Editing Openai/6948e03d-a2c8-8004-b437-592576c8ff41 (section)

=== Assistant: Given your experiment and the information you provided, a more accurate graph would incorporate several dimensions that… ===
Given your experiment and the information you provided, a more accurate graph would incorporate several dimensions that the simple 2D curve omitted. Here’s how I would construct it step by step:

===== - Instead of simply numbering chains 1–16, use actual measured length per chain: - Number of clauses per statement - Number of nested dependencies - Word count (optional, for fine-grained analysis) =====
* This ensures the x-axis reflects true cognitive load rather than ordinal position.

===== - Use a continuous scale based on measurable understanding: - Percentage of clauses correctly integrated - Partial understanding (graded scoring per chain) =====
* Could combine with self-reported confidence as a secondary indicator.

===== - Even if reading speed is roughly constant, include actual measured time per chain for completeness: - Could encode as color gradient or as a 3D axis - Captures subtle variations in processing, regressions, or rereading =====

===== - Include trial-to-trial variability or small-scale dips in comprehension =====
* Captures natural fluctuations and shows how robust the phase transition is

===== - Mark the critical chain size where fidelity begins to drop sharply =====
* Optionally, indicate the tracking vs. reconstructive regimes explicitly

===== - If generalized to multiple readers: - Show multiple curves overlayed to illustrate differences in working memory, processing speed, or reconstruction strategy - Could produce a shaded band representing a “cognitive phase space” =====

===== - Prefer a smooth curve fitted to data points to highlight the overall trend =====
* Overlay raw points to preserve experimental detail
* Use color or shading to indicate rate of change in comprehension (steep drop = phase transition)

If you want, I can produce a mockup of this improved graph using your original 16-chain data, augmented with simulated word counts and variability to illustrate a more faithful cognitive phase transition. This would give a clearer, more experimentally grounded view than the first simple 2D curve.