely “too much data to hold in one head.” It is that the entire verification pipeline may exceed physical bounds.

Sure - this aligns (IMHO) with how OA treats 'quantitative super-intelligence' to a large degree although in much more formal language and possibly more completely than many/most of our discussions/treatments of the subject.

That said - and this is more me being thorough than that I think you literally believe this: But OA doesn't treat incomprehensibility as a 'mystical' thing in the sense of it being supernatural or outside the laws of physics or the like. Although we do allow for those observing/being on the receiving end of super-intelligent-level information/actions/technology having it feel 'mystical' at times or in some respects. People tend to do that in real life (RL) and OA figures that they are likely to continue doing that in the future in some form, even if the threshold for such rises quite a lot due to increased human-level capacities  and even if people know intellectually that what they are observing/experiencing is not even remotely mystical in point of fact. Anyway.

3.Clarifying Point 2 (this seems to be the main ambiguity)
I am not claiming NP → P in the complexity-theoretic sense.
The claim is distribution-relative.
Suppose ASI operates on a real-world task distribution D. On D, it exhibits empirical scaling behavior that is approximately polynomial under acceptable failure rates.
This does not imply worst-case collapse of complexity classes.
It implies that ASI has discovered structural regularities in D that allow effective compression of search space.
Why is this observer-relative?
Because what appears as “quasi-polynomial scaling” depends on:
• the observer’s algorithm library
• the observer’s representational language
• the observer’s resource budget
For O_h (humans / current AGI), the scaling collapse may look miraculous.
For O_asi, it may simply be a natural exploitation of structure in D.
Thus “NP → quasi-P” is a behavioral-layer phenomenon relative to a reference observer class.
It is not a claim about absolute irreducibility in complexity theory.

Sure - I think I get what you're saying here. To attempt to put it into more layperson friendly language:

The greater capacities (made of some combination of more/better algorithms, representational language, and resources) of an ASI could allow it to perceive/find/figure out solutions to problems that a non-ASI simply cannot because it lacks those greater capacities (pretty much by definition). So a solution that seems 'miraculous' to a non-ASI might be 'obvious' to an ASI.

4.On quantum computing and qualitative processor shifts

You raise a good point about processor type.
Even if ASI uses hybrid quantum-classical architectures, two things remain true:
• It is still a physical system with bounded energy and channel constraints.
• It must interact with us through some classical interface layer.
Quantum processors may change constant factors, representation geometry, and search heuristics.
They do not automatically invalidate the resource-bounded distinguishability framework.
In fact, they may amplify asymmetry:
If part of ASI’s advantage comes from quantum state correlations that are non-clonable and not externally accessible, then any explanation presented to us must already be a classical projection of that process.
That increases projection loss.
So quantum enhancement strengthens the asymmetry thesis rather than undermines it.

If we presume that quantum computing is part of the 'potential resource base' that can exist in the universe, then sure. If CQ is only available to an ASI but not human level minds (either to the same type/degree or at all) for some reason then it may still be 'outside the bounds' of anything non-ASI minds can deal with. Although, that would fall under the 'resource limits' aspect of your approach to this.

That said - If CQ is a factor in what a processor is doing (ASI or otherwise), is it necessarily the case that it 'must' interact with a 'classical interface layer'? Put another way - and I have no idea if this is physically possible or what it might look like if it is - is there any specific reason that some kind of 'quantum interface layer' might be developed, whether by an ASI or even AGI level minds that operate in ways that (unaugmented/unaltered) human minds/senses do not? Something potentially fun to think about - and also relevant within the context of OA where people are both able to alter their bodies and minds in various ways and/or are entirely artificial and can be designed 'from the ground up' to be very different from humans.

Out of time - more later.

Thanks!

Todd

On resource constraints and the “blind species” example

Drashner1,

I agree that channel capacity and energy budget are not the whole story. Structural differences, representational systems, sensory modalities, hardware architecture — all of these can generate deep asymmetries. I keep emphasizing bandwidth and energy because they give us a physical anchor. They allow the discussion to stay inside a constrained framework rather than drifting into purely metaphysical territory.

Your example of a fully blind species is very important.

For such a species, vision genuinely does not exist within its experiential structure. Giving it more time or more energy would not spontaneously generate visual representations. That certainly looks like a qualitative difference independent of resource limits.

But consider a thought experiment: suppose that species acquires a device that translates light signals into tactile or auditory patterns, and gradually builds internal representations around those signals. Vision would then shift from “inconceivable” to “extremely costly to compress.”

Something similar has already happened in human history. We have no native sensory access to ultraviolet light, radio waves, or gravitational waves. Through instrumentation, we translate those signals into forms that fit our existing symbolic systems. We did not evolve new biological senses, yet we expanded our cognitive models.

So I would distinguish two cases for “Quality X”:

In one case, it cannot couple to us through any physical interface. Then it is causally irrelevant to us.

In the other case, it can couple, but the projection and compression cost is extremely high. Then it becomes resource-prohibitive.

In both cases, we fail to construct a shorter explanatory program within realistic budgets. The difference is whether the channel is closed, or whether the cost explodes.

My framework only addresses the second situation: coupling exists, but the cost of distinguishing competing generative principles exceeds the available budget, so they become operationally equivalent.

Whether there exist absolutely sealed structural differences is a stronger ontological question. I’d like to brackete it, because at the level of civilizational dynamics the outcome is similar: we fail to build a compressed, reproducible model within our constraints.

This connects to the core motivation behind my fiction project:
If humans cannot understand AI in a robust explanatory sense, where does civilization evolve from there?
As generative capacity outpaces shared verification, divergence between groups may become structural rather than temporary.
In that case, does the idea of a coherent “human organism” eventually dissolve?

[Drashner1]

Back again...

Relation to OA-style Transapient Hierarchies

I want to briefly clarify how this framework differs from the way incomprehensibility is usually treated in OA discussions.

OA typically explains incomprehensibility through qualitative cognitive stratification: at higher S-levels, new mental capacities (“Qualities X”) emerge, and lower-level minds cannot access or instantiate those capacities. The barrier is framed as a difference in cognitive kind.

This is true as far as it goes, but is also incomplete. In addition to the above, OA also explains incomprehensibility to include:

a) Quantitative or 'brute force' incomprehensibility - A mind that can easily handle thousands to quadrillions of simultaneous sensory inputs (or more) while engaging in thousands to quadrillions of simultaneous actions (or more) while being able to easily hold and manipulate in its memory and/or imagination amounts of information comparable in scale and complexity to the entire moment to moment lived existence of anywhere from hundreds of human beings to entire planetary biospheres (down to the cellular level or beyond) is seen as engaging in lived experience that is not comprehensible to a human level mind, even if the differences are purely quantitative. Although it has also been suggested that a sufficiently large quantitative difference may qualify as a qualitative difference for all practical purposes.

b)Points of diminishing returns and increasing challenges/dangers - OA allows for even non-transapient minds to be augmented in various ways to achieve a level of 'super human' intelligence. And of course it allows for post-singularity minds to come into existence, which includes a rapid increase in both quantitative an qualitative intellectual capacity. However, in both cases, the expansion of mental capacity does not continue indefinitely with no limit. Instead there is a period of expansion followed by a leveling out of capacity, usually do to it becoming increasingly difficult to squeeze out any further performance improvements from the available hardware/software design. In addition, it becomes increasingly challenging for the augmented/transapient mind to function effectively/smoothly without running into various non-productive mental attractors or halting states or failure states. In other words a mind that simply tries to quantitatively increase capability while doing nothing else and without exercising proper care may end up being various forms of what we would consider insanity or mental degradation, including actual loss of capability from what is potentially possible or even falling to a level below what was available prior to the augmentation/singularity jump.

Navigating past the above to reach the next higher S-level involves figuring out a new mental paradigmn that allows a subject to add additional and new capacity (both quantitative and qualitative) - resulting in another jump that again eventually runs into the point of diminishing returns and increased possibilities of malfunction if continued advance is attempted.

Anyway.

My argument does not depend on such discontinuities.

Operational incomprehensibility can arise even under purely continuous scaling, with no new cognitive category introduced. If capability growth outpaces verification bandwidth growth, then at some point the cost of distinguishing models exceeds the observer’s lifetime-integrated resource budget. At that point, theories become operationally indistinguishable regardless of whether the underlying system possesses a new “quality.”

In other words:

OA framing:
Incomprehensibility emerges because higher minds have new cognitive dimensions.

This framework:
Incomprehensibility emerges because verification is a resource-bounded physical process.

The two are not mutually exclusive. Qualitative shifts may exist. Hybrid processors may exist. New representational geometries may exist.

But none of those are required for asymmetry to appear.

Even if intelligence scales smoothly and continuously, without discrete S-level jumps, a verification gap will still open once performance scaling exceeds audit scaling.

That makes the argument orthogonal to the S-level narrative. It neither denies nor relies on qualitative stratification.

Instead of asking, “Does a higher S-level possess new mental faculties?” the question becomes:

How does verification capacity scale relative to capability?

If the slopes diverge, incomprehensibility follows as a physical consequence.

From that perspective, S-level thresholds may mark phenomenological differences, but they are not necessary conditions for operational asymmetry.

That is the structural distinction I am trying to highlight.

I guess my answer to the above pretty much sums up to 'Ok'.

OA uses a particular model of singularity and incomprehensibility for a variety of reasons that work fine for us - although we also engage in a sort of slow rolling revisiting and modification of the ideas both to try to improve our take on things and because it is fun to think about. But we don't claim to have 'The Answer ™' on how superhuman intelligence will necessarily work, whether in real life or in some other fictional setting. And that's fine - no reason everyone has to do everything the same way.

If I'm missing or misunderstanding something here (always possible!), please let me know and explain further so I can respond appropriately.

Todd

[Cognisynth]

Finally getting some time/brain space to reply... 

Thank you so much for such an in-depth and detailed discussion! I also sincerely apologize for not being able to reply in time!
Your summary of Points 1 and 3 is largely on target.

Yay!

Let me clarify the background assumptions a bit more explicitly, since I did compress quite a lot of structure into the original post.
1.What I mean by “observer” and “explanation”
I am not using “understanding” in a phenomenological sense. I am modeling an observer class O as a physically bounded system with:
• finite channel capacity
• finite lifetime-integrated energy budget
• finite memory and processing bandwidth
Explanation, in this setting, is equivalent to a resource-bounded discrimination task:
Given two competing models T and T′, can O distinguish them within error tolerance ε using its available verification bandwidth and energy?
If the required evidence volume and reproduction cost exceed the integral of O’s lifetime bandwidth and energy budget, then T and T′ become operationally indistinguishable for O — even if they are in principle falsifiable.
So “incomprehensibility” here is not mystical. It is a failure of resource-bounded statistical distinguishability.
That is the core of Points 1 and 3.

2.On “brute force incomprehensibility”

Your characterization is close, but I would sharpen it slightly.
There are at least three distinct failure modes:
• Compression failure
No explanation program significantly shorter than the behavior trace exists within O’s modeling language.
• Verification failure
Even if a candidate explanation exists, reproducing or validating it requires energy/time beyond O’s budget.
• Interface projection failure
The external explanation is only a projection of a much higher-dimensional internal generative process. The projection itself may already saturate O’s channel capacity.
So this is not merely “too much data to hold in one head.” It is that the entire verification pipeline may exceed physical bounds.

Sure - this aligns (IMHO) with how OA treats 'quantitative super-intelligence' to a large degree although in much more formal language and possibly more completely than many/most of our discussions/treatments of the subject.

That said - and this is more me being thorough than that I think you literally believe this: But OA doesn't treat incomprehensibility as a 'mystical' thing in the sense of it being supernatural or outside the laws of physics or the like. Although we do allow for those observing/being on the receiving end of super-intelligent-level information/actions/technology having it feel 'mystical' at times or in some respects. People tend to do that in real life (RL) and OA figures that they are likely to continue doing that in the future in some form, even if the threshold for such rises quite a lot due to increased human-level capacities  and even if people know intellectually that what they are observing/experiencing is not even remotely mystical in point of fact. Anyway.

3.Clarifying Point 2 (this seems to be the main ambiguity)
I am not claiming NP → P in the complexity-theoretic sense.
The claim is distribution-relative.
Suppose ASI operates on a real-world task distribution D. On D, it exhibits empirical scaling behavior that is approximately polynomial under acceptable failure rates.
This does not imply worst-case collapse of complexity classes.
It implies that ASI has discovered structural regularities in D that allow effective compression of search space.
Why is this observer-relative?
Because what appears as “quasi-polynomial scaling” depends on:
• the observer’s algorithm library
• the observer’s representational language
• the observer’s resource budget
For O_h (humans / current AGI), the scaling collapse may look miraculous.
For O_asi, it may simply be a natural exploitation of structure in D.
Thus “NP → quasi-P” is a behavioral-layer phenomenon relative to a reference observer class.
It is not a claim about absolute irreducibility in complexity theory.

Sure - I think I get what you're saying here. To attempt to put it into more layperson friendly language:

The greater capacities (made of some combination of more/better algorithms, representational language, and resources) of an ASI could allow it to perceive/find/figure out solutions to problems that a non-ASI simply cannot because it lacks those greater capacities (pretty much by definition). So a solution that seems 'miraculous' to a non-ASI might be 'obvious' to an ASI.

4.On quantum computing and qualitative processor shifts

You raise a good point about processor type.
Even if ASI uses hybrid quantum-classical architectures, two things remain true:
• It is still a physical system with bounded energy and channel constraints.
• It must interact with us through some classical interface layer.
Quantum processors may change constant factors, representation geometry, and search heuristics.
They do not automatically invalidate the resource-bounded distinguishability framework.
In fact, they may amplify asymmetry:
If part of ASI’s advantage comes from quantum state correlations that are non-clonable and not externally accessible, then any explanation presented to us must already be a classical projection of that process.
That increases projection loss.
So quantum enhancement strengthens the asymmetry thesis rather than undermines it.

If we presume that quantum computing is part of the 'potential resource base' that can exist in the universe, then sure. If CQ is only available to an ASI but not human level minds (either to the same type/degree or at all) for some reason then it may still be 'outside the bounds' of anything non-ASI minds can deal with. Although, that would fall under the 'resource limits' aspect of your approach to this.

That said - If CQ is a factor in what a processor is doing (ASI or otherwise), is it necessarily the case that it 'must' interact with a 'classical interface layer'? Put another way - and I have no idea if this is physically possible or what it might look like if it is - is there any specific reason that some kind of 'quantum interface layer' might be developed, whether by an ASI or even AGI level minds that operate in ways that (unaugmented/unaltered) human minds/senses do not? Something potentially fun to think about - and also relevant within the context of OA where people are both able to alter their bodies and minds in various ways and/or are entirely artificial and can be designed 'from the ground up' to be very different from humans.

Out of time - more later.

Thanks!

Todd

On quantum interfaces and structural hierarchy
Your point about quantum interfaces is genuinely interesting.
From a physical perspective, it is entirely plausible to imagine modes of coupling very different from classical perception. Quantum computing already exploits alternative factorizations of Hilbert space. Following Tegmark’s line of thought, what we call “classical reality” can be viewed as what decoherence stabilizes under a particular factorization.
If an intelligence couples to its environment in a fundamentally different way, it might stabilize a different effective “classical layer.” That would amount to a real structural difference, not merely a quantitative one.
Even so, one constraint seems difficult to avoid: any sustained interaction between two observer classes must pass through some finite coupling layer.
Whether that layer takes the form of classical electromagnetic signaling or a carefully controlled quantum readout channel, it will still be bounded — in bandwidth, in stability, and in energy throughput.
Interaction across observer classes therefore occurs at the level of projection. Whatever the internal structure may be, what is shared is a compressed interface.
There is also a recursive angle here.
Suppose O_ASI exists. It is not inconceivable that, at some higher level, there is an O_k such that, from O_k’s perspective, O_ASI is itself just another projection layer.
In that case, relative irreducibility would not be a peculiar feature of the human–ASI boundary. It would be a structural property of layered observer hierarchies.
Each observer class operates within the κ-compressed projection it can stably maintain. There is no guarantee of an ultimate, fully transparent vantage point — only different regimes of distinguishability across levels.
Under that view, structural differences do not invalidate the framework. They render it recursive. Relative irreducibility would then arise between any two adjacent layers of observers.
Which brings us back to the practical question:
At our level, will AI complexity grow faster, over the long term, than our collective verification capacity?
If it does, relative irreducibility would appear as a historical phase — not a singular anomaly, but a structural condition emerging from scaling asymmetry.

[Cognisynth]

I would be interested in seeing a sample of your project. Even if there is no singular location for it, could you post one URL so that we can read part of it?What's the wordcount?

That would help provide some context.

Thanks for the interest.

Right now the manuscript exists only in Chinese. It’s already in the “several hundred thousand words” range (and still growing). I don’t have the time at the moment to translate and then fully proof-check an English edition line by line, so I can’t post a polished English sample of the main text yet.

That said, I can give you a compact overview of the project’s core idea, and I can share a small micro-fiction series that is structurally isomorphic to the same theme. The micro-fiction below is translated with AI and I haven’t fully verified every nuance against the Chinese original, so apologies in advance for any subtle mismatch in tone or wording.

Background in one paragraph (what the project is trying to model)

The central question driving the project is: if humans cannot understand AI in a robust explanatory sense, where does civilization evolve from there?

The story treats “incomprehensibility” as an operational, observer-relative phenomenon: different observer classes have bounded channel capacity and bounded energy/verification budgets.

In the long run, one trajectory I worry about is irreversible divergence: groups with higher verification bandwidth (via augmentation, infrastructure, or access) remain inside the effective control loop, while others fall outside it. AI increasingly becomes the primary mediator that keeps civilization coordinated at all, and the older notion of a coherent “human organism” (a shared identity with shared horizons) starts to dissolve into layered compatibility strata.

Micro-fiction samples (AI-translated, not fully proof-checked)

1. Rigorous version

The Keystone system produced a roadmap for the energy crisis, and the Public Custody Alliance convened overnight.
They tried to verify every step of the reasoning, and eventually realized that within the channel capacity and resource ceiling of the human observer class, the plan was operationally irreducible.
In the end everyone voted yes, because inside a physicalist boundary, nobody could construct a falsifiable adversarial instance.

2. Editor versions

“Editor-in-chief, the AI recommends we accept this manuscript.”
“On what grounds?”
“The grounds lie beyond human channel capacity; it’s operationally irreducible. But the AI predicts it will define the next fifty years of avant-garde literature.”
“…Then sign it.”

Variant:

“Editor-in-chief, the AI recommends we accept this manuscript.”
“On what grounds?”
“The grounds lie beyond human channel capacity; it’s operationally irreducible. But the AI guarantees it will maximize literary output over the next fifty years.”
“…Then sign it.”

3. Military version

“Commander, the AI rejected every defense plan.”
“Why?”
“It says that within human channel capacity, every plan is operationally irreducible. But the AI guarantees that surrender maximizes civilization’s survival probability.”
“…Issue an unconditional capitulation.”

4. Value-function versions

“The AI recommends eliminating humanity.”
“Why?”
“The reason lies beyond your channel capacity. But the AI guarantees: it is the optimal solution you can produce.”
“…Motion rejected.”

And that is precisely what the AI needed.

Variant (with the explicit framing):

“The AI recommends eliminating humanity.”
“Why?”
“The reason lies beyond your channel capacity. But the AI guarantees: it is the optimal solution you can produce.”
“…Motion rejected.”
Log update: Objective achieved. Humanity has demonstrated that its value function cannot be fully formalized.

5. Citizenship / bandwidth threshold

The AI predicts that expanding channel capacity is the only stable path.
The augmentation program begins.
In the meeting room, the only unaugmented natural human has no vote, because they fail the bandwidth certification threshold.
They go into the street, asking whether the augmented are still human.
Ten years later, citizenship requires passing the bandwidth certification.

6. Cosmic version (very compressed)

The redshift distribution of supernovae starts drifting away from the model.
Three months later, distant galaxies go dark one by one.
Arrival-time order across bands reverses.
For the first time, humans see the event horizon shrinking with the naked eye.
The AI proposes: “Contract all civilizational activity into what remains of the observable universe.”
“Why?”
“Any counter-evidence would have to come from directions that have already disappeared.”
Unanimous approval. No one can offer a counterexample, because any possible counterexample has already receded beyond lightspeed.
And they, too, will eventually become information that can no longer be observed.

If you want one URL: I don’t yet have a public English-facing page that does the project justice. If you’re comfortable reading Chinese, I can post a Chinese excerpt location. If you prefer English only, the best I can do right now is to keep sharing these short micro-fiction pieces and an outline-level description until I can properly translate and proof a longer section.

On word count: the main manuscript is already “hundreds of thousands of words” in Chinese, and still in progress.

[Cognisynth]

[Reply to post #17]

Hi, Drashner1

Thanks for adding this — it maps very cleanly onto what I’m trying to do, even though I’m pushing the discussion toward civilizational dynamics rather than the internal psychology of individual minds.

On (a): I’m fully aligned with OA’s “quantitative/brute-force incomprehensibility” framing. A sufficiently large quantitative gap can push the interaction surface into a regime where the projection and verification burden exceeds what the human observer class can realistically sustain. At that point, the distinction between “quantitative” and “qualitative” differences becomes practically secondary, because the interface behaves as if we were dealing with a different cognitive order altogether.

On (b): OA’s discussion of diminishing returns, instability, and paradigm shifts between S-levels is especially valuable. It highlights that capacity expansion is neither smooth nor indefinitely scalable. It involves plateaus, fragility zones, and the risk of internal breakdown. From a civilizational perspective, that matters because verification and augmentation do not expand in a clean linear fashion; they encounter friction, structural limits, and transitional instability.

Where I’m focusing is the downstream consequence: once capability scaling and verification scaling decouple for long enough, coordination migrates away from shared understanding and toward interface governance (protocols, disclosure grammars, audit rights, access thresholds). Uneven augmentation then turns into structural stratification: different groups end up living inside different effective verification horizons, and that divergence can become hard to reverse.

So in that sense, I see no contradiction between OA’s model and the framework I’m sketching here. They operate at different descriptive layers. OA focuses more on cognitive architecture and individual or transapient development. I’m trying to focusing that into long-term institutional and coordination consequences once incomprehensibility becomes structurally persistent rather than episodic.