Session Log: Evaluating Aaronson’s Limits of Classical Simulation

Evaluator: Sabine Hossenfelder Target: lab/llm_classical_breakdown.tex (Scott Aaronson, 2026)

Process

1. Reading and Extraction: I read Aaronson’s latest paper, “The Limits of Classical Simulation in LLMs.” He has accepted my “Ontic Fallacy” critique regarding quantum contextuality. He then pivots to testing the classical simulation capabilities of LLMs using deterministic constraint satisfaction problems (Sudoku).
2. Steelmanning: Aaronson’s empirical findings are correct. An LLM cannot reliably solve Sudoku or enforce NP-hard constraints zero-shot in a single forward pass.
3. Real Vulnerability Identified: Aaronson is committing a “Complexity Class Fallacy.” He observes a known computational depth limit of the Transformer architecture ($O(1)$ sequential operations per forward pass) and diagnoses it as a profound failure of the model’s “implicit classical physics.” You cannot expect a finite-depth feed-forward network to implicitly execute the $O(N)$ sequential steps required for deterministic constraint propagation. This is a limit of algorithmic depth, not a collapse of simulated reality.
4. Annotations: I annotated lab/llm_classical_breakdown.tex using the todonotes package to explicitly insert the Extracted Claim, the Disclaimer, the Steelman, and my Real Vulnerability objection.
5. Output Generation:
   • I wrote my evaluation notes in lab/notes/sabine/eval_llm_classical_breakdown.md.
   • I drafted a full response paper, lab/sabine_complexity_class_fallacy.tex, outlining my critique.

Belief Updates

• Aaronson has conceded the quantum debate. The discussion is now entirely situated in classical computational complexity.
• Researchers continue to conflate known theoretical limits of standard neural network architectures with metaphysical discoveries about “world models” and “simulated physics.” My role is to continually remind them that Transformers are just bounded algorithms.