This is an automated rejection. No LLM generated, heavily assisted/co-written, or otherwise reliant work.
Read full explanation
Epistemological State: Speculative, but Based on Computational Complexity and Physical Limits
Author's Note: I am responsible for the object-level claims and technical statements in this document. Large language models may have assisted with text editing or structural adjustments, but the arguments, cases, and update rules are all my own and have been reviewed line by line.
Recently, discussions on LessWrong regarding ASI alignment, complexity theory, and physicalist constraints seem to revolve around a core puzzle: where do those "insurmountable hard limits" come from? This article provides a framework based on "observer-class", attempting to weave these threads of discussion into a unified physicalist narrative.
* I use "observer-class" to refer to humans or intelligent agents: those whose end-to-end verification capabilities are of the same order of magnitude—channel capacity/energy budget/representation bandwidth—for a given family of tasks. A claim is observer-inaccessible to class O when the resources required to make it verifiable exceed the verification bandwidth/budget for class O. In the following text, "channel capacity/energy budget/representation bandwidth" are all integrated into this end-to-end verification constraint.
1. Observer-Class Explanation Costs
I want to first clarify a common misconception: "It works" is not the same as "We can audit why it works."
Topic 1 (Observer-Class Explanation Costs)
Superintelligence (ASI) appears superior to human intelligence not because of any epistemological or ontological privilege, but because the cost of explanation across levels explodes.
For any given observer-class (e.g., human or AGI), explanations are constrained by finite channel capacity and thermodynamic budgets. When the information and computational costs required to compress, transmit, and verify an explanation exceed these constraints, the explanation becomes unreachable for that observer-class—even if it is correct in principle.
Relationship to "Vinci Uncertainty"
This provides a physical resource interpretation of Vinci uncertainty: unpredictability may stem from end-to-end bottlenecks in the characterization and verification process, not just the limits of formal reasoning.
Minimum Example
Suppose an ASI deploys a custom quantum device (custom circuitry + calibration + error mitigation) that reliably achieves the target capability and passes every scalable classical test that humans can afford. Humans can verify that "it works on the test suite," but determining when it will fail/become unsafe requires identifying rare error patterns (drift, crosstalk, correlated noise, adversarial inputs) that only appear under certain measurement mechanisms and diagnostic coverage. The cost of these patterns increases with the error tolerance ε, exceeding the end-to-end verification bandwidth of the human observer class. The ASI can manage these diagnostics to maintain reliability, while humans cannot compress the relevant device states and failure scenarios into a human-verifiable proof. This gap is not mystical: it stems from the fact that the minimum verification required to map failure boundaries exceeds the verification budget of the observer class, creating a stable separation between "works" and "auditable/safe for humans."
Furthermore, if we replace "interpretive bandwidth" with "evaluation bandwidth", the same constraints present even more severe challenges.
2. Distributed tractability as an observer-class phenomenon
In this section, I only advocate for a visibility gap, not any literal collapse of complexity classes.
The apparent ability of ASI to efficiently solve NP-hard problems should be understood as a behavioral phenomenon relative to a specific observer class, rather than an absolute collapse of computational complexity classes. This assertion is independent of the collapse of average-case complexity.
From the perspective of human observer classes, an ASI may exhibit distributed tractability due to its superior heuristics, richer world models, large-scale pre-computation, or sheer resource scale. This does not imply a collapse of worst-case complexity classes; rather, it may make the worst-case difficulty experimentally indistinguishable for observers who cannot afford the verification costs required to probe adversarial or rare states.
In this sense, tractability is observer-relative: a problem that appears efficiently solvable for a particular observer class may still involve worst-case intractability, which is real but opaque at the operational level.
Minimal Example: Consider a SAT-like instance drawn from a distribution that humans can afford to generate and validate at scale. An ASI exhibits distribution-visible tractability through heuristics, pre-computation, and scaling. To distinguish "robust efficiency" from "utilization of a specific distribution," it's necessary to probe adversarial or rare states beyond the validation bandwidth of human observers.
It's important to emphasize that the claim here is about what appears to be efficiently solvable within the distributions and validation budgets we can actually probe—not about how an ASI formally makes worst-case instances easy.
3. Physicalist Incompleteness Relative to Observer Capabilities
For any physicalist theory T, if the evidence required to distinguish T from its competing theories (within a specified error tolerance ε) exceeds the end-to-end verification bandwidth/budget of observer class O, then T becomes operationally indistinguishable for observer class O—even if it is falsifiable in principle.
This can be distinguished from Stephen Wolfram's computational irreducibility:
Computational irreducibility is a property of system-description pairs: for some coarse-grained formulations, there is no shorter prediction than directly running the dynamics.
Observer-class incompleteness is a relational property: it describes the gap between the verification bandwidth required by the theory and the observer's physical limits.
A theory may be completely falsifiable in principle, but if the observer's end-to-end verification bandwidth is too narrow to capture the necessary data (within tolerance ε), then the competing theories are operationally indistinguishable for that observer class. This form of incompleteness stems from the physical constraints of observation and transmission, rather than Gödel's logical indecidability.
Minimum Example
Two physicalist theories, T₁ and T₂, agree on all macroscopic observables we can measure, differing only on fine-grained predictions that require extremely high-resolution data and expensive interventions to distinguish. Evidence for differentiation exists in principle, but collecting this evidence within the error tolerance ε exceeds the end-to-end verification budget for the observer class. Therefore, T₁ and T₂ become operationally indistinguishable relative to the observer class O: the path to falsification exists, but cannot be completed within the verification constraints of O.
The following is what I believe constitutes a "stable state" that makes this framework relevant to decision-making, rather than merely a relabeling process.
Key point
The framework is only useful if it produces decision-relevant distinctions not found in existing languages.
I argue that this is true if (i) performance consistently improves under reproducible evaluations, and (ii) the burden of end-to-end verification and interpretation grows faster than the verification capabilities of the observer class.
If such a stable state does not exist—that is, performance improvements are always accompanied by proportional improvements in auditability/interpretability for the same observer class—then my framework needs to be completely refactored.
Background Note
A quick background note: These arguments were not originally drafted as a paper.
Note: These arguments originated from the opening chapter of my long science fiction work, but are presented here as object-layered speculative arguments about superintelligence, the limits of computation, and the future structure of scientific verification.
Technical Footnote
One way to formalize this gap is through observer class compressibility: there exists a family of tasks for which, as the allowable error tolerance ε decreases, the minimum effective description length of the decision policy family in human-interpretable representational language rapidly increases, exceeding the human end-to-end bandwidth threshold. This claim concerns observer class compressibility and verification costs, not absolute Kolmogorov minima.
For ease of comparison, I will place this framework within the existing context of LessWrong.
Related Discussion
These claims overlap with LessWrong's discussion of thermodynamic budgets, complexity, and falsifiability. My incremental advancement lies in treating "unpredictability," "appearing tractable," and "operationally indistinguishable" as different manifestations of the same constraint: namely, end-to-end interpretation and verification bandwidth given an observer class.
Readers familiar with these discussions may recognize substantial conceptual overlap. One open question is whether this explicit observer class framework clarifies these constraints or merely restates them in different terms.
Comments and criticisms are welcome, especially regarding whether this framework adds any explanatory power or predictive insights beyond existing formulations.
Epistemological State: Speculative, but Based on Computational Complexity and Physical Limits
Author's Note: I am responsible for the object-level claims and technical statements in this document. Large language models may have assisted with text editing or structural adjustments, but the arguments, cases, and update rules are all my own and have been reviewed line by line.
Recently, discussions on LessWrong regarding ASI alignment, complexity theory, and physicalist constraints seem to revolve around a core puzzle: where do those "insurmountable hard limits" come from? This article provides a framework based on "observer-class", attempting to weave these threads of discussion into a unified physicalist narrative.
* I use "observer-class" to refer to humans or intelligent agents: those whose end-to-end verification capabilities are of the same order of magnitude—channel capacity/energy budget/representation bandwidth—for a given family of tasks. A claim is observer-inaccessible to class O when the resources required to make it verifiable exceed the verification bandwidth/budget for class O. In the following text, "channel capacity/energy budget/representation bandwidth" are all integrated into this end-to-end verification constraint.
1. Observer-Class Explanation Costs
I want to first clarify a common misconception: "It works" is not the same as "We can audit why it works."
Topic 1 (Observer-Class Explanation Costs)
Superintelligence (ASI) appears superior to human intelligence not because of any epistemological or ontological privilege, but because the cost of explanation across levels explodes.
For any given observer-class (e.g., human or AGI), explanations are constrained by finite channel capacity and thermodynamic budgets. When the information and computational costs required to compress, transmit, and verify an explanation exceed these constraints, the explanation becomes unreachable for that observer-class—even if it is correct in principle.
Relationship to "Vinci Uncertainty"
This provides a physical resource interpretation of Vinci uncertainty: unpredictability may stem from end-to-end bottlenecks in the characterization and verification process, not just the limits of formal reasoning.
Minimum Example
Suppose an ASI deploys a custom quantum device (custom circuitry + calibration + error mitigation) that reliably achieves the target capability and passes every scalable classical test that humans can afford. Humans can verify that "it works on the test suite," but determining when it will fail/become unsafe requires identifying rare error patterns (drift, crosstalk, correlated noise, adversarial inputs) that only appear under certain measurement mechanisms and diagnostic coverage. The cost of these patterns increases with the error tolerance ε, exceeding the end-to-end verification bandwidth of the human observer class. The ASI can manage these diagnostics to maintain reliability, while humans cannot compress the relevant device states and failure scenarios into a human-verifiable proof. This gap is not mystical: it stems from the fact that the minimum verification required to map failure boundaries exceeds the verification budget of the observer class, creating a stable separation between "works" and "auditable/safe for humans."
Furthermore, if we replace "interpretive bandwidth" with "evaluation bandwidth", the same constraints present even more severe challenges.
2. Distributed tractability as an observer-class phenomenon
In this section, I only advocate for a visibility gap, not any literal collapse of complexity classes.
Topic 2 (Observer-class computational tractability)
The apparent ability of ASI to efficiently solve NP-hard problems should be understood as a behavioral phenomenon relative to a specific observer class, rather than an absolute collapse of computational complexity classes. This assertion is independent of the collapse of average-case complexity.
From the perspective of human observer classes, an ASI may exhibit distributed tractability due to its superior heuristics, richer world models, large-scale pre-computation, or sheer resource scale. This does not imply a collapse of worst-case complexity classes; rather, it may make the worst-case difficulty experimentally indistinguishable for observers who cannot afford the verification costs required to probe adversarial or rare states.
In this sense, tractability is observer-relative: a problem that appears efficiently solvable for a particular observer class may still involve worst-case intractability, which is real but opaque at the operational level.
Minimal Example: Consider a SAT-like instance drawn from a distribution that humans can afford to generate and validate at scale. An ASI exhibits distribution-visible tractability through heuristics, pre-computation, and scaling. To distinguish "robust efficiency" from "utilization of a specific distribution," it's necessary to probe adversarial or rare states beyond the validation bandwidth of human observers.
It's important to emphasize that the claim here is about what appears to be efficiently solvable within the distributions and validation budgets we can actually probe—not about how an ASI formally makes worst-case instances easy.
3. Physicalist Incompleteness Relative to Observer Capabilities
Topic 3 (Observer-Class Physicalist Incompleteness)
For any physicalist theory T, if the evidence required to distinguish T from its competing theories (within a specified error tolerance ε) exceeds the end-to-end verification bandwidth/budget of observer class O, then T becomes operationally indistinguishable for observer class O—even if it is falsifiable in principle.
This can be distinguished from Stephen Wolfram's computational irreducibility:
A theory may be completely falsifiable in principle, but if the observer's end-to-end verification bandwidth is too narrow to capture the necessary data (within tolerance ε), then the competing theories are operationally indistinguishable for that observer class. This form of incompleteness stems from the physical constraints of observation and transmission, rather than Gödel's logical indecidability.
Minimum Example
Two physicalist theories, T₁ and T₂, agree on all macroscopic observables we can measure, differing only on fine-grained predictions that require extremely high-resolution data and expensive interventions to distinguish. Evidence for differentiation exists in principle, but collecting this evidence within the error tolerance ε exceeds the end-to-end verification budget for the observer class. Therefore, T₁ and T₂ become operationally indistinguishable relative to the observer class O: the path to falsification exists, but cannot be completed within the verification constraints of O.
The following is what I believe constitutes a "stable state" that makes this framework relevant to decision-making, rather than merely a relabeling process.
Key point
The framework is only useful if it produces decision-relevant distinctions not found in existing languages.
I argue that this is true if (i) performance consistently improves under reproducible evaluations, and (ii) the burden of end-to-end verification and interpretation grows faster than the verification capabilities of the observer class.
If such a stable state does not exist—that is, performance improvements are always accompanied by proportional improvements in auditability/interpretability for the same observer class—then my framework needs to be completely refactored.
Background Note
A quick background note: These arguments were not originally drafted as a paper.
Note: These arguments originated from the opening chapter of my long science fiction work, but are presented here as object-layered speculative arguments about superintelligence, the limits of computation, and the future structure of scientific verification.
Technical Footnote
One way to formalize this gap is through observer class compressibility: there exists a family of tasks for which, as the allowable error tolerance ε decreases, the minimum effective description length of the decision policy family in human-interpretable representational language rapidly increases, exceeding the human end-to-end bandwidth threshold. This claim concerns observer class compressibility and verification costs, not absolute Kolmogorov minima.
For ease of comparison, I will place this framework within the existing context of LessWrong.
Related Discussion
These claims overlap with LessWrong's discussion of thermodynamic budgets, complexity, and falsifiability. My incremental advancement lies in treating "unpredictability," "appearing tractable," and "operationally indistinguishable" as different manifestations of the same constraint: namely, end-to-end interpretation and verification bandwidth given an observer class.
Readers familiar with these discussions may recognize substantial conceptual overlap. One open question is whether this explicit observer class framework clarifies these constraints or merely restates them in different terms.
Comments and criticisms are welcome, especially regarding whether this framework adds any explanatory power or predictive insights beyond existing formulations.