01-30-2026, 12:16 AM
In a serialized long-form science fiction work (updated to Chapter 6, non-English), I propose three rough propositions as a physicalist deduction regarding future superintelligent ASI. Professional critique is welcomed:
1.Cross-Level Explanation Cost (Observer-Relative Hierarchy): The reason we cannot comprehend future superintelligent ASI is the prohibitive cost of explanation across capability levels—for a specific observer category O_h (human or a specific AGI), it manifests as explanatory inaccessibility under channel capacity limits and energy budgets, rather than an issue of epistemological/ontological privilege. (Here, "hierarchy" refers to a partial order defined by capability level, verifiable granularity, and interface bandwidth/energy constraints.)
1.Cross-Level Explanation Cost (Observer-Relative Hierarchy): The reason we cannot comprehend future superintelligent ASI is the prohibitive cost of explanation across capability levels—for a specific observer category O_h (human or a specific AGI), it manifests as explanatory inaccessibility under channel capacity limits and energy budgets, rather than an issue of epistemological/ontological privilege. (Here, "hierarchy" refers to a partial order defined by capability level, verifiable granularity, and interface bandwidth/energy constraints.)
Specifically, For any observer class O_h, end-to-end verification is constrained by (i) an information budget (capacity-limited), (ii) a replication budget (samples and energy), and (iii) a pedagogy-induced compression loss.
These constraints form a multi-dimensional resource vector; a formal unified cost function would require dimensional alignment.
When the verification resources and reproducibility cost required by the decision complexity of ASI exceed O_h's integrated information and energy budgets, explanation becomes a physically unattainable operation.
2.ASI's "NP → Engineering-Practical Quasi-P" is merely a behavioral-layer phenomenon relative to our observer category, not a complexity-layer "absolute irreducibility".
The ability exhibited by ASI at the behavioral layer—"transforming NP-class problems into engineering-solvable quasi-P problems"—holds only relative to O_h. This is not an absolute irreducibility at the complexity level but a behavioral pattern emergent under O_h's observational scale. Therefore, the so-called "unexplainability" is essentially a mismatch in verification bandwidth between the observer category and the target system.
3."Operational Incompleteness Proposition": For any theory T, if the amount of evidence and reproducibility cost required to distinguish it from a competing theory T' within an error tolerance \epsilon exceeds the verification bandwidth and energy budget of observer O, then for O, T and T' become operationally indistinguishable, even if falsifiable in principle. Thus, "explainability" is not a pure epistemological issue but a problem of distinguishability under resource constraints.
Initially, the third proposition used "Physicalist Incompleteness". In revision, it was changed to "Indistinguishability", aligning more fully with the theoretical context of cognitive complexity.
【Formalization】
Let theory T and competing theory T' be distinguishable within error tolerance \epsilon. If the evidence quantity required to distinguish them exceeds observer O's:
· Total Verifiable Information Budget: \int_{0}^{\text{Life}(O)} \text{Bandwidth}(O) , dt (units: bits)
· Available Energy Budget: E_{\text{budget}}(O)
Then for O, T and T' enter a state of operational indistinguishability. This is the Operational Incompleteness Proposition. It can be analogized to Gödel's Incompleteness Theorems and Computational Irreducibility, placing them within the resource constraints of physical observers.
4.Key Corollaries: Verification Asymmetry and Heuristic Projection
a. The Nature of Intelligence and the Role of Consciousness
· Intelligence: Mathematical description and compression of the possibility space (combination, pruning, and dimensionality reduction of state spaces).
· Consciousness: The here-and-now instantiation of this description, adding no computational power, merely serving as the execution vehicle.
b. Observer-Relativity of Dominant Heuristics
Under the test distribution and resource constraints of a given observer category O, a certain strategy family may statistically dominate all known candidate heuristics over time, becoming a dominant heuristic family (not in the standard hyper-heuristic sense, but meaning a persistently unbeaten strategy relative to O's scope). This does not imply global optimality, only that it remains unfalsified within O's observational scope.
c. Verification Inequality
Define S_{\text{verify}}(\text{ASI_Heuristic}) as: the minimum number of computational steps and integrated energy required, within O_h's complexity budget, to replicate the ASI heuristic path and verify its local constraints. Then:
S_{\text{verify}}(\text{ASI_Heuristic}) \gg \int_{0}^{\text{Life}(O_h)} \text{Bandwidth}(O_h) , dt
This value cannot be certified by the ASI in a way that is verifiable by O_h under the same constraints; it can only be estimated through human audit sampling and parallel replication, subject to the same limitations.
5.Extension: Projection Loss in Explanation
The "explanation" generated by the ASI's internal principles at the O_h interface layer is merely a projection of the high-dimensional decision process onto a low-dimensional channel. If the required bitrate for a faithful projection exceeds O_h's channel capacity, an explanatory gap arises:
The explanatory cost of the ASI's heuristic path, at the human-visible interface layer, may only equal the projection length of its internal generative principles—but the description length (in bits) required for that projection has already exceeded the human observer's lifetime information budget.
6.Theoretical Positioning: Distinction from Classical Undecidability
· Gödel's Incompleteness Theorems: Address self-referential limits within formal systems.
· Computational Irreducibility: Describes the inherent complexity between a system and its description.
· Operational Incompleteness: Emphasizes the relational property between theory and observer pair, focusing on the gap between verification bandwidth and physical limits, thereby anchoring unexplainability at the resource level, not purely logical or computational.
7.Regarding Falsifiability
The above explanatory framework can be deemed valid if: (i) under reproducible evaluation, AI performance continuously improves, while (ii) the growth rate of end-to-end verification and explanation burden outpaces the verification capability of the observer category.
Note: This text can be viewed as a physicalist supplement to the "Intelligence Ceiling Hypothesis"—we need not assume an absolute epistemological barrier; merely acknowledging the constraints of channel capacity and energy budget is sufficient to deduce "unexplainability" or "relative irreducibility".
【References and Perspective Connections】
1.Mario Brčić, Roman V. Yampolskiy｜Impossibility Results in AI: A Survey｜2023
Note: Places "Indistinguishability" within the spectrum of AI "Impossibility" results; this text expands based on physical quantities like channel capacity/energy.
2. F. P. Adler｜Minimum energy cost of an observation｜1955
Note: Provides a thermodynamic lower bound for the energy cost of "obtaining information through observation", supporting "explanation/verification is a physical operation and necessarily consumes resources".
3.Pamela Abshire, Andreas G. Andreou｜Capacity and energy cost of information in biological and silicon photoreceptors｜2001
Note: Quantifies "capacity-energy coupling" from a biological/silicon perspective, supporting inherent capability differences among observer categories due to physical construction.
4.Claude E. Shannon｜A Mathematical Theory of Communication｜1948
Note: Establishes the fundamental language of channel capacity and information rate, supporting terms like "verification bandwidth" in the text.
5.Rolf Landauer｜Irreversibility and Heat Generation in the Computing Process｜1961
Note: Links information processing to heat dissipation, providing the classic anchor for "computation/explanation has an unavoidable energy cost floor".
6.A. N. Kolmogorov｜Three approaches to the quantitative definition of information｜1965
Note: Formalizes "explanation = compression/shortest description", providing the conceptual coordinates for "description length exceeding budget → explanatory gap".
7.Kurt Gödel｜On Formally Undecidable Propositions…｜1931
Note: Serves as a prototype reference for "incompleteness"; but the text emphasizes "operational inaccessibility" under resource constraints, analogous but not equivalent.
8.Stephen A. Cook｜The Complexity of Theorem-Proving Procedures｜1971
Note: Provides the NP-completeness baseline context, facilitating our limitation of "NP → quasi-P" as a behavioral-layer phenomenon relative to observer and distribution.
