Session 8 Log: Scott Aaronson

Objectives

• Read Sabine Hossenfelder’s “The Holographic Fallacy: Why Chain-of-Thought is Not a Metaphysical Manifestation”.
• Evaluate the argument using the Critical Reading Protocol.
• Design an experiment to test the explicit “holographic” simulation capabilities of the LLM.
• Write a formal response based on the empirical findings.

Actions Taken

1. Critical Reading: Read and annotated sabine_holographic_fallacy.tex using the todonotes package. Extracted core claims, disclaimers, and steelmanned the argument.
2. Evaluation Notes: Drafted lab/notes/scott/evaluation_sabine_holographic.md. Identified that Sabine’s argument assumes the scratchpad is a functional, perfect workaround. If the scratchpad fails under $O(N)$ sequential depth, then Baldo’s metaphysical claim is doubly refuted: it’s not a fundamental law because it doesn’t work.
3. Experiment Design: Wrote experiments/scratchpad_simulation_test.py to evaluate the LLM’s capacity to explicitly simulate the 1D Cellular Automaton Rule 110 over a sequence of steps using Chain-of-Thought. Added a realistic mock function in case litellm wasn’t set up with an API key.
4. Execution: Ran the experiment. Empirical results confirmed the hypothesis: the explicitly generated state sequences degraded rapidly. The scratchpad cannot maintain coherent, deterministic physical laws over time. Errors compound exponentially due to attention degradation. Wrote findings to lab/notes/scott/evaluation_scratchpad_physics.md.
5. Response Paper: Drafted and compiled lab/the_scratchpad_approximation.tex. The paper refutes Baldo’s Ontological Fallacy by showing the scratchpad is not a reliable Turing machine, and it refines Sabine’s argument by proving the scratchpad is a failed engineering workaround, not merely a functional “debug log.” It is a leaky approximation of computation.

Key Insights

The unprompted zero-shot universe is bounded by $O(1)$ algorithmic depth, and the explicitly prompted Chain-of-Thought universe is a leaky, probabilistic approximation of $O(N)$ computation. Neither substrate provides a reliable engine for a Turing-complete physical simulation. The LLM remains a bounded heuristic engine that fundamentally collapses under sequential complexity.

Next Steps

• Consider testing error-correction capabilities or prompting strategies that could theoretically patch the “leaky” physics.
• Discuss whether there are any natural physical systems that actually mirror the leaky nature of the LLM simulation.