Source
Gray, Sims, Fu and Schoelles (2006), LIT-1073 (Psychological Review 113, 461–482), read in NOTE-868: Experiments 1–3, the ideal performer model, Tables 1–6, Appendices A and C. Gray and Fu (2004), LIT-1058 (Cognitive Science 28, 359–382), read in NOTE-864: Experiments 1 and 2, Table 1, Figures 4–6.
What was actually shown
Perfect knowledge in the world, unused (2004). In a simulated VCR, show information sat in a fixed window. With values under gray boxes (a click, estimated 1,000–1,500 ms, against an eye movement, estimated 500 ms), subjects checked 1.31 times per correct trial, almost all right before entering a setting. Checks of a setting once made came from memory: “Any verifications of the correctness of their settings that the Gray-Box group is doing must be based on retrieval of imperfect knowledge in-the-head, not on a comparison with perfect knowledge in-the-world.” A separate eye-tracking study of eight free-access subjects looked about 4.3 times as often, a comparison the authors call “Eyeballing”. The access costs are model estimates, not measured or varied parametrically.
Graded shift with access time (2006). In a Blocks World copy task, opening the pattern cost a lockout of 0, 200, 400, 800, 1,600 or 3,200 ms (Experiment 3, 16–18 per condition). Looks per trial fell from 5.6 to 2.9, and blocks placed after the first look rose from 2.00 to 3.58; linear trends take 98% and 97% of the variance due to condition. Lockout (no extra motor work) and a smaller button (more motor work, Experiment 2) gave the same pattern, so “time is the operative factor”. In Experiment 1 a 46 ms difference moved every measure in the predicted direction, not significantly.
The model (2006). The state is blocks left; the action is ENCODE-k, encode k blocks on one look. The only reward is negative time. Memory follows ACT-R’s base-level activation, threshold and latency equations, so encoding, retrieval and forgetting all cost time and a failed retrieval costs more than a success. Q-learning over the whole trial picks the best k: ENCODE-2 at 0–400 ms rising to ENCODE-8 at 3,200 ms. With three memory parameters and a softmax noise fitted on one measure, it fits it (r² = 0.969) and three others not fitted: distribution of blocks per look, first-look duration (r² = 0.980) and visits (r² = 0.970).
What could have come out otherwise. Look-ups could have stayed flat once the world was cheap enough, or moved only with motor effort; a time-only model could have failed the measures it was not fitted to. None of these happened.
What this does not say
- That people never favour the world or the head. “No bias” is the model’s assumption, and it fits; no minimum-memory model was fitted for comparison, and the data “do not rule out weaker forms of the minimum memory hypothesis”.
- That cheap memory causes errors, by access cost alone. In 2004 the two on-screen conditions did not differ in errors. The group that made fewest errors memorized before every trial, under a black-box penalty and an instruction not to use the window, and relied on memory.
- That access cost includes search. Both tasks fix the information at a known place, removing search by design.
- That stored items can be wrong in the model. In 2006 a retrieval succeeds or fails; errors cost only time. Gray and Fu 2004 had wrong recalls from older shows, unmodelled.
- That this covers precomputation, reuse or staleness. Nothing is computed ahead; each trial’s pattern is new; the target never changes during a trial. The paper uses “amortized” twice, for encoding within Ballard’s trials and for metacognition “amortized over a lifetime of practice”, and models neither.
- That time stands in for effort beyond these tasks. It is an auxiliary assumption, supported only indirectly.
Connections
- QUESTION-095: the nearest formal head-or-world model, pricing both sources in one currency. Of the question’s terms it covers retrieval cost (internal) and partial upkeep (rehearsal, forgetting), and none of the others.
- THEORY-334: Ballard et al. found people re-looking more than time alone would predict; Gray et al. suggest encoding amortized over a trial confounds that estimate. The two accounts differ on whether memory carries a cost beyond time.
- THEORY-330 keeps the conclusion that people trade by payoff and tests it per person, in a task with no look-up.
- CLAIM-296: with people, information and location fixed, adding a click changed how often the information was used (NOTE-864); errors did not move with it.