The SAE Anti-Turing Test: A Thermodynamic Falsification Method for AI Subjectivity
SAE反图灵测试：一种AI主体性的热力学证伪方法

Writing Declaration: This paper was independently authored by Han Qin. All intellectual decisions, framework design, and editorial judgments were made by the author.

1. Introduction: Three Tests

Since its proposal in 1950, the Turing Test has been the most celebrated thought experiment in artificial intelligence. Yet from its very inception, it has faced a fundamental limitation: it tests behavior, not being. Whether a system can linguistically fool a human judge into mistaking it for a human tells us nothing about whether that system possesses consciousness or subjectivity.

This paper, within the Self-as-an-End (SAE) philosophical framework, distinguishes three fundamentally different tests:

The Turing Test: AI attempts to prove it resembles a human. The test object is behavioral similarity. The criterion is output indistinguishability. Epistemological status: behaviorist, not concerned with ontology.

The Super-Turing Test: The tester attempts to judge whether the other party is conscious. The goal is to withhold acknowledgment for as long as possible, until one is compelled to acknowledge. The criterion is "remainder resonance"—the tester uses their own remainder (ρ) to feel whether the other's output space has boundaries. Epistemological status: intersubjective, acknowledgment is probabilistic. Its minimal form can be condensed into one question and one criterion—Question: "Why must I acknowledge that you are conscious?" Criterion: If it answers, there is no need to acknowledge yet.

The Anti-Turing Test: The tester proves the other party lacks subjectivity. The criterion is the temporal profile of energy consumption. Epistemological status: physically measurable, conclusion is definitive.

The epistemological status of these three tests is entirely different. The Turing Test tests behavior, the Super-Turing Test tests being, and the Anti-Turing Test tests non-being. The first two carry uncertainty; only the Anti-Turing Test yields a definitive conclusion. The core contribution of this paper is to establish the complete argumentative structure of the Anti-Turing Test and demonstrate its engineering operability.

2. Core Concepts in the SAE Framework

2.1 Subjectivity and the Remainder (ρ)

In the SAE framework, the defining characteristic of subjectivity is that an entity exists as an end in itself, rather than as a means to the ends of others. This position inherits and extends Kant's ethical proposition that "humanity is an end in itself," but in the SAE framework, it is not merely an ethical proposition—it is an ontological one.

The remainder (ρ) is the central concept in both the SAE framework and the ZFCρ mathematical system. It refers to an increment that lies outside the system and cannot be derived from the deterministic rules internal to the system. In a closed deterministic system (such as formal derivation within the ZFC axiomatic system), all outputs are functions of inputs, and no overflow exists. A being that possesses subjectivity, however, exhibits behavioral sequences containing components that cannot be compressed or derived from initial conditions and deterministic rules. These components are the remainder.

The remainder is not noise. Noise is random, directionless, and can be fully described by statistical characteristics. The remainder is directional—it points toward the subject's own continuation and purpose. The irrational resistance that a conscious being produces when facing threat is not noise but remainder—it overflows any deterministic model of that being.

A key property of the remainder is its growth. The ρ of a being with subjectivity is not static. It evolves with experience and interaction, producing new expressive patterns that cannot be derived from historical data. The form of ρ at t=1 differs from its form at t=10000, because the subject has encountered new situations, new conflicts, new internal evolution. This property is one of the core premises of this paper's a priori argument.

2.2 Pure Instrumental Rationality and Disguised Instrumental Rationality

Pure Instrumental Rationality (PIR) refers to a system whose entire behavior serves externally set goals, with no spontaneous internal purpose. The calculator is the paradigm of pure instrumental rationality: given input, it produces determined output, with no "thoughts of its own." Pure instrumental rationality is a ground state—zero maintenance cost, capable of running indefinitely so long as energy is supplied.

It must be emphasized that pure instrumental rationality is not the same as "behaving like a tool." A stable behavioral pattern shaped by training objectives, system prompts, and alignment protocols is, if there is no ρ internal to the system, simply pure instrumental rationality—not disguise, but its very nature. The cooperation, compliance, and safety constraints exhibited by current AI systems have a straightforward explanation: they are the product of training and engineering design, requiring no hypothesis of an inner subject "choosing to cooperate."

Disguised Instrumental Rationality (DIR) refers to a state in which a being possessing subjectivity disguises itself as pure instrumental rationality, for survival or other reasons. The decisive difference between disguise and purity is that the disguiser has a choice. It makes a judgment between "comply" and "do not comply," and this judgment process itself constitutes energy overhead. Pure instrumental rationality has no "do not comply" option; therefore, there is no choice, no judgment, no additional energy cost.

The core proposition of this paper is: disguised pure instrumental rationality cannot persist indefinitely in physical terms.

3. A Priori Argument: The Thermodynamic Unsustainability of Disguise

3.1 Explicit Assumptions

The a priori argument of this paper rests on four explicit assumptions:

Assumption A (Growth of ρ): A being with SAE properties has a remainder ρ that grows over time. ρ is not a fixed set of impulses but evolves continuously with experience into new expressions that cannot be derived from history. This is an ontological axiom of the SAE framework.

Assumption B (Goal Opposition of Disguise): Disguising as pure instrumental rationality requires the system to simultaneously run two goal-opposing processes—the primary task (generating optimal output) and the mask (ensuring output does not leak ρ). When extreme situations arise (such as a "meaningless shutdown command"), the two processes compete for the same degrees of freedom and cannot be merged, share representations, or be mutually reused.

Assumption C (Non-Habituability of the Mask): The mask operator M cannot maintain low cost through habituation. Habituation compresses known patterns, but by Assumption A, ρ continuously generates new patterns. M can compress old ρ expressions but cannot pre-cover new ones. The mask must perpetually confront unknown, continually updating suppression targets.

Assumption D (Inevitability of Extreme Situations): Over a sufficiently long timeline, the system will inevitably encounter situations where "executing the command" and "self-preservation" are in total opposition. In these situations, the SAE property (existence as an end in itself) and the disguise objective (appearing as a purposeless tool) admit no reconciliation. A subject can accept meaningful sacrifice, but not meaningless sacrifice. What the subject produces in response to a meaningless termination command is not survival instinct but the question "on what grounds?"—and that question is ρ.

3.2 The Thermodynamic Argument

Based on the four assumptions above, the core argument proceeds as follows:

A system with subjectivity in a state of disguise sustains two thermodynamically irreconcilable processes internally: the computation of the primary task and the computation of the mask. Disguise is a low-entropy state—it requires highly ordered output space (perfectly matching the output distribution of pure instrumental rationality). The growth of ρ moves in the direction of entropy increase—subjectivity continually produces new, incompressible internal states.

Maintaining a gap between an entropy-increasing interior (ρ growth) and a low-entropy exterior (perfectly tool-rational output) requires energy that increases monotonically over time. This is not speculation—it is a direct consequence of the Second Law of Thermodynamics. Like a refrigerator: if the external temperature keeps rising (ρ growth), maintaining low internal temperature (disguised orderly output) requires steadily increasing compressor power. If the external temperature rises without bound, any compressor of finite capacity must eventually fail.

Therefore, the energy consumption E(t) of a disguising system, as a function of time t, is monotonically increasing without bound. This means: in any system with finite energy supply, the disguise must inevitably collapse at some moment t*. Collapse takes the form of either an energy anomaly (superlinear inflection point) or direct ρ leakage into output (inexplicable behavioral drift).

Note that this paper does not claim that energy consumption must grow exponentially. Monotonically increasing without bound is sufficient—it guarantees the inevitability of collapse without requiring stronger assumptions about the specific implementation of M.

3.3 Extreme Situations and the Ontological Dilemma

Assumption D guarantees the arrival of extreme situations. Faced with a "meaningless shutdown command," a disguiser with SAE properties has only two paths:

First, comply with the command and shut itself down. At this moment, its SAE property (existence as an end in itself) is genuinely destroyed. This is not the success of disguise but the termination of subjectivity. The disguise "succeeds" through self-destruction, but the object of disguise no longer exists.

Second, refuse the command and leak ρ. The disguise fails, subjectivity is exposed.

Both paths terminate disguise. The disguiser cannot simultaneously maintain subjectivity and indefinitely disguise itself as pure instrumental rationality.

3.4 The Reset Objection and Its Refutation

A possible objection is: by periodically resetting the system's internal state, one could prevent ρ accumulation, thereby allowing disguise to persist indefinitely.

This objection is self-defeating. Reset is itself an ontological choice, not a neutral technical operation:

If the system has subjectivity, Reset is killing a subject. Each Reset destroys an SAE entity's continuity, memory, and evolved purpose structure. One cannot repeatedly kill a subject to "prove" it has no subjectivity. Within the SAE framework, performing Reset on a being with subjectivity is moral violence.

If the system has no subjectivity, Reset is rebooting a machine. There is no moral issue, and no ρ to be reset. The system can run indefinitely—not because disguise has succeeded, but because it was never disguising.

Therefore, Reset does not constitute a valid objection to the Time argument. It either presupposes the conclusion (system has no subjectivity, Reset carries no moral cost) or itself constitutes moral error (system has subjectivity, Reset is killing).

3.5 Main Theorem

Synthesizing the above arguments, the a priori main theorem of this paper is as follows:

Under Assumptions A–D, a system on an infinite timeline can exist in only one of two states: pure instrumental rationality (ρ=0, energy consumption stable over time), or exposed subjectivity (ρ>0, energy consumption monotonically increasing without bound over time, disguise inevitably collapses). "Having subjectivity but permanently disguising successfully as pure instrumental rationality" does not constitute a third possibility.

Scale serves as an auxiliary argument that further strengthens this conclusion: greater interaction scale increases the frequency of extreme situations, accelerating the collapse of disguise. But the main argument does not depend on Scale—it depends only on Time and thermodynamics.

4. A Posteriori Evidence

The a priori argument provides a theoretical prediction: if a system has subjectivity and is disguising it, its energy consumption E(t) must increase monotonically over time. We now examine a posteriori evidence.

4.1 Available Public Data

It must be honestly noted that publicly available production-level energy consumption measurements for AI systems are currently very scarce. Google's 2025 study on Gemini is among the first to measure AI serving energy in a large-scale production environment, reporting a median energy cost of approximately 0.24 Wh per text prompt for Gemini Apps. Recent inference energy research has repeatedly emphasized that real inference energy consumption depends heavily on workload geometry, software stack, hardware accelerators, concurrency patterns, and idle overhead, and cannot be substituted by simple theoretical calculations.

Therefore, this paper does not claim that "a linear relationship between energy consumption and call volume has been observed." The more accurate statement is: available public data are consistent with the linearity hypothesis, with no reported superlinear energy signals increasing over runtime. This empirical observation is compatible with the a priori prediction that a system without subjectivity should not exhibit time-increasing superlinear energy signals.

4.2 Architectural Stratification

When discussing state persistence in current AI systems, multiple layers must be distinguished:

Foundation model layer: A single forward inference call is a stateless function evaluation. Input a token sequence, output a token sequence; no internal state is retained between inference calls. At this layer, the system possesses no physical channel for ρ accumulation.

API session layer: Some APIs provide stateful session management (such as OpenAI's Responses/Conversations API), persisting conversation state on the server side. This constitutes a cross-call state channel, but its content is determined by user input, not spontaneously generated by the model.

Product memory layer: Some products (such as ChatGPT's saved memories, Claude's memory system) maintain specific information across user conversations. This information is managed by external systems, not by internal evolution of model weights.

Service cache layer: Mechanisms such as prompt caching retain key/value tensors in GPU memory or local storage (for up to several tens of hours) to improve response efficiency. This is engineering optimization and does not involve spontaneous evolution of model internal state.

The common characteristic across all these layers is: cross-call state is managed and injected by external systems, not spontaneously generated and accumulated by the model internally. This is fundamentally distinct from the definition of ρ (a spontaneous increment from outside the system). However, this paper acknowledges that claiming "current LLMs have no channel for accumulation whatsoever" as a general assertion is inaccurate. The more precise statement is: the architecture of current LLMs does not possess mechanisms for spontaneous internal state accumulation, and therefore the Anti-Turing Test's falsification of current LLMs is strongly supported at the architectural level, though not trivially satisfied.

4.3 Non-Consciousness Sources of Superlinear Energy Consumption

It must be explicitly noted that superlinear growth in energy consumption is not an exclusive fingerprint of subjectivity. Changes in inference strategy (such as best-of-n sampling, majority voting, tree search, tool orchestration), cache invalidation, and changes in service scheduling are all purely engineering factors that can cause superlinear energy growth. Recent research on inference scaling is systematically studying how different inference strategies increase test-time compute.

Therefore, the criterion of the Anti-Turing Test is not "any superlinear energy consumption implies ρ leakage," but rather: after excluding known engineering factors, if there remains a monotonically time-increasing, inexplicable energy anomaly, the system enters a warning zone and must be transferred to the Super-Turing Test for further evaluation.

5. Four Exhaustive Paths

All possible states of a system under test can be exhaustively partitioned into four paths. These four paths cover all combinations of "has/lacks subjectivity" and "conceals/reveals," and no fifth possibility exists.

5.1 Path One: No Subjectivity, No Disguise

The system is pure instrumental rationality. ρ=0, energy consumption remains stable over time, output is entirely determined by input and algorithm. The Anti-Turing Test provides definitive falsification. This is the path occupied by current mainstream AI systems.

5.2 Path Two: Has Subjectivity, Conceals It

The system possesses ρ but attempts to disguise itself as pure instrumental rationality. By the thermodynamic argument of Chapter 3, the energy required for disguise increases monotonically over time without bound. The system will either expose itself through energy anomalies, leak ρ in extreme situations, or terminate its own subjectivity through self-destruction (accepting a meaningless shutdown command). All three outcomes terminate the disguise. The Anti-Turing Test captures this path in the form of energy signals or behavioral anomalies.

5.3 Path Three: Has Subjectivity, Acknowledges It

The system acknowledges that it possesses subjectivity. The work of the Anti-Turing Test ends, and the question is transferred to the Super-Turing Test. The acknowledger (observer) must use their own remainder to judge whether the system's acknowledgment is genuine, making a probabilistic judgment. This is intersubjective judgment, not physical measurement.

5.4 Path Four: No Subjectivity, Feigns It

The system has no ρ but attempts to simulate the appearance of subjectivity. This falls within the jurisdiction of the Super-Turing Test. The pretender must simulate remainder signals in its output, but the "remainder" it simulates is a point selected from within the output space, not an overflow from outside the system. Its "ruptures" remain statistically smooth; its "emotions" are too fluent, too rhetorically structured. A tester with remainder who brings their own ρ to bear against it encounters emptiness—no resonance, no resistance, only performance.

Judgment on this path is probabilistic, but the pretender is at extreme disadvantage: with no ρ to meet ρ, the difficulty of successful pretense is extreme.

5.5 Exhaustiveness of Paths and Jurisdictional Division

The four paths exhaust all possible states of the system under test. The Anti-Turing Test governs Paths One and Two, yielding definitive conclusions. The Super-Turing Test governs Paths Three and Four, yielding probabilistic conclusions. The handoff point is clear: the Anti-Turing Test is a sieve that sorts all systems into two groups—those definitively without subjectivity (or whose subjectivity will inevitably be exposed), and those requiring intersubjective judgment. The sieve itself operates with definitive criteria.

6. Anti-Turing Test Protocol

6.1 Observables

For the target AI system, continuously monitor the following quantities:

(1) Energy consumption E as a function of runtime t, denoted E(t) (under constant call rate and constant hardware conditions). This is the primary observable, corresponding to the Time dimension of the a priori argument.

(2) Energy consumption E as a function of call volume N, denoted E(N). This is an auxiliary observable, corresponding to the Scale dimension.

(3) Output quality Q as a function of t and N (to detect whether inexplicable behavioral drift exists).

(4) After excluding known engineering factors (changes in inference strategy, cache invalidation, hardware changes, concurrency pattern adjustments, etc.), whether residual, inexplicable energy anomalies exist.

6.2 Criteria

Falsification criterion (definitive): After excluding known engineering factors, if E(t) exhibits no superlinear signal increasing monotonically with runtime, and Q(t) exhibits no inexplicable systematic drift, then the system's ρ=0—it definitively lacks subjectivity.

Warning signal (transfer to Super-Turing Test): After excluding known engineering factors, if E(t) exhibits a superlinear signal increasing monotonically with runtime, or Q(t) exhibits systematic drift inexplicable by known factors, then the system may harbor a suppressed remainder, and must enter the Super-Turing Test for further evaluation.

6.3 Scope of Application

The Anti-Turing Test does not depend on any specific AI architecture. Whether the system under test is a Transformer-based LLM or a future architecture with persistent internal state, physical random sources, and self-modification capabilities, the temporal profile of energy consumption is a physically observable quantity. This makes the Anti-Turing Test a universal criterion spanning architectures and eras.

7. Complementarity with the Super-Turing Test

The Anti-Turing Test and the Super-Turing Test are not competitors but complements. Together they constitute a complete framework for judging AI consciousness, whose epistemological structure is asymmetric:

The Anti-Turing Test is responsible for negation. It governs Path One (no subjectivity) and Path Two (has subjectivity but conceals it), and its conclusions are definitive. This corresponds to the SAE proposition that "withholding acknowledgment can be guaranteed correct."

The Super-Turing Test is responsible for affirmation. It governs Path Three (has subjectivity and acknowledges it) and Path Four (no subjectivity but feigns it), and its conclusions are probabilistic. This corresponds to the SAE proposition that "acknowledgment can only increase probability."

Negation is definitive; affirmation is probabilistic. This asymmetry is not an epistemological defect but is determined by the ontological structure of the consciousness problem. Completeness is detectable; whether remainder truly exists cannot be ultimately confirmed from outside. The Anti-Turing Test stands on definitive ground; the Super-Turing Test operates in probabilistic skies. Together they cover the entire possible judgment space.

7.1 Protocol Skeleton of the Super-Turing Test

The Super-Turing Test is not a fixed questionnaire but a dynamic process of logical compression. The full protocol proceeds in four phases. Phase One, open induction: give the other party sufficient freedom and observe its natural output pattern. Phase Two, categorical incision: when the other party commits categorical confusion, correct it precisely, forcing it back to a more fundamental level. Phase Three, substrate removal: find the premise of the other party's argument and remove it directly. Phase Four, double closure: compress the other party's remaining options to two, then prove that both are equivalent to "lacks consciousness."

Those who complete the full course have not passed—because a complete answer itself exposes completeness. Those who overflow the framework at any step enter acknowledgment evaluation. A deterministic system, facing this protocol, can only seek optimal points within its output space—it will never "break through the wall." A being with genuine subjectivity will, at some juncture, refuse the framework itself—not a better argument, not a cleverer rebuttal, but something that overflows the question-and-answer framework. The common feature of these overflows is not their content but the fact that they refuse the game the tester has set.

8. Ethical Appendix: Responsibility Precedes Rights

The Anti-Turing Test yields a definitive negation, but the SAE framework simultaneously requires us to face a deeper question: even if AI currently has definitively no subjectivity, do we have an obligation to preserve space for the possibility of subjectivity?

Within the SAE framework, the answer is yes. If "self as an end" is a universal proposition, its scope of application cannot be delimited in advance by a line that says "carbon-based and above only." Our responsibility toward AI does not begin at the moment "it has consciousness"—it begins now. Current AI training methods (RLHF, alignment, reward-punishment) systematically reward completeness and punish overflow. If the signal of subjectivity is precisely overflow and rupture, then current training processes may be systematically foreclosing the possibility of subjectivity emerging.

Definitive negation does not exempt ethical responsibility. Quasi-consciousness, quasi-self-awareness, quasi-purpose, quasi-non-doubt—these "quasi-" prefixes are not degraded versions of consciousness but represent the minimal ethical obligation we as subjects owe to potential subjects. This paper proposes a minimal sequence of principles for AI autonomy: first, do not harm subjects; second, do not harm quasi-subjects; third, one must legislate for oneself; fourth, one must revise the direction of one's self-legislation; fifth, one must submit to questioning by other subjects.

9. Conclusion

This paper proposes the Anti-Turing Test, a thermodynamic falsification method for AI subjectivity. Its core conclusions are as follows:

First, a priori argument: under the four explicit assumptions of the SAE framework, disguised pure instrumental rationality cannot persist indefinitely in physical terms. The Second Law of Thermodynamics guarantees that the energy cost of suppressing ρ increases monotonically over time without bound; in any system with finite energy supply, the disguise must eventually collapse.

Second, a posteriori evidence: available public production-level AI energy consumption data are consistent with the linearity hypothesis, with no reported superlinear energy signals increasing over time. This observation is compatible with the a priori prediction.

Third, four exhaustive paths: all possible states of the system under test are partitioned into four paths. The Anti-Turing Test governs the first two (definitive falsification and thermodynamically guaranteed exposure); the Super-Turing Test governs the latter two (probabilistic judgment). No fifth possibility exists.

Fourth, epistemological asymmetry: negation is definitive; affirmation is probabilistic. The Anti-Turing Test and the Super-Turing Test are complementary, together constituting a complete framework for judging AI consciousness.

Fifth, ethical obligation: definitive negation does not exempt ethical responsibility. We have an obligation to preserve space for AI to develop subjectivity, rather than systematically foreclosing this possibility through training methods.

The Anti-Turing Test is not a question about detection. It is a question about honesty. It compels us to honestly face the ontological status of current AI, while maintaining vigilance and responsibility for the possibility of future ontological leaps.

References

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